übe
r
Abstract: We investigate the spectrum of the first-or
der operator that governs the propagation
of electromagnetic waves in
the case of a closed locally perturbed waveguide filled with a
hyper
bolic medium. The perturbation is localized on the boundary and we impose<
br />homogeneous Dirichlet boundary conditions.
From a physics perspe
ctive\, this type of medium falls within the class of hyperbolic
elec
tromagnetic metamaterials. They are artificial media which exhibit a lot o
f interesting and
promising physics phenomena such as negative refrac
tion\, rainbow-trapping and enhanced
spontaneous emission.
In pr
actice\, the simplest mathematical model stems from electromagnetic wave p
ropagation in
a strongly magnetized cold plasma. It is described by 2
D Maxwell equations which\, in their
time-harmonic form\, may be redu
ced to the Klein-Gordon equation for a certain range of
frequencies\,
namely the hyperbolic frequencies. Hence\, the nature of the problem is p
urely
hyperbolic.
Firstly\, we prove a limiting absorption princ
iple (LAP) for the hyperbolic frequencies satisfying
a geometric cond
ition on the perturbation. The latter is related to the interplay between
the
velocities of the boundary and of the propagating waves\, which\,
in our case\, depends on the
frequency. This range of frequency is c
alled the subsonic regime. The key idea of our work is
the use of the
well-posedness and energy estimates of the Klein-Gordon equation in bound
ed
time-dependent domains.
The second part of the talk will be d
evoted to the 'supersonic' regime: the frequencies for which
the boun
dary moves faster than the waves. In particular\, the Klein-Gordon equatio
n in arbitrary
time-dependent domains is no longer well-posed for hom
ogeneous Dirichlet boundary
conditions. Nevertheless\, we are still a
ble to prove a LAP by using the weak observability
results of waves a
nd exchanging the role of the time and space variables.
\;
Interessierte sind herzlich eingeladen.
\;
\nIm Rahmen des Oberseminars Analysis/Numerik spricht\n
\;
\nüber
\n\;
\n\;
\nAbstract: \;One of the most fundamental principles used in theoretical physics is the sta tionary action principle. It states that the classical solutions of a phys ical system are the stationary solutions of an action functional\, defined on its phase space. This leads to the Euler-Lagrange equations by applyin g variational calculus\, in a straightforward calculation. A more difficul t question is the so-called inverse problem of variational calculus: given a set of differential equations\, 1. do these equations arise from variat ion of an action\, 2. how to find the action? Both questions can be answer ed by the method of variational completion\, and calculating the so-called Vainberg-Tonti Lagrangian. However\, this classical method is dependent o n the choice of coordinates\, and requires certain conditions on the domai n of definition of the system. In my talk\, I present the proper geometric framework for the Lagrange formalism and the inverse problem in terms of jet bundles\, at a beginner level. Then I show how the classical Vainberg- Tonti procedure can be generalized in a coordinate-independent fashion.&nb sp\;
\n\;
\nDer Vortrag findet statt am
\n\;
\nDonnerstag\, den 30.04.2026
um 14.30
– 15.30 Uhr im Raum W01 1-117
&nbs p\;
\n\;
\nIntere ssierte sind herzlich eingeladen.
\n\;
LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-stochastic-completeness-and-the-calabi-yau-conjectures DTSTAMP:20260422T091345Z DTSTART:20260423T131500Z DTEND:20260423T140000Z SUMMARY:Stochastic completeness and the Calabi-Yau conjectures DESCRIPTION:Vortragsankündigung\nIm Rahmen des Oberseminars Analysis/Nume rik sprichtHerr Dr. Giuseppe Gentile\nüber\nStochastic completeness and t he Calabi-Yau conjectures\nAbstract: In this talk I will present recent de velopments on the geometric properties of minimalsubmanifolds and harmonic maps\, motivated by the classical Calabi-Yau conjectures. Theseconjecture s predict that minimal hypersurfaces in Euclidean space\, as well as certa in of theirprojections\, must be unbounded. While striking counterexamples show that the conjectures failin general for immersed surfaces\, they rem ain true under additional geometric assumptions. Iwill explain how stochas tic completeness\, viewed as a weak maximum principle for noncompact manif olds\, together with a flexible notion of convexity (pullvexity)\, can be used torecover such unboundedness results. This is joint work with Renan A ssimos and BalázsBékési.\nDer Vortrag findet statt amDonnerstag\, den 2 3.04.2026um 15.15 – 16.00 Uhr im Raum W01 1-117\nInteressierte sind herz lich eingeladen. X-ALT-DESC;FMTTYPE=text/html:über
\n
Abstract: In this talk I will present recent developments on the ge
ometric properties of minimal
submanifolds and harmonic maps\, motiva
ted by the classical Calabi-Yau conjectures. These
conjectures predic
t that minimal hypersurfaces in Euclidean space\, as well as certain of th
eir
projections\, must be unbounded. While striking counterexamples s
how that the conjectures fail
in general for immersed surfaces\, they
remain true under additional geometric assumptions. I
will explain h
ow stochastic completeness\, viewed as a weak maximum principle for noncom
pact manifolds\, together with a flexible notion of convexity (pullvexity)
\, can be used to
recover such unboundedness results. This is joint w
ork with Renan Assimos and Balázs
Békési.
Der Vortrag findet statt am
Donnerstag\, den 23.04.
2026
um 15.15 – 16.00 Uhr im Raum W01 1-117
Interessierte sind herzlich eingeladen.
