BEGIN:VCALENDAR VERSION:2.0 PRODID:-//TYPO3/NONSGML Calendarize//EN BEGIN:VEVENT UID:calendarize-geometry-number-theory-algorithms-and-applications-in-cryp tography-1 DTSTAMP:20260211T124025Z DTSTART;VALUE=DATE:20260305 DTEND;VALUE=DATE:20260307 SUMMARY:Geometry\, Number Theory\, Algorithms and Applications in Cryptogr aphy DESCRIPTION:This is a joint\, local workshop of groups at the universities of Groningen and Oldenburg.\nOrganisers: Florian Hess (Universität Olden burg)\, Jan Steffen Müller (Universität Groningen)\nEvent link: https:// uol.de/mathematik/gntaac-2\n\n X-ALT-DESC;FMTTYPE=text/html:

This is a joint\, local workshop of groups at the universities of Groningen and Oldenburg.

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Organisers: Flori an Hess (Universität Oldenburg)\, Jan Steffen Müller (Universität Groni ngen)

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Event link: htt ps://uol.de/mathematik/gntaac-2

\n\n LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-multidimensional-gamblers-problem DTSTAMP:20251208T093453Z DTSTART:20260128T161500Z SUMMARY:Multidimensional Gambler's Problem DESCRIPTION:Vortragsankündigung\nIm Rahmen des Kolloquiums spricht\nHerr Prof. Dr. Vitali Wachtel (Universität Bielefeld)\nüber\n MULTIDIMENSIO NAL GAMBLER’S PROBLEM\nAbstract: In this talk I will discuss a multidime nsional extension of the classicalgambler's problem. This extension has be en introduced by Diaconis and Ethier. Considerthe case of three players\, 1\, 2\, and 3\, having initial capitals A\, B\, and C units. Ateach round a pair of players is chosen (uniformly at random) and a fair coin flip ism ade resulting in the transfer of one unit between these two players. Event ually\, oneof the players is eliminated and play continues with the remain ing two. I shallconcentrate on probability that the richest player will be eliminated first in the casewhen the total capital A+B+C goes to infinity . Our approach is based on the connectionto harmonic measures for multidim ensional random walks in cones.\nDer Vortrag findet statt am\nMittwoch\, d en 28.01.2026 um 17.15 Uhr im Raum W01 0-006\nInteressierte sind herzlich eingeladen.  X-ALT-DESC;FMTTYPE=text/html:

Vortragsankü ndigung

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Im Rahmen des Kolloquiums sp richt

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Herr Prof. Dr. \;V itali Wachtel (Universität Bielefeld)

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über

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 \;MULT IDIMENSIONAL GAMBLER’S PROBLEM

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Abstract: In this talk I will discuss a multidi mensional extension of the classical
gambler's problem. This extensio n has been introduced by Diaconis and Ethier. Consider
the case of th ree players\, 1\, 2\, and 3\, having initial capitals A\, B\, and C units. At
each round a pair of players is chosen (uniformly at random) and a fair coin flip is
made resulting in the transfer of one unit betwee n these two players. Eventually\, one
of the players is eliminated an d play continues with the remaining two. I shall
concentrate on proba bility that the richest player will be eliminated first in the case
w hen the total capital A+B+C goes to infinity. Our approach is based on the connection
to harmonic measures for multidimensional random walks in cones.

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Der Vortrag findet statt am

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Mittwoch\, den 28.01.2026 um 17 .15 Uhr im Raum W01 0-006

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Interessierte sind herzlich eingeladen. \;

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-uncertainty-quantification-for-bifurcating-dynamical-syste ms DTSTAMP:20251021T133158Z DTSTART:20251029T161500Z SUMMARY:Uncertainty Quantification for Bifurcating Dynamical Systems DESCRIPTION:Vortragsankündigung\n \nIm Rahmen des Kolloquiums spricht\nF rau Kerstin Lux-Gottschalk\nEindhoven University of Technology\nDepartment of Mathematics and Computer Science\nEindhoven\, Netherlands\ne-mail: k.m .lux@tue.nl\n \n \nUncertainty Quantification for Bifurcating Dynamical Systems\nüber \nABSTRACT\nMany real-world systems can be modeled in term s of systems of differential equations. Oftentimes\, they have inherently nonlinear dynamics which can induce sudden\, large and irreversible change s when an external forcing parameter is varied. We analyze these bifurcati ons in the realm of uncertainty [1]. In this talk\, we will consider param eter uncertainty. This arises naturally when model parameters need to be e stimated from measurement data or cannot even be measured directly but nee d to be inferred from other observable quantities.\n \nWe will see that p arameter uncertainty can crucially alter the bifurcation landscape.\nI wil l illustrate this by an example from climate science\, the Atlantic Meridi onal Overturning Circulation\, where we model tipping points (TPs) in term s of bifurcations [2]. The system is of particular importance for the Nort h Atlantic heat transport. We highlight the uncertain locations of TPs alo ng the arising probabilistic bifurcation curves. Moreover\, we provide an original combination of sensitivity analysis\nand bifurcation theory allow ing to quantify the distance between family of bifurcation curves for diff erent input parameter distributions. Thereby\, we contribute to an uncerta inty quantification of high impact\, low likelihood climate outcomes.\n \ nThis talk covers some joint work with Christian Kuehn (Technical Universi ty of Munich)\, Peter Ashwin (University of Exeter\, UK)\, Richard Wood (M et Office\, UK)\, Jonathan Baker (Met Office\, UK)\, Oliver Ernst (TU Che mnitz) and Björn Sprungk (TU Freiberg).\n \nREFERENCES\n[1] C. Kuehn and K. Lux. Uncertainty Quantification of Bifurcations in Random Ordinary Dif fer-ential Equations. SIAM J. Appl. Dyn. Syst.\, 20(4):2295–2334\, 2021. \n[2] K. Lux\, P. Ashwin\, R. Wood\, and C. Kuehn. Assessing the impact of parametric uncertainty on tipping points of the atlantic meridional overt urning circulation. Environmental Research Letters\, 17(7):075002\, 2022. \n \n \nDer Vortrag findet statt am\nMittwoch\, den 29.10.2025 um 17.15 Uhr im Raum W01 0-006\nKaffee/Tee um 16.45 Uhr im Raum W1 2-213\nInteressi erte sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Vortrag sankündigung

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 \;

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Im Rahmen des Kolloquiums spricht

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Frau Kerstin Lux-Gottscha lk

\n

Eindhoven University of Technology

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< span lang="EN-GB" dir="ltr">Department of Mathematics and Computer Science

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Eindhoven\, Netherlands

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e-mail: k.m.lux@tue.nl

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 \;\n

 \;

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Uncertainty Quantification for Bifurcating Dyna mical Systems

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über
 \;

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ABSTRACT

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Many real-world systems can be mode led in terms of systems of differential equations. Oftentimes\, they have inherently nonlinear dynamics which can induce sudden\, large and irrevers ible changes when an external forcing parameter is varied. We analyze thes e bifurcations in the realm of uncertainty [1]. In this talk\, we will con sider parameter uncertainty. This arises naturally when model parameters n eed to be estimated from measurement data or cannot even be measured direc tly but need to be inferred from other observable quantities.

\n

 \;

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We will see that parameter uncertainty can crucially alter t he bifurcation landscape.

\n

I will illustrate this by an example from climate science\ , the Atlantic Meridional Overturning Circulation\, where we model tipping points (TPs) in terms of bifurcations [2]. The system is of particular im portance for the North Atlantic heat transport. We highlight the uncertain locations of TPs along the arising probabilistic bifurcation curves. More over\, we provide an original combination of sensitivity analysis\n

and bifurcation th eory allowing to quantify the distance between family of bifurcation curve s for different input parameter distributions. Thereby\, we contribute to an uncertainty quantification of high impact\, low likelihood climate outc omes.

\n

 \;

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This talk covers some joint work with Chri stian Kuehn (Technical University of Munich)\, Peter Ashwin (University of Exeter\, UK)\, Richard Wood (Met Office\, UK)\, Jonathan Baker (Met Offic e\, \;UK)\, Oliver Ernst (TU Chemn itz) and Björn Sprungk (TU Freiberg).

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 \;

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R EFERENCES

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[1] C. Kuehn and K. Lux. Uncertainty Quantification of Bifurcatio ns in Random Ordinary Differ-ential Equations. SIAM J. Appl. Dyn. Syst.\, 20(4):2295–2334\, 2021.

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[2] K. Lux\, P. Ashwin\, R. Wood\, and C. Kuehn. Assessing the impact of parametric uncertainty on tipping points of the atlantic me ridional overturning circulation. \;Environmental Research Lett ers\, 17(7):075002\, 2022.

