\n
As part of the Advanced Seminar on Analysis and Numerics\,
\n\n
\n
Abstract
\n
The key idea is to locally transform the Dira c operator under general boundary conditions on a conical domain near the singularities into a perturbed Dirac operator under MIT boundary condition s on the model cones. This process introduces a perturbation that can be d ealt with using the Kato–Rellich theorem. In the model case\, the theory relies heavily on the separation ansatz and a spectral gap on the link of the cone\, which ultimately ensures self-adjointness and regularity."
\n\n
As part of the advanced seminar Analysis/Nume rics
\nab out
\nAbstract: The uncertainty principle in harmonic analysis st
ates that a non-zero function and
its Fourier transform cannot be sim
ultaneously too sharply localised. There are numerous
precise mathema
tical formulations of this meta-theorem.
The talk is based on collaborative work with Lenny Neyt (Univer
sity of Vienna).
The t
alk will take place on Thursday\, 18 June 2026
at 14:30 - 15:30 in ro
om W01 1-117
\n
LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-affine-chabauty DTSTAMP:20260609T134005Z DTSTART:20260616T170000Z SUMMARY:Affine Chabauty DESCRIPTION:Lecture announcement\nIn the context of the advanced seminar A lgebra\nMr Martin Lüdtke\n(University of Oldenburg)\nTitle: Affine Chabau ty\n \nAbstract: Given a hyperbolic curve Y defined over the integers and a finite set of primes S\, the theorems of Siegel\, Mahler\, and Faltings guarantee that the set of S-integral points Y(Z_S) is finite.\nDetermining this set in practice is a difficult problem for which no general method i s known. In the case of projective curves\, Chabauty's method can often be used to produce a finite subset of the p-adic points containing the ratio nal points. I present a Chabauty method for affine curves based on embedd ing the curve in its generalised Jacobian and constraining the image of th e S-integral points via arithmetic intersection theory. This is joint work with M. Leonhardt.\n \nThe lecture will take place on\n \nTuesday\, 16 Ju ne 2026at 17:00 in room W01 0-006\n \n \nInterested parties are cordially invited. X-ALT-DESC;FMTTYPE=text/html:
In the context of the advanced s eminar Algebra
\n(University of Oldenburg)
\n\n< p class="text-center">Abstract: Given a hyperbolic curve Y defined over the integers and a finite set of primes S\, the theorems of Siegel\, Mahler\, and Faltings guarantee tha t the set of S-integral points Y(Z_S) is finite.\n
Determining this set in practice is a difficult problem for which no general method is known. In the case of projective curves\, Chabauty's method can often be used to produce a finit e subset of the p-adic points containing the rational points. I present a Chabauty method for affine curves based on embedding the curve in its gen eralised Jacobian and constraining the image of the S-integral points via arithmetic intersection theory. This is joint work with M. Leonhard t.
\n\n
The lecture w ill take place on
\n\n
Tuesday\, 16 June 2026
at 17:00 in room W01 0-006<
/p>\n
\n
\n
Inter ested parties are cordially invited.
LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-generic-homogeneous-polynomial-mappings-of-c4-to-c4-and-th eir-singularities DTSTAMP:20260609T135138Z DTSTART:20260616T160000Z SUMMARY:GENERIC HOMOGENEOUS POLYNOMIAL MAPPINGS OF C4 TO C4 AND THEIR SING ULARITIES DESCRIPTION:Lecture announcement\nAs part of the advanced seminar Algebra\ n \nDr Joao Pissolato\n(Sao Carlos)\n \n \nThe lecture will take place on\ nTuesday\, 16 June 2026at 16:00 in room W01 0-006\nInterested parties are cordially invited. X-ALT-DESC;FMTTYPE=text/html:As part of the advanced seminar Algebra
\n\n
\n
<
br />
The lecture will take place on
\nTuesday\, 16 June 2026
at 16:00 in room W
01 0-006
Interested parties are cordi ally invited.
LOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-finsler-spacetime-geometry-and-the-gravitational-field-of- kinetic-gases DTSTAMP:20260528T110930Z DTSTART:20260611T143000Z DTEND:20260611T153000Z SUMMARY:Finsler spacetime geometry and the gravitational field of kinetic gases DESCRIPTION:Lecture announcement\n \nAs part of the advanced seminar Analy sis/Numerics\nDr Christian Pfeifer\n(ZARM\, University of Bremen)\nabout\n Finsler spacetime geometry and the gravitational field of kinetic gases\n \nAbstract: Pseudo-Finsler manifolds generalise pseudo-Riemannian manifold s in a straightforward manner. The geometry of a Finslerian manifold is de rived from a general pseudo-norm\, analogously to how the geometry of pseu do-Riemannian manifolds is derived from a metric tensor. In physics\, pseu do-Finsler geometry is a viable and highly interesting candidate for an ex tended geometry of spacetime that can provide an improved description of g ravitational interaction beyond general relativity\, potentially offering a geometric understanding of dark matter and dark energy. From a mathemati cal perspective the study of pseudo-Finsler geometry offers\, among others \, interesting applications to optimisation problems\, inequalities or the question of metrizabillity of affine connections.\nIn this talk\, I will discuss the Finsler gravity framework as extension of general relativity\, and demonstrate that in homogeneous and isotropic symmetry\, the Finsler gravity equation possesses solutions that describe an accelerated expandin g universe\, without the need of a cosmological constant or any other addi tional fields. I will introduce the concept of Finsler spacetimes and thei r classification according to their deviation from pseudoRiemannian geomet ry. Afterwards I will focus on the Finsler gravity equation\, the coupling between Finsler geometry and the kinetic gas\, and how the Finsler gravit y equation takes a Friedmann equation like form in homogeneous and isotrop ic symmetry. Finally we will see that this Finsler Friedmann equation allo ws for vacuum solutions that describe an exponentially expanding universe\ , which is a first direct indication that Finsler spacetimes are capable t o address the nature of dark energy. \n \nThe lecture will take place on\n Thursday\, 11 June 2026 at 14:30 - 15:30 in room W01 1-117\nInterested par ties are cordially invited. X-ALT-DESC;FMTTYPE=text/html:\n
As part of the advanced seminar Analysis/Numerics
\nabout
\n\n
Abstract: Pseudo-Finsler manifolds generalise pseudo-Riemannian manifolds in a stra ightforward manner. The geometry of a Finslerian manifold is derived from a general pseudo-norm\, analogously to how the geometry of pseudo-Riemanni an manifolds is derived from a metric tensor. In physics\, pseudo-Finsler geometry is a viable and highly interesting candidate for an extended geom etry of spacetime that can provide an improved description of gravitationa l interaction beyond general relativity\, potentially offering a geometric understanding of dark matter and dark energy. From a mathematical perspec tive the study of pseudo-Finsler geometry offers\, among others\, interest ing applications to optimisation problems\, inequalities or the question o f metrizabillity of affine connections.
\nIn this talk\, I will discuss the Finsler gravit y framework as extension of general relativity\, and demonstrate that in h omogeneous and isotropic symmetry\, the Finsler gravity equation possesses solutions that describe an accelerated expanding universe\, without the n eed of a cosmological constant or any other additional fields. I will intr oduce the concept of Finsler spacetimes and their classification according to their deviation from pseudoRiemannian geometry. Afterwards I will focu s on the Finsler gravity equation\, the coupling between Finsler geometry and the kinetic gas\, and how the Finsler gravity equation takes a Friedma nn equation like form in homogeneous and isotropic symmetry. Finally we wi ll see that this Finsler Friedmann equation allows for vacuum solutions th at describe an exponentially expanding universe\, which is a first direct indication that Finsler spacetimes are capable to address the nature of da rk energy.
\n\n
The lecture will take place on
\nThursday\, 11 June 20 26 at 14:30 - 15:30 in room W01 1-117
\nInterested parties are cordially
invited.
\n
As part of the advanced seminar Analysis/Numerics
\nabout
\n\n
Abstract: In this talk\ , we study the spectral properties of manifolds with singularities obtaine d as quotients of the hyperbolic upper half-plane by Hecke triangle groups . These manifolds are geometrically complicated (they may have infinite vo lume and up to two types of singularities)\, but simple from the perspecti ve of the fundamental group (having only two generators and one relation). To study their spectral properties\, we consider the associated Selberg z eta functions\, whose zeros correspond to resonances of the surfaces. We s how that the Selberg zeta function can be approximated by determinants of finite matrices throughout its domain of holomorphy. For certain manifolds \, such approximations allow to compute the base eigenvalues of the Laplac e operators to 50-digit precision within 5 seconds using interval arithmet ic. Additionally\, we investigate the location of non-real resonances and observe that\, for large funnel widths\, they appear to organize into reso nance chains almost satisfying functional equations involving the Riemann zeta function.
\n\n
Interested parties are cordially invited.
a
bout
Abstract: We investigate the spectrum of the first
-order operator that governs the propagation
of electromagnetic waves
in the case of a closed locally perturbed waveguide filled with a
hy
perbolic medium. The perturbation is localized on the boundary and we impo
se
homogeneous Dirichlet boundary conditions.