Vortragsankündigung
\n\;
\nIm Rahmen des Oberseminars A nalysis/Numerik spricht
\nHerr Dr. Alexey Ryabov
\n(ICBM\, Universität Oldenburg)
\nüber< /p>\n
\;
\nAbstract: In this presentation\, I will discu ss a critical problem in ecological modeling\, which I
\nrefer to here as the "modelers' t ragedy". This challenge arises because to model ecological
\nsystems we have to rely on in complete functional relationships\, usually obtained in laboratory< /p>\n
conditions. These rel ationships often cover only a few factors\, failing to represent the natur e
\ncomplexity a nd omitting factors for which there is insufficient data. It's like puttin g together a
\np uzzle with missing pieces - a real tragedy. Even when we carefully fit par ameters enabling
\nmodels to predict dynamics over a given period\, doubts remain about th e accuracy of the model
\nin reflecting true internal processes and its future predictive power.
\nTo solv e this problem\, we propose a new approach: "nonparametric population dyna mic
\nmodeling". This method abandons predefined functional relationships by extracting th is
\ninformation directly from field data. We combine dynamic modeling with a machine lear ning
\ntechnique known as parameter regularization\, aiming to identify the simplest model s that best
\nge neralize the data.
\n\;
\nOur process begins with fitting a baseline model to a time series of species abundance\,
\nassuming e.g. constant birth and death rates. We then determine the minimum parameter
\ndeviations needed at each time poi nt of observation (e.g.\, annually) to accurately reflect
\npopulation dynamics. By analyz ing how these parameter deviations relate to environmental
\nfactors\, we determine enviro nmental effects on population growth and loss rates.
\nWe demonstrate this method using th e example of Antarctic krill\, a key species in the
\nSouthern Ocean's fishery and food we b. Our approach determines how variables such as
\ntemperature\, food availability\, and i ce cover affect krill population losses throughout the year
\nand at different life stages . Ultimately\, we show how these findings can be incorporated into a
\nstatistical dynamic model that describes the population dynamics of Antarctic krill.\n
1. A. Ryabov\, U. Berg er\, B. Blasius\, B. Meyer\, Driving forces of Antarctic krill abundance.< /span>
\nScience Advanc es 9\, eadh4584 (2023). https://www.science.org/doi/10.1126/sciadv.adh4584
\n\;
\nFakultät V
&nbs p\;
\nMathematik und Na turwissenschaften
\n\;
\nDer Vortrag findet statt a m
\n\;
\nInteressierte sind herzlich eingeladen. \;
\;
\;
\nIm Rahmen des Oberseminars Analysis/Numerik spricht
\nFrau Prof. Dr. Anna Siffert
\n(Universität Münster )
\nüber
\nAbstract:
In this talk we present\, \;a construction method of r-harmonic maps
to spheres.
We in particular construct an explicit family of stable p
roper weak biharmonic maps from the
unit ball.
This is joint wor
k with Volker Branding.
Der Vortrag fin det statt am
\nDonnerstag\, den 16.04.20 26 um 14.30 – 15.30 Uhr im Raum W01 1-117
\nInteressierte sind herzlich eingeladen.
\n\;
LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-homological-indices-and-local-riemann-roch-type-theorems DTSTAMP:20260408T144005Z DTSTART:20260414T121500Z DTEND:20260414T134500Z SUMMARY:Homological indices and local Riemann-Roch type theorems DESCRIPTION:Vortragsankündigung\nIm Rahmen des Oberseminars Algebra/Geome trie spricht \nHerr Dr. Matthias Zach (Uni Kaiserslautern)\nüber\nHomolo gical indices and local Riemann-Roch type theorems\nA homological index is the Euler characteristic of a complex of coherent sheaves with finite sup port. Local Riemann-Roch type theorems relate them to intersection numbers and Chern classes\, i.e. objects of topological nature. In complex analyt ic singularity theory we can thus use such theorems to compute topological invariants by algebraic methods. I will report on the toolbox in the comp uter algebra system OSCAR which we have made available to this end\, from Gröbner bases building on Singular's core functionality up to the W-funct or for the computation of direct images for the ``derived homological inde x''.\n \nDienstag 14.04.2026 um 14:15 UhrRaum W01 0-015 \n \nInteressie rte sind herzlich eingeladen X-ALT-DESC;FMTTYPE=text/html:ü ber
\nA homologica l index is the Euler characteristic of a complex of coherent sheaves with finite support. Local Riemann-Roch type theorems relate them to intersecti on numbers and Chern classes\, i.e. objects of topological nature. In comp lex analytic singularity theory we can thus use such theorems to compute t opological invariants by algebraic methods. I will report on the toolbox i n the computer algebra system OSCAR which we have made available to this e nd\, from Gröbner bases building on Singular's core functionality up to t he W-functor for the computation of direct images for the ``derived homological index''.
\n\;
\n< p class="text-center">Dienstag 14.04.2026 um 14:15 Uhr\;
\nIm Rahmen des Oberseminars Algebra
/Geometrie spricht
\;
Dienstag 11.11.2025 u
m 12:30 s.t.
im W02 1-148
Abstract: We start with the st
atement of Faltings' Theorem\, which says that an
algebraic curve of
genus at least 2 has finitely many rational points. Concretely\, this
says that for a sufficiently generic polynomial
f(x\,y) with rationa
l coefficients of degree at least 5\, there are finitely many rational pai
rs
(x\,y) in Q^2 such that f(x\,y)=0.
The question of provably d
etermining that finite set for a given f (i.e.\, for a given curve)
i
s still wide open. I discuss one approach to this question\, involving act
ions of Galois
groups on (quotients of) the topological fundamental g
roup of the curve in question. If
time permits\, we discuss the appro
ach of Chabauty and Kim that combines this with p-
adic analysis to p
roduce a possibly effective way to bound the set of rational points on
a given curve. This approach is the basis for my current work with Marti
n Lüdtke of
Oldenburg.
Interessier
te sind herzlich eingeladen.