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 \;

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 \;

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Der Vortrag f indet statt am

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Mittwoch \, den 29.10.2025 um 17.15 Uhr im Raum W01 0-006

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Kaffee/Tee um 16.45 Uhr im Raum W1 2-213

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Interessierte sind herzlich eingeladen.

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-geraden-auf-kubischen-hyperflaechen-bruecken-zwischen-alge braischer-geometrie-und-diskreten-strukturen DTSTAMP:20250630T125816Z DTSTART:20250709T151500Z SUMMARY:Geraden auf kubischen Hyperflächen Brücken zwischen Algebraische r Geometrie und diskreten Strukturen DESCRIPTION:Vortragsankündigung\n \nIm Rahmen des Kolloquiums spricht\nH err Christian Lehn\nüber\nGeraden auf kubischen Hyperflächen\nBrücken z wischen Algebraischer Geometrie und diskreten Strukturen\n \nAbstract:\nG eraden auf kubischen Hyperflächen faszinieren Geometer seit mehr als 150 Jahren. Meilensteine sind das Theorem von Cayley-Salmon (1849) über Gerad en auf kubischen Flächen sowie die Arbeiten von Clemens-Griffiths (1972) über Geraden auf kubischen Hyperflächen der Dimension drei. In beiden Fä llen gibt es starke Verbindungen zu diskreten Strukturen in der Geometrie. Nach einer Einführung in die Thematik werde ich eine neue Invariante vor stellen\, die diese Verbindung weiter unterstreicht und unter anderem Anwe ndungen in der Arithmetik hervorgebracht hat.\n \nDer Vortrag findet stat t am\nMittwoch\, den 09.07.2025 um 17.15 Uhr im Raum W01 0-006\n \nKaffee /Tee um 16.45 Uhr im Raum W1 2-213\nInteressierte sind herzlich eingeladen .   X-ALT-DESC;FMTTYPE=text/html:

Vortragsankündigung

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 \;

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Im Rahmen des Kolloquiums spricht

\n

Herr Christian Lehn

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über

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Geraden auf kubischen Hyperflä chen

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Brücken zwischen Algebraischer Geometrie und diskreten Struktur en

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 \;

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Abstract:

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Geraden auf kubischen Hyperflächen faszi nieren Geometer seit mehr als 150 Jahren. Meilensteine sind das Theorem vo n Cayley-Salmon (1849) über Geraden auf kubischen Flächen sowie die Arbe iten von Clemens-Griffiths (1972) über Geraden auf kubischen Hyperfläche n der Dimension drei. In beiden Fällen gibt es starke Verbindungen zu dis kreten Strukturen in der Geometrie. Nach einer Einführung in die Thematik werde ich eine neue Invariante vorstellen\, die diese Verbindung weiter u nterstreicht und unter anderem Anwendungen in der Arithmetik hervorgebrach t hat.

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 \;

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Der Vortrag findet statt am

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Mittwoch\, den 09.07.2 025 um 17.15 Uhr im Raum W01 0-006

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 \;

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Kaffe e/Tee um 16.45 Uhr im Raum W1 2-213

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Interessierte sind herzlich eingeladen. \ ;
 \;

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-the-finite-cell-method-basic-idea-adaptivity-and-mixed-pro blems DTSTAMP:20250605T141158Z DTSTART:20250625T151500Z SUMMARY:The Finite Cell Method: Basic Idea\, Adaptivity\, and Mixed Proble ms DESCRIPTION:Vortragsankündigung\nIm Rahmen des Kolloquiums spricht\nHerr Prof. Dr. Andreas Rademacher (Universität Bremen)\nDer Vortrag findet sta tt am Mittwoch\, den 25.06.2025 um 17.15 Uhr im Raum W01 0-006\nTitel: The Finite Cell Method: Basic Idea\, Adaptivity\, and Mixed Problems\n\nAbstr act: The meshing of complex or time-dependent domains is one of the fundam ental challenges in the finite element method (FEM). Fictitious domains ar e one approach to meeting this challenge. The actual domain is embedded in a larger and simply structured domain. The approximation of the actual do main is then carried out by introducing a regularized truncation function into the partial differential equation (PDE) to be solved. The application of the FEM to the resulting problem leads to the finite cell method (FCM) . Here\, the truncation function must now be approximated with sufficient accuracy within the framework of the numerical calculation of integrals\, for which suitable summed quadrature formulas must be constructed. In this talk\, we discuss the basic idea of FCM and especially the construction o f the summed quadrature formulas. Furthermore\, we discuss the existing a priori error estimates.\n\nIn practical applications\, the question arises whether the quadrature formulas are sufficiently accurate or not. In this talk\, we present an approach based on a posteriori error estimators\, wh ich constructs a suitable quadrature based on adaptive algorithms. The oth er errors (error from the domain approximation\, discretization errors of the FEM\, numerical error) are also included and equilibrated. The derivat ion of the error estimators uses the dual weighted residual (DWR) method. The fundamental challenge lies in the separation of the individual error c omponents and the appropriate approximation of the analytical error identi ty.\n\nA second fundamental problem with the FCM is the realization of (in homogeneous) Dirichlet boundary conditions on the real boundary\, if it do es not coincide with the fictitious boundary\, since the techniques common ly used in the FEM cannot be applied. One approach that is commonly used i n the literature is the integration by means of an additional penalty term with all the associated advantages and especially disadvantages\, such as the difficult choice of the penalty parameter. Therefore\, mixed approach es for the realization of Dirichlet boundary conditions are presented and analyzed. However\, ensuring inf-sup stability contradicts numerical perfo rmance. This is why we provide an outlook on techniques that ensure both b ased on stabilized mixed methods.\n \nKaffee/Tee um 16.45 Uhr im Raum W1 2-213 \nInteressierte sind herzlich eingeladen.  X-ALT-DESC;FMTTYPE=text/html:

Vortragsankündigung

\n

Im Rahmen des Kolloquiums spricht

\n

Herr Prof. Dr. Andreas Rademac her (Universität Bremen)

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Der Vortrag findet statt am Mittwoch\, den 25.06.2025 um 17.15 Uhr im Raum W01 0-006

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Titel: The Finite Cell Method: Basic Idea\, Adaptivity\, and Mixed Problems

\n\n

Abstract: The meshing of complex or time-dependent domains is one of the fundamental challenges in the finite element method (FEM). Fictitious dom ains are one approach to meeting this challenge. The actual domain is embe dded in a larger and simply structured domain. The approximation of the ac tual domain is then carried out by introducing a regularized truncation fu nction into the partial differential equation (PDE) to be solved. The appl ication of the FEM to the resulting problem leads to the finite cell metho d (FCM). Here\, the truncation function must now be approximated with suff icient accuracy within the framework of the numerical calculation of integ rals\, for which suitable summed quadrature formulas must be constructed. In this talk\, we discuss the basic idea of FCM and especially the constru ction of the summed quadrature formulas. Furthermore\, we discuss the exis ting a priori error estimates.

\n\n

I n practical applications\, the question arises whether the quadrature form ulas are sufficiently accurate or not. In this talk\, we present an approa ch based on a posteriori error estimators\, which constructs a suitable qu adrature based on adaptive algorithms. The other errors (error from the do main approximation\, discretization errors of the FEM\, numerical error) a re also included and equilibrated. The derivation of the error estimators uses the dual weighted residual (DWR) method. The fundamental challenge li es in the separation of the individual error components and the appropriat e approximation of the analytical error identity.

\n\n

A second fundamental problem with the FCM is the realiza tion of (inhomogeneous) Dirichlet boundary conditions on the real boundary \, if it does not coincide with the fictitious boundary\, since the techni ques commonly used in the FEM cannot be applied. One approach that is comm only used in the literature is the integration by means of an additional p enalty term with all the associated advantages and especially disadvantage s\, such as the difficult choice of the penalty parameter. Therefore\, mix ed approaches for the realization of Dirichlet boundary conditions are pre sented and analyzed. However\, ensuring inf-sup stability contradicts nume rical performance. This is why we provide an outlook on techniques that en sure both based on stabilized mixed methods.