From a physics per
spective\, this type of medium falls within the class of hyperbolic
e
lectromagnetic metamaterials. They are artificial media which exhibit a lo
t of interesting and
promising physics phenomena such as negative ref
raction\, rainbow-trapping and enhanced
spontaneous emission.
In
practice\, the simplest mathematical model stems from electromagnetic wav
e propagation in
a strongly magnetized cold plasma. It is described b
y 2D Maxwell equations which\, in their
time-harmonic form\, may be r
educed to the Klein-Gordon equation for a certain range of
frequencie
s\, namely the hyperbolic frequencies. Hence\, the nature of the problem i
s purely
hyperbolic.
Firstly\, we prove a limiting absorption pr
inciple (LAP) for the hyperbolic frequencies satisfying
a geometric c
ondition on the perturbation. The latter is related to the interplay betwe
en the
velocities of the boundary and of the propagating waves\, whic
h\, in our case\, depends on the
frequency. This range of frequency i
s called 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 bo
unded
time-dependent domains.
The second part of the talk will b
e devoted to the 'supersonic' regime: the frequencies for which
the b
oundary moves faster than the waves. In particular\, the Klein-Gordon equa
tion in arbitrary
time-dependent domains is no longer well-posed for
homogeneous Dirichlet boundary
conditions. Nevertheless\, we are stil
l able to prove a LAP by using the weak observability
results of wave
s and exchanging the role of the time and space variables.
Interested parties are cordially invited.
\n
As part of the advanced seminar Analysis/Numerics
\n\n
about< /span>
\n\n
\n
Abstract: One of the most fundamental principles used in theoretical physics is the stationary action principle. It states that the classical solutions of a physical system are the stationary solu tions of an action functional\, defined on its phase space. This leads to the Euler-Lagrange equations by applying variational calculus\, in a strai ghtforward calculation. A more difficult question is the so-called inverse problem of variational calculus: given a set of differential equations\, 1. do these equations arise from variation of an action\, 2. how to find t he action? Both questions can be answered by the method of variational com pletion\, and calculating the so-called Vainberg-Tonti Lagrangian. However \, this classical method is dependent on the choice of coordinates\, and r equires certain conditions on the domain of definition of the system. In m y talk\, I present the proper geometric framework for the Lagrange formali sm and the inverse problem in terms of jet bundles\, at a beginner level. Then I show how the classical Vainberg-Tonti procedure can be generalised in a coordinate-independent fashion.
\n\n
The lecture will take place on
\n\n
Thursday\, 30.04.
2026
at 14.30 - 15.30 in room W01 1-117
\n
\n
Intere sted parties are cordially invited.
\nLOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-stochastic-completeness-and-the-calabi-yau-conjectures DTSTAMP:20260422T091345Z DTSTART:20260423T151500Z DTEND:20260423T160000Z SUMMARY:Stochastic completeness and the Calabi-Yau conjectures DESCRIPTION:Lecture announcement\nAs part of the advanced seminar Analysis /Numerics\,Dr Giuseppe Gentile will speak\nabout\nStochastic completeness and the Calabi-Yau conjectures\nAbstract: In this talk I will present rece nt developments on the geometric properties of minimalsubmanifolds and har monic maps\, motivated by the classical Calabi-Yau conjectures. Theseconje ctures predict that minimal hypersurfaces in Euclidean space\, as well as certain of theirprojections\, must be unbounded. While striking counterexa mples show that the conjectures failin general for immersed surfaces\, the y remain true under additional geometric assumptions. Iwill explain how st ochastic completeness\, viewed as a weak maximum principle for noncompact manifolds\, together with a flexible notion of convexity (pullvexity)\, ca n be used torecover such unboundedness results. This is joint work with Re nan Assimos and BalázsBékési.\nThe lecture will take place onThursday\, 23.04.2026at 15.15 - 16.00 in room W01 1-117\nInterested parties are cord ially invited. X-ALT-DESC;FMTTYPE=text/html:
about
\n
Abstract: In this talk I will present recent developments on t
he geometric properties of minimal
submanifolds and harmonic maps\, m
otivated by the classical Calabi-Yau conjectures. These
conjectures p
redict that minimal hypersurfaces in Euclidean space\, as well as certain
of their
projections\, must be unbounded. While striking counterexamp
les show that the conjectures fail
in general for immersed surfaces\,
they remain true under additional geometric assumptions. I
will expl
ain how stochastic completeness\, viewed as a weak maximum principle for n
oncompact manifolds\, together with a flexible notion of convexity (pullve
xity)\, can be used to
recover such unboundedness results. This is jo
int work with Renan Assimos and Balázs
Békési.
The lecture will take place on
Thursday\, 23.0
4.2026
at 15.15 - 16.00 in room W01 1-117
Interested parties are cordially invited.