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 \;

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Kaffee/Tee um 16.45 Uhr im Raum W1 2-213 \;

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Interessierte sin d herzlich eingeladen. \;

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-modelling-of-stochastic-interest-rates DTSTAMP:20250108T122527Z DTSTART:20250129T161500Z SUMMARY:Modelling of stochastic interest rates DESCRIPTION:Vortragsankündigung\nIm Rahmen des Kolloquiums spricht\nHerr Prof. Dr. Mogens Bladt\, \nDepartment of Mathematical Sciences\, Universi ty of Copenhagen\nüber\nModelling of stochastic interest rates\n \nInter est rates play an important role in insurance modelling\, particularly in the pricing of longterm insurance products such as life insurance policies . We consider the so-called Markovian interest rate model\, where interest rates are assumed to change according to an underlying Markov process. In each state of the Markov process\, the spot interest rate is assumed eith er to be constant or a deterministic function. Either way\, the Markovian interest rate models form a dense class of interest models that can approx imate any interest rate model. e.g. the oftenused SDE-driven models.\n \n In this talk\, we show how to achieve such approximations by linking the M arkovian interest rate models to a class of tractable and dense distributi ons known as phase-type distribution. The link to phase-type theory emerge s from the price of a zero–coupon bond being identical to the survival f unction of a phase-type distribution.\n \nWith the phase-type toolbox at hand\, we can calibrate a Markovian interest model to observed bond prices or theoretical models\, obtain explicit formulas for related quantities s uch as yield curves and swap rates\, and deal with negative interest rates . A number of illustrative examples will be provided.\n \nThe Markovian i nterest rates have the further advantage of integrating particularly well into the so-called multi-state Markov models often used in life insurance modelling (in some countries).\n \nDer Vortrag findet statt am\n \nMittw och\, den 29.01.2025 um 17.15 Uhr im Raum W01 0-006\n \nKaffee/Tee um 16. 45 Uhr im Raum W1 2-213\n \nInteressierte sind herzlich eingeladen.\n \n Fakultät V\nMathematik und Naturwissenschaften   X-ALT-DESC;FMTTYPE=text/html:

Vortragsankündigung

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Im Rahmen des Kolloquiums spricht

\n

Herr Prof. Dr. Mogens Bladt\,&nbs p\;

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Department of Mathematical Sciences\, University of Copenhagen

\n

über< /span>

\n

Model ling of stochastic interest rates

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 \;

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Interest rates play an important role in insurance modelling\, particularly in the pricing of longterm insurance products such as life insurance policies. W e consider the so-called Markovian interest rate model\, where interest ra tes are assumed to change according to an underlying Markov process. In ea ch state of the Markov process\, the spot interest rate is assumed either to be constant or a deterministic function. Either way\, the Markovian int erest rate models form a dense class of interest models that can approxima te any interest rate model. e.g. the oftenused SDE-driven models.\n

 \;

\n

In this talk\, we show how to achieve such approximations by linking the Markovian interest rate models to a class of tractable and de nse distributions known as phase-type distribution. The link to phase-type theory emerges from the price of a zero–coupon bond being identical to the survival function of a phase-type distribution.

\n

 \;

\n

With the phase-type toolbox at hand\, we can calibrate a Markovian interes t model to observed bond prices or theoretical models\, obtain explicit fo rmulas for related quantities such as yield curves and swap rates\, and de al with negative interest rates. A number of illustrative examples will be provided.

\n

 \;

\n

The Markovian interest rates have the fur ther advantage of integrating particularly well into the so-called multi-s tate Markov models often used in life insurance modelling (in some countri es).

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Der Vortrag findet statt am

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 \;

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Mittwoch\, den 29.01.2025 um 17.15 Uhr im Raum W01 0-006

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Kaffee/Tee um 16.45 Uhr im Raum W1 2-2 13

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Interessierte sind herzlich eingeladen.

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 \;

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Fakultät V

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Mathematik und Naturwissenschaften \;
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LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-on-uncertainty-quantification-of-eigenvalue-problems DTSTAMP:20241120T093919Z DTSTART:20241204T161500Z SUMMARY:On uncertainty quantification of eigenvalue problems DESCRIPTION:Vortragsankündigung\nIm Rahmen des Kolloquiums spricht\nHerr Prof. Dr. Jürgen Dölz (Universität Bonn)\nüber\nTitle: On uncertainty quantification of eigenvalue problems\n \nAbstract:\n \nEigenvalue probl ems have manifold applications in engineering\, physics and medicine\, and their (numerical) solution is nowadays well understood in most cases. How ever\, since real-world circumstances typically deviate in an unforeseeabl e and seemingly random fashion from the ideal (computational) environment\ , the real-world solutions of the eigenvalue problem also deviate in a ran dom fashion from the simulation results. This implies that the eigenpairs of the eigenvalue problem are also random. We investigate stochastic quant ities of interest of eigenpairs of higher but finite multiplicity and disc uss why for multiplicity larger than one\, only the stochastic quantities of interest of the eigenspaces are meaningful. To do so\, we characterize the Fréchet derivatives of the eigenpairs with respect to the perturbatio n and provide a new linear characterization for eigenpairs of higher multi plicity. As a side result\, we prove local analyticity of the eigenspaces. Based on the Fréchet derivatives of the eigenpairs we discuss a meaningf ul Monte Carlo sampling strategy for multiple eigenvalues and develop an u ncertainty quantification perturbation approach. We discuss numerical exam ples to illustrate the theoretical results\, including an example of a thr ee dimensional particle accelerator based on real-world data.\n \nDer Vor trag findet statt am\n \nMittwoch\, den 04.12.2024 um 17.15 Uhr im Raum W 01 0-006 Kaffee/Tee um 16.45 Uhr im Raum W1 2-213\n \nInteressierte sind herzlich eingeladen   X-ALT-DESC;FMTTYPE=text/html:

Vortragsankündigung

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Im Rahmen des Kolloquiums spricht

\ n

Herr Prof. Dr . Jürgen Dölz (Universität Bonn)

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über

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Title: On uncertainty quantification of eigenvalue problems

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 \;

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Abstract:

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 \;

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Eigenvalue problems have manifold applications in engineering\, phy sics and medicine\, and their (numerical) solution is nowadays well unders tood in most cases. However\, since real-world circumstances typically dev iate in an unforeseeable and seemingly random fashion from the ideal (comp utational) environment\, the real-world solutions of the eigenvalue proble m also deviate in a random fashion from the simulation results. This impli es that the eigenpairs of the eigenvalue problem are also random. We inves tigate stochastic quantities of interest of eigenpairs of higher but finit e multiplicity and discuss why for multiplicity larger than one\, only the stochastic quantities of interest of the eigenspaces are meaningful. To d o so\, we characterize the Fréchet derivatives of the eigenpairs with res pect to the perturbation and provide a new linear characterization for eig enpairs of higher multiplicity. As a side result\, we prove local analytic ity of the eigenspaces. Based on the Fréchet derivatives of the eigenpair s we discuss a meaningful Monte Carlo sampling strategy for multiple eigen values and develop an uncertainty quantification perturbation approach. We discuss numerical examples to illustrate the theoretical results\, includ ing an example of a three dimensional particle accelerator based on real-w orld data.

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 \;

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Der Vortrag findet statt am

\n< p class="text-center"> \;

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Mittwoch\, den 04.12.2024 um 17.15 Uhr im Raum W01 0-006 Kaffee/Tee um 16.45 Uhr im Raum W1 2-213

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Interessierte sind herzlich eingeladen \;
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LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-hodge-riemann-relations-for-convex-valuations DTSTAMP:20240604T125954Z DTSTART:20240703T151500Z SUMMARY:Hodge-Riemann relations for convex valuations DESCRIPTION:Vortragsankündigung\n \nIm Rahmen des Kolloquiums spricht\n  \nHerr Prof. Dr. Andreas Bernig (Uni Frankfurt)\nüber\n \nHodge-Riemann relations for convex valuations\n \nThe so-called Kähler package consist s of a Poincaré duality\, a hard Lefschetz theorem and the HodgeRiemann r elations. The origin goes back to the cohomology theory of compact Kähler manifolds\, but similar structures appeared in the last few years in many different areas in mathematics such as algebraic geometry\, combinatorics and polytope theory and have far reaching consequences.\n \nAfter explai ning some of these structures\, I will report on a recent project with Jan Kotrbatý (Charles University Prague) and Thomas Wannerer (Friedrich-Schi ller University Jena) where we introduce a Kähler package for convex valu ations. As a consequence\, we find quadratic inequalities for mixed volume s that generalize the fundamental Alexandrov-Fenchel inequality.\n \nDer Vortrag findet statt am\nMittwoch\, 03.07.2024 um 17.15 Uhr im Raum W01 0- 006\nKaffee/Tee um 16.45 Uhr im Raum W1 2-213\n \nInteressierte sind herz lich eingeladen.\n  X-ALT-DESC;FMTTYPE=text/html:

Vortragsankündigung

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 \;

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Im Rahmen des Kolloquiums spricht

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 \;

\n< h3 class="text-center">Herr Prof. Dr. And reas Bernig (Uni Frankfurt)\n

< span class="fontstyle1">über

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 \;\n

Hodge-Riemann relations for convex valuations

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 \;

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The so-ca lled Kähler package consists of a Poincaré duality\, a hard Lefschetz th eorem and the HodgeRiemann relations. The origin goes back to the cohomolo gy theory of compact Kähler manifolds\, but similar structures appeared i n the last few years in many different areas in mathematics such as algebr aic geometry\, combinatorics and polytope theory and have far reaching con sequences.

\n

 \;

\n

After explaining some of these structures \, I will report on a recent project with Jan Kotrbatý (Charles Universit y Prague) and Thomas Wannerer (Friedrich-Schiller University Jena) where w e introduce a Kähler package for convex valuations. As a consequence\, we find quadratic inequalities for mixed volumes that generalize the fundame ntal Alexandrov-Fenchel inequality.

\n

&nb sp\;

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Der Vortrag find et statt am

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Mittwoch\, 03.07.2024 um 17.15 Uhr im Raum W01 0-006

\n

Kaffee/Tee um 16.4 5 Uhr im Raum W1 2-213

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Interessierte sind h erzlich eingeladen.

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 \; LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-singular-and-applications DTSTAMP:20240614T091302Z DTSTART:20240619T151500Z SUMMARY:Singular and Applications DESCRIPTION: Vortragsankündigung\n Im Rahmen des Kolloquiums spricht Herr Prof. Dr. Gerhard Pfister\, Universität Kaiserslautern\n Singular and Ap plications\n The aim of the talk is to show how computer algebra can be us ed to solve problems in algebra and algebraic geometry. At the beginning t he concept of a Gröbner basis as a basic tool in computer algebra will be introduced. A counter example in singularity theory is the next task: The re are complete intersection singularities with exact Poincare complexes b ut not quasi-homogeneous. A result in group theory proved by using algebra ic geometry and Singular is the characterization of simple solvable groups by 2-variable identities. The next problem is the question: how to solve a Sudoku using algebraic geometry and Gröbner bases? A result in classifi cation of singularities\, the classification of simple 0-dimensional isola ted complete intersection singularities\, will be at the end of the talk.\ n Der Vortrag findet statt am Mittwoch\, den 19.06.2024 um 17.15 Uhr im Ra um W01 0-006\n Kaffee/Tee um 16.45 Uhr im Raum W1 2-213\n Interessierte si nd herzlich eingeladen.\n Fakultät V Mathematik und Naturwissenschaften X-ALT-DESC;FMTTYPE=text/html:


Vortragsankündigung

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Im Rahmen des Kolloquiums spricht
Herr Prof. Dr. Gerhard Pfister\, Universität Kaiserslautern

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Singular and Applications

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The aim of the talk is to show how computer algebra can be used to solve problems in algebra and algebraic geometry. At the beginning the concept of a Grö bner basis as a basic tool in computer algebra will be introduced. A count er example in singularity theory is the next task: There are complete inte rsection singularities with exact Poincare complexes but not quasi-homogen eous. A result in group theory proved by using algebraic geometry and Sing ular is the characterization of simple solvable groups by 2-variable ident ities. The next problem is the question: how to solve a Sudoku using algeb raic geometry and Gröbner bases? A result in classification of singularit ies\, the classification of simple 0-dimensional isolated complete interse ction singularities\, will be at the end of the talk.

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Der Vortrag findet statt am Mittwoch\, den 19.06.2024 um 17.15 Uhr im R aum W01 0-006

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Kaffee/Tee um 16.45 Uhr im Raum W1 2 -213

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Interessierte sind herzlich eingeladen.

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Fakultät V
Mathematik und
Naturwissensch aften

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-veraenderte-lernausgangslagen-im-fach-mathematik-befunde-u nd-betrachtungen-zur-studierfaehigkeit-von-studierenden-und-zur-studierend enfaehigkeit-von-hochschulen DTSTAMP:20240605T151600Z DTSTART:20240612T151500Z SUMMARY:Veränderte Lernausgangslagen im Fach Mathematik – Befunde und B etrachtungen zur „Studierfähigkeit“ von Studierenden und zur „Studi erendenfähigkeit“ von Hochschulen DESCRIPTION:Vortragsankündigung\n\nIm Rahmen des Kolloquiums spricht\nHer r Prof. Dr. Andreas Büchter (Universität Duisburg-Essen)\nüber\nVeränd erte Lernausgangslagen im Fach Mathematik – Befunde und Betrachtungen zu r „Studierfähigkeit“ von Studierenden und zur „Studierendenfähigke it“ von Hochschulen\n\nInstitutionen der beruflichen und akademischen Au sbildung klagen seit jeher über eine aus ihrer Sicht nicht hinreichend ge gebene Ausbildungs- oder Studierfähigkeit der nachwachsenden Generation. Dennoch greift es zu kurz\, entsprechende Klagen als „alte Leier“ abzu tun und sich nicht genauer mit durchaus feststellbaren Veränderungen ause inanderzusetzen. Eine differenzierte Diagnose ist sogar besonders wichtig\ , um in den prinzipiell nie endenden Prozessen der Unterrichtsentwicklung und Studienreform effektive Maßnahmen ergreifen zu können.\n\nIm Vortrag werden entsprechend veränderte Lernausgangslagen im Bereich des Übergan gs von der Schule in die Hochschule für das Fach Mathematik betrachtet. N eben feststellbaren Fachleistungen\, die zuletzt während der Corona-Pande mie (teilweise erheblich) zurückgegangen sind\, und institutionellen Rahm enbedingungen für Unterricht wird auch auf die Art und Weise geblickt\, w ie Mathematik heute in der Schule inszeniert wird. Diese Befunde und Betra chtungen sollen zu einer gemeinsamen Diskussion über Handlungsoptionen im Schul- und im Hochschulbereich anregen.\n\nDer Vortrag findet statt am\nM ittwoch\, den 12.06.2024 um 17.15 Uhr im Raum W01 0-006\n\nKaffee/Tee um 1 6.45 Uhr im Raum W01 2-213\n\nInteressierte sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Vortragsankündi gung

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Im Rahmen des Kolloquiums spricht

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Herr Prof. Dr. Andreas Bü chter (Universität Duisburg-Essen)

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über

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Veränderte Lern ausgangslagen im Fach Mathematik – Befunde und Betrachtungen zur „Stud ierfähigkeit“ von Studierenden und zur „Studierendenfähigkeit“ von Hochschulen

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Instituti onen der beruflichen und akademischen Ausbildung klagen seit jeher über e ine aus ihrer Sicht nicht hinreichend gegebene Ausbildungs- oder Studierfä higkeit der nachwachsenden Generation. Dennoch greift es zu kurz\, entspre chende Klagen als „alte Leier“ abzutun und sich nicht genauer mit durc haus feststellbaren Veränderungen auseinanderzusetzen. Eine differenziert e Diagnose ist sogar besonders wichtig\, um in den prinzipiell nie endende n Prozessen der Unterrichtsentwicklung und Studienreform effektive Maßnah men ergreifen zu können.

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Im Vor trag werden entsprechend veränderte Lernausgangslagen im Bereich des Übe rgangs von der Schule in die Hochschule für das Fach Mathematik betrachte t. Neben feststellbaren Fachleistungen\, die zuletzt während der Corona-P andemie (teilweise erheblich) zurückgegangen sind\, und institutionellen Rahmenbedingungen für Unterricht wird auch auf die Art und Weise geblickt \, wie Mathematik heute in der Schule inszeniert wird. Diese Befunde und B etrachtungen sollen zu einer gemeinsamen Diskussion über Handlungsoptione n im Schul- und im Hochschulbereich anregen.

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Der Vortrag findet statt am

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Mittwoch\, den 12.06.2024 um 17.15 Uhr im Raum W01 0-006\n\n

Kaffee/Tee um 16.45 Uhr im Raum W01 2-21 3

\n\n

Interessierte sind herzlich e ingeladen.