Lecture announcement
\n\n
As part of the advanced seminar An alysis/Numerics
\nDr Alexey Ryabov
\n(ICBM\, University of Oldenburg)
\nabout
\n\n
Abstract: In this presentation\, I will discuss a critical probl em in ecological modelling\, which I
\nrefer to here as the "modelers' tragedy". This chal
lenge arises because to model ecological
systems we have to rely on incomplete functiona l relationships\, usually obtained in laboratory
\nconditions. These relationships often c over only a few factors\, failing to represent the nature
\ncomplexity and omitting factor s for which there is insufficient data. It's like putting together a
\npuzzle with missing pieces - a real tragedy. Even when we carefully fit parameters enabling
\nmodels to predi ct dynamics over a given period\, doubts remain about the accuracy of the model
\nin refle cting true internal processes and its future predictive power.
\ nTo solve this problem\, w e propose a new approach: "nonparametric population dynamic
\nmodelling". This method aban dons predefined functional relationships by extracting this
\ninformation directly from fi eld data. We combine dynamic modelling with a machine learning
\ ntechnique known as parame ter regularisation\, aiming to identify the simplest models that best gene ralize the
\ngen eralise the data.
\n\n
Our process begins with fitting a baseli ne 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 point of o bservation (e.g.\, annually) to accurately reflect
\npopulation dynamics. By analysing how these parameter deviations relate to environmental
\nfactors\, we determine environmental effects on population growth and loss rates.
\nWe demonstrate this method using the examp le of Antarctic krill\, a key species in the
\nSouthern Ocean's fishery and food web. Our approach determines how variables such as
\ntemperature\, food availability\, and ice cove r affect krill population losses throughout the year
\nand at different life stages. Ultim ately\, we show how these findings can be incorporated into a
\nstatistical dynamic model that describes the population dynamics of Antarctic krill.
\n1 A. Ryabov\, U. Berger\, B. Blasius\, B. Meyer\, Driving forces of Antarctic krill abundance.\n
Science Advances 9\, e adh4584 (2023). https://www.science.org/doi/10.1126/sciadv.adh4584< /p>\n
\n
School V
\n\n
Mathematics and Natural Sciences< /p>\n
\n
The lecture will take place on
\nThursday\, 23.04.2026 a t 14.15 - 15.15 in room W01 1-117
\n\n
Interested part
ies are cordially invited.
\n
As part of the advanced seminar Analysis/Numerics
\n(University of Münster )
\nabout
\nAbs
tract: In this talk we present\,
a construction method of r-harmonic maps to spheres.
We in particular
construct an explicit family of stable proper weak biharmonic maps from t
he
unit ball.
This is joint work with Volker Branding.
The lecture will take place on
\nThursday\, 16.04.2026 at 14.30 - 15.30 in room W01 1-11 7
\nInterested parties are cordially in vited.
\nLOCATION: END:VEVENT BEGIN:VEVENT UID:calendarize-homological-indices-and-local-riemann-roch-type-theorems DTSTAMP:20260408T144005Z DTSTART:20260414T141500Z DTEND:20260414T154500Z SUMMARY:Homological indices and local Riemann-Roch type theorems DESCRIPTION:Lecture announcement\nIn the context of the advanced seminar A lgebra/Geometry \nDr Matthias Zach (University of Kaiserslautern)\nabout\n Homological indices and local Riemann-Roch type theorems\nA homological in dex is the Euler characteristic of a complex of coherent sheaves with fini te support. Local Riemann-Roch type theorems relate them to intersection n umbers and Chern classes\, i.e. objects of topological nature. In complex analytic singularity theory we can thus use such theorems to compute topol ogical invariants by algebraic methods. I will report on the toolbox in th e computer algebra system OSCAR which we have made available to this end\, from Gröbner bases building on Singular's core functionality up to the W -functor for the computation of direct images for the ``derived homologica l index''.\n \nTuesday 14.04.2026 at 14:15Room W01 0-015 \n \nInterested p arties are cordially invited X-ALT-DESC;FMTTYPE=text/html:
about
\nA homologi cal index is the Euler characteristic of a complex of coherent sheaves wit h finite support. Local Riemann-Roch type theorems relate them to intersec tion numbers and Chern classes\, i.e. objects of topological nature. In co mplex analytic singularity theory we can thus use such theorems to compute topological invariants by algebraic methods. I will report on the toolbox in the computer algebra system OSCAR which we have made available to this end\, from Gröbner bases building on Singular's core functionality up to the W-functor for the computation of direct images for t he ``derived homological index''.
\n\n
Tuesday 14.04.2026 at 14:15
Room W01 0-015
\n