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-patterns-interfaces-and-dynamics DTSTAMP:20240521T095405Z DTSTART:20240522T151500Z SUMMARY:Patterns\, interfaces and dynamics DESCRIPTION:Vortragsankündigung\n \nIm Rahmen des Kolloquiums spricht\n  \nHerr Jens Rademacher (Universität Hamburg)\n \nüber\n \nPatterns\, i nterfaces and dynamics\n \nPatterns\, as coherent structures in space and time\, permeate our perception and the physical world. We sense sound and vibration waves\, and we organise observations in patterns and symmetries . Nonlinear effects enter when these are “far" from equilibrium\, leadin g to self-organized emergent phenomena as in water waves\, vegetation patt erns\, and action potentials. Paradigmatic nonlinear structures are interf aces that separate regions of different patterns\, such as material phase boundaries or magnetic domain walls. In this talk I take a mathematical pe rspective and introduce some concepts\, approaches\, and results from this fascinating field.\n \nDer Vortrag findet statt am\n \nMittwoch\, den 2 2.05.2024 um 17.15 Uhr im Raum W01 0-006\n \nKaffee/Tee um 16.45 Uhr im R aum W01 2-213\n \nInteressierte sind herzlich eingeladen X-ALT-DESC;FMTTYPE=text/html:

Vortragsankündigung

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 \;

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Im Rahmen des Kolloquiums spricht

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\n< h4 class="text-center">Herr Jens Rademach er (Universität Hamburg)\n

&nb sp\;

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über

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Patterns\, interfaces and dynamics\n

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Patterns\, as coherent structures in space and time\, permea te our perception and the physical world. We sense sound and vibration wav es\, and we organise observations in patterns and symmetries. Nonlinear ef fects enter when these are “far" from equilibrium\, leading to self-orga nized emergent phenomena as in water waves\, vegetation patterns\, and act ion potentials. Paradigmatic nonlinear structures are interfaces that sepa rate regions of different patterns\, such as material phase boundaries or magnetic domain walls. In this talk I take a mathematical perspective and introduce some concepts\, approaches\, and results from this fascinating f ield.

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Der Vortrag findet statt am

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 \;

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Mittwoch\, den 22.05.2024 um 17.15 Uhr im Raum W01 0-006

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Kaffee/Tee um 16.45 Uhr im Raum W01 2-213

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Interessierte sind herzlich eingeladen

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-insuring-model-uncertainty DTSTAMP:20240508T112156Z DTSTART:20240515T151500Z SUMMARY:Insuring Model Uncertainty DESCRIPTION:Model uncertainty\, also known as Knightian uncertainty\, has become a major research topic in recent years. On the decision-theoretic s ide\, various approaches show how one can successfully capture model uncer tainty with the help of mathematical models. The lecture reviews recent mo del of preferences under Knightian uncertainty. These approaches are close ly related to attempts to quantify risk in finance.\nA particular focus wi ll be on the so-called smooth model\, an ambiguity-averse version of a sec ondorder Bayesian Ansatz\, that goes back to Klibanoff\, Marinacci\, and M ukerji (Econometrica 2005). We will study its axiomatic foundations and di scuss the relationship of this approach with statistics\, in particular th e issue of identification of models (Denti\, Pomatto\, Econometrica 2022). Moreover\, we show how the smooth model is related to variational and coh erent risk measures.\nWe then investigate consequences of model uncertaint y for the insurance market. We study the case where the typical consumer i n the economy is ambiguity-averse with smooth ambiguity preferences and th e set of priors is point identified\, i.e.\, the true law can be recovered ex post empirically from observed events. The identifiability of models a llows to write insurance contracts on models\, with important economic con sequences. We are able to construct a representative agent who\, in genera l\, has also smooth ambiguity preferences\, yet with a model-dependent amb iguity attitude. We illustrate our results in the classic Wilson framework of risk sharing where the representative agent has modelindependent ambig uity attitude and insurance against ambiguity can be explicitly computed.\ n\nDer Vortrag findet statt am Mittwoch\, den 15.05.2024 um 17.15 Uhr im R aum W01 0-006\nKaffee/Tee um 16.45 Uhr im Raum W1 2-213\nInteressierte sin d herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Model uncertainty \, also known as Knightian uncertainty\, has become a major research topic in recent years. On the decision-theoretic side\, various approaches show how one can successfully capture model uncertainty with the help of mathe matical models. The lecture reviews recent model of preferences under Knig htian uncertainty. These approaches are closely related to attempts to qua ntify risk in finance.

\n

A particula r focus will be on the so-called smooth model\, an ambiguity-averse versio n of a secondorder Bayesian Ansatz\, that goes back to Klibanoff\, Marinac ci\, and Mukerji (Econometrica 2005). We will study its axiomatic foundati ons and discuss the relationship of this approach with statistics\, in par ticular the issue of identification of models (Denti\, Pomatto\, Econometr ica 2022). Moreover\, we show how the smooth model is related to variation al and coherent risk measures.

\n

We then investigate consequences of model uncertainty for the insurance marke t. We study the case where the typical consumer in the economy is ambiguit y-averse with smooth ambiguity preferences and the set of priors is point identified\, i.e.\, the true law can be recovered ex post empirically from observed events. The identifiability of models allows to write insurance contracts on models\, with important economic consequences. We are able to construct a representative agent who\, in general\, has also smooth ambig uity preferences\, yet with a model-dependent ambiguity attitude. We illus trate our results in the classic Wilson framework of risk sharing where th e representative agent has modelindependent ambiguity attitude and insuran ce against ambiguity can be explicitly computed.

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Der Vortrag findet statt am Mittwoch\, den 15.05.2024 um 17.15 Uhr im Raum W01 0-006

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Kaffee/Tee um 16.45 Uhr im Raum W1 2-213

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Interessiert e sind herzlich eingeladen.

LOCATION: Raum W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-high-dimensional-approximation-making-life-easy-with-kerne ls DTSTAMP:20240212T090809Z DTSTART:20240320T160000Z SUMMARY:High dimensional approximation – making life easy with kernels DESCRIPTION:Im Rahmen des Kolloquiums spricht\nHerr Prof. Dr. Ian H. Sloan \, University of New South Wales (Sydney)\nüber\nHigh dimensional approxi mation – making life easy with kernels\n \nHigh dimensional approximati on problems commonly arise from parametric PDE problems in which the param etric input depends on very many independent univariate random variables. Often (as in the method of “generalized polynomial chaos”\, or GPC) th e dependence on the parametric variables is approximated by multivariate p olynomials\, leading to exponentially increasing difficulty and cost (expr essed as the “curse of dimensionality”) as the dimension increases. Fo r this reason sparsity of coefficients is a major focus in all implementat ions of GPC.\n \nIn this lecture we develop a different approach\, one in which there is no need for sparsification\, and no curse of dimensionalit y. The method\, proposed in a 2022 paper with Frances Kuo\, Vesa Kaarnioja \, Yoshihito Kazashi and Fabio Nobile\, uses kernel interpolation with per iodic kernels\, with the kernels located at lattice points\, as advocated long ago by Hickernell and colleagues.\n \nThe lattice points and the ker nels depend on parameters called “weights”. In the 2022 paper the reco mmended weights were “SPOD” weights\, leading to an L2 error independe nt of dimension but with a cost growing as the square of the number of lat tice points. A newer 2023 paper with Kuo and Kaarnioja introduced “seren dipitous” weights\, for which the cost grows only linearly with both dim ension and number of lattice points\, allowing practical computations in a s many as 1\,000 dimensions. The rate of convergence proved in the above p apers was of the order n-α/2\, for interpolation using the reproducing ke rnel of a space with mixed smoothness of order α. However\,a new result w ith Vesa Kaarnioja doubles the proven convergence rate to n-α.\n \nDer V ortrag findet statt am Mittwoch\, den 20.03.2024 \num 17.15 Uhr im Raum W0 1 0-006\n \nKaffee/Tee um 16.45 Uhr im Raum W1 2-213\n \nInteressierte s ind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Im Rahmen des Kolloquiums spricht

\n

He rr Prof. Dr. Ian H. Sloan\, University of New South Wales (Sydney)< /strong>

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über\n

High dimensional approximation – making life ea sy with kernels

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 \ ;

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High dimensional ap proximation problems commonly arise from parametric PDE problems in which the parametric input depends on very many independent univariate random va riables. Often (as in the method of “generalized polynomial chaos”\, o r GPC) the dependence on the parametric variables is approximated by multi variate polynomials\, leading to exponentially increasing difficulty and c ost (expressed as the “curse of dimensionality”) as the dimension incr eases. For this reason sparsity of coefficients is a major focus in all im plementations of GPC.

\n

 \;

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In this lecture we develop a d ifferent approach\, one in which there is no need for sparsification\, and no curse of dimensionality. The method\, proposed in a 2022 paper with Fr ances Kuo\, Vesa Kaarnioja\, Yoshihito Kazashi and Fabio Nobile\, uses ker nel interpolation with periodic kernels\, with the kernels located at latt ice points\, as advocated long ago by Hickernell and colleagues.

\n

 \;

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The lattice points and the kernels depend on parameters calle d “weights”. In the 2022 paper the recommended weights were “SPOD” weights\, leading to an L2 error independent of dimension but with a cost growing a s the square of the number of lattice points. A newer 2023 paper with Kuo and Kaarnioja introduced “serendipitous” weights\, for which the cost grows only linearly with both dimension and number of lattice points\, all owing practical computations in as many as 1\,000 dimensions. The rate of convergence proved in the above papers was of the order n-α/2\, for interpolation u sing the reproducing kernel of a space with mixed smoothness of order α. However\,a new result with Vesa Kaarnioja doubles the proven convergence r ate to n-α.

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Der Vortrag findet statt am Mittwoch\, den 20.03.2024

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um 17.15 Uhr im Raum W01 0-006

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 \;

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Kaffee/Tee um 16.45 Uhr im Ra um W1 2-213

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Interessierte sind herzlich eingeladen.

LOCATION:W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-dirk-langemann-1 DTSTAMP:20240129T092409Z DTSTART:20240131T161500Z SUMMARY:Vortrag: Dirk Langemann DESCRIPTION:Thema: "Mathematische Modellierung der Entwicklung metabolisch er Resistenzen" \nAbstract:\nDie Entwicklung von Resistenzen von beispiels weise Unkräutern und Bakterien wird als Anpassungsprozess an veränderte Umweltbedingungen modelliert. Die Kopplung von Wachstum und Vererbung für Genotypen\, die sich in mehreren Gen-Orten unterscheiden\, erlaubt die Er klärung beobachtbarer Szenarien. Das verwendetet System gewöhnlicher Dif ferentialgleichungen enthält zudem im Vererbungsmechanismus eine Tensorpr odukt-Struktur\, die zur Diskussion allgemeinerer Fragen der Modellierung einlädt.\nVortragender: Dirk Langemann\, TU Braunschweig\, Institut für Partielle Differentialgleichungen\nDer Vortrag findet statt am\nMittwoch\, den 31.01.2024  um 17.15 Uhr im Raum W01 0-006\nInteressierte sind herzl ich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Thema: "Mathematische Modellierung der Entwicklung metabolischer Resistenzen"

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Abstract:

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Die Entwi cklung von Resistenzen von beispielsweise Unkräutern und Bakterien wird a ls Anpassungsprozess an veränderte Umweltbedingungen modelliert. Die Kopp lung von Wachstum und Vererbung für Genotypen\, die sich in mehreren Gen- Orten unterscheiden\, erlaubt die Erklärung beobachtbarer Szenarien. Das verwendetet System gewöhnlicher Differentialgleichungen enthält zudem im Vererbungsmechanismus eine Tensorprodukt-Struktur\, die zur Diskussion al lgemeinerer Fragen der Modellierung einlädt.

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Vortragender: Dirk Langemann\, TU Braunschweig\, Institu t für Partielle Differentialgleichungen

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Der Vortrag findet statt am

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Mittwoch\, den 31.01.2024 \; um 17.15 Uhr im Raum W01 0-006

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Interessierte sind herzlich e ingeladen.

LOCATION:W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-prof-dr-dietmar-pfeifer-1 DTSTAMP:20240129T092520Z DTSTART:20240117T161500Z SUMMARY:Vortrag: Prof. Dr. Dietmar Pfeifer DESCRIPTION:Titel: „Generating unfavourable VaR scenarios under Solvency II with patchwork copulas”\nAls zentrale Idee des Vortrags präsentiere n wir ein allgemeines\, einfaches Patchwork-Konstruktionsprinzip für mult ivariate Copulas\, mit dem ungünstige VaR (d.h. Value at Risk) Szenarios unter Beibehaltung der gegebenen RisikoRandverteilungen möglich sind. Die s ist insbesondere für die sog. Internen Modelle oder auch die Säule II (ORSA) unter Solvency II von Bedeutung. Da es unrealistisch erscheint\, da ss sich das potenziell absolute ungünstigste Szenario in der Wirklichkeit materialisiert\, bilden "fast ungünstigste" Szenarien wie in diesem Vort rag angesprochen insbesondere in höheren Dimensionen gute Modellierungsal ternativen. Unser Ansatz kann als Spezialfall der sog. Ordinalen Summen au fgefasst werden\, die in zwei Dimensionen sogar das absolut ungünstigste VaRSzenario abbilden. Der Vortrag wird in Deutsch gehalten.\nDer Vortrag f indet statt am\nMittwoch\, den 17.01.2024  um 17.15 Uhr im Raum W01 0-006 \nKaffee/Tee 16.45 Uhr im Raum W1 2-213\n \nInteressierte sind herzlich e ingeladen.\n  X-ALT-DESC;FMTTYPE=text/html:

Titel : „Generating unfavourable VaR scenarios under Solvency II with p atchwork copulas”

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Als zen trale Idee des Vortrags präsentieren wir ein allgemeines\, einfaches Patc hwork-Konstruktionsprinzip für multivariate Copulas\, mit dem ungünstige VaR (d.h. Value at Risk) Szenarios unter Beibehaltung der gegebenen Risik oRandverteilungen möglich sind. Dies ist insbesondere für die sog. Inter nen Modelle oder auch die Säule II (ORSA) unter Solvency II von Bedeutung . Da es unrealistisch erscheint\, dass sich das potenziell absolute ungün stigste Szenario in der Wirklichkeit materialisiert\, bilden "fast ungüns tigste" Szenarien wie in diesem Vortrag angesprochen insbesondere in höhe ren Dimensionen gute Modellierungsalternativen. Unser Ansatz kann als Spez ialfall der sog. Ordinalen Summen aufgefasst werden\, die in zwei Dimensio nen sogar das absolut ungünstigste VaRSzenario abbilden. Der Vortrag wird in Deutsch gehalten.

\n

Der Vortrag findet statt am

\n

Mittwoch\, den 17.01.2024 \; um 17.15 Uh r im Raum W01 0-006

\n

Kaffee/Tee 16.45 Uhr im Raum W1 2-213

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 \;

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Interessierte sind herzlich eingeladen.< /p>\n

 \;

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-pd-dr-habil-joachim-kerner-1 DTSTAMP:20240129T092551Z DTSTART:20230712T151500Z SUMMARY:Vortrag: PD Dr. habil. Joachim Kerner DESCRIPTION:Titel: „Recent results on spectral properties of quantum gra phs and Archimedean tilings”\nAbstract: In the first part of the talk we study the spectrum of finite compact quantum graphs and compare the eigen values of two different self-adjoint realizations of a given Schrödinger operator. We derive an explicit expression for the limiting value of the a verage of the differences of the eigenvalues and discuss its geometrical i nterpretation. In this context we shall also establish a so-called local W eyl law for general (local) self-adjoint boundary conditions. In the secon d part of the talk we shall have a look at the discrete normalized Laplaci an on Archimedean tilings with the aim of identifying those tilings for wh ich there exist infinitely degenerate eigenvalues (so-called flat bands). Our main purpose will then be to investigate robustness of existing flat b ands with respect to perturbations of the Laplacian. Our investigations wi ll lead to the identification of one particular Archimedean tiling - the S uper–Kagome tiling – whose spectral properties are outstandingly rich. This talk is based on joint work with P. Bifulco (Hagen)\, M. Täufer (Ha gen)\, and J. Wintermayr (Wuppertal).\nDer Vortrag findet statt am Mittwoc h\, den 12.07.2023 um 17:15 Uhr im Raum W01 0-006\nInteressierte sind herz lich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Titel: „Recent results on spectral properties of quantum graphs and Archimedean tilings”

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Abstract: In the first part of the ta lk we study the spectrum of finite compact quantum graphs and compare the eigenvalues of two different self-adjoint realizations of a given Schrödi nger operator. We derive an explicit expression for the limiting value of the average of the differences of the eigenvalues and discuss its geometri cal interpretation. In this context we shall also establish a so-called lo cal Weyl law for general (local) self-adjoint boundary conditions.
I n the second part of the talk we shall have a look at the discrete normali zed Laplacian on Archimedean tilings with the aim of identifying those til ings for which there exist infinitely degenerate eigenvalues (so-called fl at bands). Our main purpose will then be to investigate robustness of exis ting flat bands with respect to perturbations of the Laplacian. Our invest igations will lead to the identification of one particular Archimedean til ing - the Super–Kagome tiling – whose spectral properties are outstand ingly rich. This talk is based on joint work with P. Bifulco (Hagen)\, M. Täufer (Hagen)\, and J. Wintermayr (Wuppertal).

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Der Vortrag finde t statt am
Mittwoch\, den 12.07.2023 um 17:15 Uhr im Raum W0 1 0-006

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Interessierte sind herzlich eingeladen.

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-im-rahmen-des-zesob-kolloquiums-1 DTSTAMP:20230623T110819Z DTSTART:20230626T143000Z SUMMARY:Vortrag im Rahmen des ZeSOB-Kolloquiums DESCRIPTION:Im Rahmen des ZeSOB-Kolloquiums spricht\nFrau Dr. Anne Vesely (Universität Bremen)\nzum Thema: „Post-selection inference in multivers e analysis“\nMontag\, 26.06.23\, 16:30 Uhr (s.t.) in W1 0-006\noder onli ne in BBB https://meeting.uol.de/b/pet-ihv-p2z-min\nAlle Interessierten au s dem IfM sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Im Rahmen des ZeSOB-Kolloquiums spricht

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Frau Dr. Anne Vesely (Universität Bremen)

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zum Thema: „Pos t-selection inference in multiverse analysis“

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Montag\, 26.06.23\ , 16:30 Uhr (s.t.) in W1 0-006

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oder online in BBB https://meeting.uol.de/b/pet-ihv-p2z-mi n

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Alle Interessierten aus dem IfM sind herzlich eingeladen.

LOCATION:W01 0-006 (https://meeting.uol.de/b/pet-ihv-p2z-min) END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-dr-kathrin-akinwunmi-1 DTSTAMP:20240129T092642Z DTSTART:20230524T151500Z SUMMARY:Vortrag: Dr. Kathrin Akinwunmi DESCRIPTION:Titel: „Algebraisches Denken im Arithmetikunterricht der Pri marstufe”\nAbstract: Algebraisches Denken ist ein grundlegender Bestandt eil des Mathematikunterrichts\, auch wenn es in den nationalen Standards d er Grundschule nicht explizit erwähnt wird. Es ist untrennbar mit dem Inh altsbereich Muster und Strukturen verwoben\, der ja bekanntlich einen wese ntlichen Kern des Mathematikunterrichts ausmacht und alle anderen Inhaltsb ereiche durchzieht. Algebraisches Denken bedeutet\, Muster zu erkunden und die ihnen zugrunde liegenden Strukturen zu verstehen. \nIm Vortrag wird zunächst eine Charakterisierung des algebraischen Denkens und eine damit verbundene Differenzierung der Begriffe Muster und Strukturen grundgelegt. Anschließend werden zwei Studien vorgestellt\, in der Verallgemeinerungs prozesse von Grundschulkindern aus epistemologischer Perspektive betrachte t werden.\nDer Vortrag findet statt am Mittwoch\, den 24.05.2023 um 17:15 Uhr im Raum W01 0-006\nInteressierte sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Titel: „Algebraisches D enken im Arithmetikunterricht der Primarstufe”

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Abstract: Algebraisches Denken ist ein grundlegender Bestandteil des Mathe matikunterrichts\, auch wenn es in den nationalen Standards der Grundschul e nicht explizit erwähnt wird. Es ist untrennbar mit dem Inhaltsbereich M uster und Strukturen verwoben\, der ja bekanntlich einen wesentlichen Kern des Mathematikunterrichts ausmacht und alle anderen Inhaltsbereiche durch zieht. Algebraisches Denken bedeutet\, Muster zu erkunden und die ihnen zu grunde liegenden Strukturen zu verstehen. \;

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Im Vortrag wird z unächst eine Charakterisierung des algebraischen Denkens und eine damit v erbundene Differenzierung der Begriffe Muster und Strukturen grundgelegt. Anschließend werden zwei Studien vorgestellt\, in der Verallgemeinerungsp rozesse von Grundschulkindern aus epistemologischer Perspektive betrachtet werden.

\n

Der Vortrag findet statt am
Mittwoch\, den 24.05.2023 um 17:15 Uhr im Raum W01 0-006

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Interessierte s ind herzlich eingeladen.

LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-svetlana-gurevich-1 DTSTAMP:20240129T092620Z DTSTART:20230517T151500Z DTEND:20230517T164500Z SUMMARY:Vortrag: Svetlana Gurevich DESCRIPTION:Titel: „Towards conservative solitons and reversibility in t ime delayed systems”\nAbstract: Delayed interactions are a ubiquitous fe ature of many real-world systems and the time lags become important in sit uations where distant\, point-wise\, nonlinear nodes exchange information propagating at a finite speed or possess finite reaction times. Nonlinear time-delay systems (TDSs) not only pose a fundamental challenge for theore tical studies but are of crucial importance for applications ranging from traffic flow dynamics and economy to active matter systems and laser physi cs\, to name just a few. Furthermore\, external time-delayed feedback cont rol loops have proven to be an efficient tool for an effective non-invasiv e stabilization of unstable dynamical states. However\, in physics\, TDSs mostly have been limited to the study of dissipative dynamics. Recently an example of a photonic system modeled by a nonlinear\, time-reversible\, c onservative time-delayed system has been shown. In this talk we start with a basic review of TDSs and then review our recent theoretical results reg arding the existence of reversible conservative TDSs considering a dispers ive microcavity containing a Kerr medium coupled to a distant external mir ror. In the long delay limit\, the normal form identifies with the nonline ar Schrödinger equation\, thereby allowing for bright and dark solitons a lthough the lack of integrability can be observed at high energies. We unv eil some of the symmetries and conserved quantities and recover the Lugiat o-Lefever equation in the weakly dissipative regime.\nDer Vortrag findet s tatt am Mittwoch\, den 17.05.2023 um 17:15 Uhr im Raum W01 0-006\nInteress ierte sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Titel: „Towards conserv ative solitons and reversibility in time delayed systems”

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Abstract: Delayed interactions are a ubiquitous feature of many real-world systems and the time lags become important in situations where distant\, point-wise\, nonlinear nodes exchange information propagating a t a finite speed or possess finite reaction times. Nonlinear time-delay sy stems (TDSs) not only pose a fundamental challenge for theoretical studies but are of crucial importance for applications ranging from traffic flow dynamics and economy to active matter systems and laser physics\, to name just a few. Furthermore\, external time-delayed feedback control loops hav e proven to be an efficient tool for an effective non-invasive stabilizati on of unstable dynamical states. However\, in physics\, TDSs mostly have b een limited to the study of dissipative dynamics. Recently an example of a photonic system modeled by a nonlinear\, time-reversible\, conservative t ime-delayed system has been shown.
In this talk we start with a basi c review of TDSs and then review our recent theoretical results regarding the existence of reversible conservative TDSs considering a dispersive mic rocavity containing a Kerr medium coupled to a distant external mirror. In the long delay limit\, the normal form identifies with the nonlinear Schr ödinger equation\, thereby allowing for bright and dark solitons although the lack of integrability can be observed at high energies. We unveil som e of the symmetries and conserved quantities and recover the Lugiato-Lefev er equation in the weakly dissipative regime.

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Der Vortrag findet s tatt am
Mittwoch\, den 17.05.2023 um 17:15 Uhr im Raum W01 0 -006

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LOCATION:W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-kai-siedenburg-1 DTSTAMP:20240129T092753Z DTSTART:20230125T161500Z SUMMARY:Vortrag: Kai Siedenburg DESCRIPTION:Since at least Pythagoras\, mathematics has shaped reasoning a bout the scientific basis of music. In this talk\, I will first discuss se lected examples of the music-math connection\, focusing on theories of mus ical scales\, consonance\, and timbre (tone quality). Among a review of ex amples on the formation of musical scales\, I will explain how recent rese arch on music perception has demonstrated nconsistencies of classic mathem atical theories of musical scales and consonance. I will make a case for f ully implemented models of auditory perception as critical tools for under standing music perception. Finally\, I will provide illustrations from my own work on the auditory modeling of the perception of timbre and pitch.\n Der Vortrag findet statt am Mittwoch\, den 25.01.2023 um 17.15 Uhr im Raum W01 0-006\nInteressierte sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Since at least Pythagoras\, mathematics ha s shaped reasoning about the scientific basis of music. In this talk\, I w ill first discuss selected examples of the music-math connection\, focusin g on theories of musical scales\, consonance\, and timbre (tone quality). Among a review of examples on the formation of musical scales\, I will exp lain how recent research on music perception has demonstrated nconsistenci es of classic mathematical theories of musical scales and consonance. I wi ll make a case for fully implemented models of auditory perception as crit ical tools for understanding music perception. Finally\, I will provide il lustrations from my own work on the auditory modeling of the perception of timbre and pitch.

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Der Vortrag findet statt am
Mittw och\, den 25.01.2023 um 17.15 Uhr im Raum W01 0-006

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LOCATION:W1 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-kolloquiumsvortrag-von-herrn-michael-j-jacobson-jr-1 DTSTAMP:20240129T092734Z DTSTART:20221130T160000Z DTEND:20221130T170000Z SUMMARY:Vortrag: Michael J. Jacobson Jr. DESCRIPTION:Titel: "Unconditional Class Group Computation and Applications "\n Abstract: Class groups of number fields have been studied since the ti me of Gauss\, and in modern times have been used in applications such as i nteger factorization and public-key cryptography. Computing class groups a nd a system of fundamental units is a challenging problem for classical co mputers\, for which no polynomial time algorithm is currently known. In ad dition\, the fastest-known algorithm for computing these invariants has th e shortcoming that the output is only correct under the assumption of the generalized Riemann hypothesis. This is fine for some cryptographic applic ations\, but in computational number theory applications such as tabulatin g class groups for testing unproved conjectures and solving Diophantine eq uations\, unconditional results are typically required. In this talk\, I w ill discuss some of the applications where unconditional results are requi red\, as well as recent results and on-going work on computing class group s and fundamental units unconditionally.\n Der Vortrag findet statt am Mit twoch\, den 30.11.2022 um 17.15 - 18.45 Uhr im Raum W01 0-006 Interessiert e sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Titel: "Unconditional Cla ss Group Computation and Applications"

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Abstract: Class groups of number fields have been studied since the time of G auss\, and in modern times have been used in applications such as integer factorization and public-key cryptography. Computing class groups and a sy stem of fundamental units is a challenging problem for classical computers \, for which no polynomial time algorithm is currently known. In addition\ , the fastest-known algorithm for computing these invariants has the short coming that the output is only correct under the assumption of the general ized Riemann hypothesis. This is fine for some cryptographic applications\ , but in computational number theory applications such as tabulating class groups for testing unproved conjectures and solving Diophantine equations \, unconditional results are typically required. In this talk\, I will dis cuss some of the applications where unconditional results are required\, a s well as recent results and on-going work on computing class groups and f undamental units unconditionally.

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Der Vortrag findet statt am
Mittwoch\, den 30.11.2022 um 17.15 - 18.45 Uhr im Raum W0 1 0-006
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LOCATION:W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-antrittsvorlesung-k-pankrashkin-g-junike-1 DTSTAMP:20240129T092831Z DTSTART:20220706T151500Z DTEND:20220706T164500Z SUMMARY:Antrittsvorlesung K. Pankrashkin+G. Junike DESCRIPTION: X-ALT-DESC;FMTTYPE=text/html: LOCATION:W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-antrittsvorlesung-m-wrobel-a-fruehbis-krueger-1 DTSTAMP:20240129T092852Z DTSTART:20220622T151500Z DTEND:20220622T164500Z SUMMARY:Antrittsvorlesung: M. Wrobel+A. Frühbis-Krüger DESCRIPTION: X-ALT-DESC;FMTTYPE=text/html: LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-vortrag-renate-scheidler-1 DTSTAMP:20240129T092916Z DTSTART:20220518T151500Z DTEND:20220518T164500Z SUMMARY:Vortrag: Renate Scheidler DESCRIPTION:Titel: "Die Ankeny-Artin-Chowla-Vermutung in echten und falsch en reell-quadratischen Ordnungen"  \nAbstract: Algebraische Zahlkörper u nd ihre Ordnungen (Unterringe) bilden einen Forschungsschwerpunkt in der Z ahlentheorie. Die einfachsten Beispiele sind die quadratischen Zahlordnung en\, die trotz ihrer relativ einfachen Struktur in vieler Hinsicht mysteri ös und Gegenstand einer Reihe bisher unbewiesener Vermutungen sind. Die s trukturellen und algebraischen Eigenschaften quadratischer Ordnungen sind grundsätzlich verschieden\, je nachdem\, ob sie Unterringe der rellen ode r lediglich der komplexen Zahlen sind. In einer unveröffentlichten Notiz aus dem Jahr 2014 machte der französische Zahlentheoretiker Henri Cohen d ie überraschende Beobachtung\, dass die Adjunktion eines Primideals an ei ne imaginär-quadratische Ordnung einen Zahlring bildet\, der genau die Ch arakteristiken einer reell-quadratischen Ordnung aufweist. Cohen bezeichte diese Ringe als "fake real quadratic orders"\, also als falsche (im Gegen satz zu echten) reell- quadratischen Ordnungen. Damit stellt sich die natü rliche Frage\, welche der oben angesprochenen Vermutungen auch auf falsche rell-quadratischen Ordungen zutreffen. Die Fundamentaleinheiten reell-qua dratischer Ordnungen von Primzahldiskriminantengeht sind Gegenstand einer solchen\, relativ umstrittenen Vermutung\, die auf Ankeny-Artin-Chowla zur ückgeht. In diesem Vortrag\, der lediglich Algebra-Grundkenntnisse voraus setzt\, stellen wir eine Version dieser Vermutung in falschen reell-quadra tischen Ordnungen vor und berichten über die Ergebnisse unserer sehr umfa ngreichen numerischen Berechnungen\, Diese Arbeit wurde gemeinsam mit mein em Kollegen Mike Jacobson und unserer ehemaligen Masters-Studentin Hongyan Wang an der Universität Calgary in Kanada durchgeführt. Der Vortrag fin det statt am Mittwoch\, den 18.05.2022 um 17.15 Uhr im Raum W01 0-006 Inte ressierte sind herzlich eingeladen. X-ALT-DESC;FMTTYPE=text/html:

Titel: "Die Ankeny-Artin-Chowla-Ve rmutung in echten und falschen reell-quadratischen Ordnungen"
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Abstract: Algebraische Zahlkörper und ihre Ordnungen (Unterringe) bilden einen Forschungsschwerpunkt in der Zah lentheorie. Die einfachsten Beispiele sind die quadratischen Zahlordnungen \, die trotz ihrer relativ einfachen Struktur in vieler Hinsicht mysteriö s und Gegenstand einer Reihe bisher unbewiesener Vermutungen sind. Die str ukturellen und algebraischen Eigenschaften quadratischer Ordnungen sind gr undsätzlich verschieden\, je nachdem\, ob sie Unterringe der rellen oder lediglich der komplexen Zahlen sind. In einer unveröffentlichten Notiz au s dem Jahr 2014 machte der französische Zahlentheoretiker Henri Cohen die überraschende Beobachtung\, dass die Adjunktion eines Primideals an eine imaginär-quadratische Ordnung einen Zahlring bildet\, der genau die Char akteristiken einer reell-quadratischen Ordnung aufweist. Cohen bezeichte d iese Ringe als "fake real quadratic orders"\, also als falsche (im Gegensa tz zu echten) reell- quadratischen Ordnungen. Damit stellt sich die natür liche Frage\, welche der oben angesprochenen Vermutungen auch auf falsche rell-quadratischen Ordungen zutreffen. Die Fundamentaleinheiten reell-quad ratischer Ordnungen von Primzahldiskriminantengeht sind Gegenstand einer s olchen\, relativ umstrittenen Vermutung\, die auf Ankeny-Artin-Chowla zurü ckgeht. In diesem Vortrag\, der lediglich Algebra-Grundkenntnisse vorausse tzt\, stellen wir eine Version dieser Vermutung in falschen reell-quadrati schen Ordnungen vor und berichten über die Ergebnisse unserer sehr umfang reichen numerischen Berechnungen\, Diese Arbeit wurde gemeinsam mit meinem Kollegen Mike Jacobson und unserer ehemaligen Masters-Studentin Hongyan W ang an der Universität Calgary in Kanada durchgeführt.
Der Vortrag findet statt am
Mittwoch\, den 18.05.2022 um 17.15 Uhr im R aum W01 0-006
Interessierte sind herzlich eingeladen.

LOCATION:W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-institutspreisverleihung-der-jahrgangsbesten-1 DTSTAMP:20240129T092938Z DTSTART:20220504T151500Z DTEND:20220504T164500Z SUMMARY:Institutspreisverleihung der Jahrgangsbesten DESCRIPTION: X-ALT-DESC;FMTTYPE=text/html: LOCATION:W01 0-006 END:VEVENT BEGIN:VEVENT UID:calendarize-habilitationsvortrag-von-herrn-schober-1 DTSTAMP:20240129T093006Z DTSTART:20220420T151500Z DTEND:20220420T164500Z SUMMARY:Habilitationsvortrag von Herrn Schober DESCRIPTION: X-ALT-DESC;FMTTYPE=text/html: LOCATION:W01 0-006 END:VEVENT END:VCALENDAR