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20. May
Mon W21
Mon, 20. May
21. May
Tue W21
Emiliano
Ambrosi
Strasbourg
Reduction modulo p of the Noether problem
Abstract.
Let k be an algebraically closed field of characteristic \( p\ge 0 \) and V a faithful k-rational representation of an \(l\)-group G. Noether's problem asks whether V/G is (stably) birational to a point. If \( l = p \), then Kuniyoshi proved that this is true, while for \( l\neq p \) Saltman constructed \(l\)-groups for which V/G is not stably rational. Hence, the geometry of V/G depends heavily on the characteristic of the field. We show that for all the groups G constructed by Saltman, one cannot interpolate between the Noether problem in characteristic 0 and p. More precisely, we show that there does not exist a complete valuation ring R of mixed characteristic (0,p) and a smooth proper R-scheme \( X \to \mathrm{Spec}(R) \) whose special fiber and generic fiber are both stably birational to V/G. The proof combines the integral p-adic Hodge theoretic results of Bhatt-Morrow-Scholze, with the study of the Cartier operator on differential forms in positive characteristic. This is a joint work with Domenico Valloni.
22. May
Wed W21
What is a spacetime and what is it good for?
Ruma
Maity
Uni Innsbruck
Finite element methods for the Landau-de Gennes minimization problem of nematic liquid crystals
Abstract.
Nematic liquid crystals represent a transitional state of matter between liquid and crystalline phases that combine the fluidity of liquids with the ordered structure of crystalline solids. These materials are widely utilized in various practical applications, such as display devices, sensors, thermometers, nanoparticle organizations, proteins, and cell membranes. In this talk, we discuss finite element approximation of the nonlinear elliptic partial differential equations associated with the Landau-de Gennes model for nematic liquid crystals. We establish the existence and local uniqueness of the discrete solutions, a priori error estimates, and a posteriori error estimates that steer the adaptive refinement process. Additionally, we explore Ball and Majumdar's modifications of the Landau-de Gennes Q-tensor model that enforces the physically realistic values of the Q tensor eigenvalues. We discuss some numerical experiments that corroborate the theoretical estimates, and adaptive mesh refinements that capture the defect points in nematic profiles.
Alexander
Suciu
Northeastern University
Alexandru
Suciu
Northeastern University
The Milnor fibrations of hyperplane arrangements
Abstract.
To each multi-arrangement \((A,m)\), there is an associated Milnor fibration of the complement \(M=M(A)\). Although the Betti numbers of the Milnor fiber \(F=F(A,m)\) can be expressed in terms of the jump loci for rank 1 local systems on \(M\), explicit formulas are still lacking in full generality, even for \(b_1(F)\). After introducing these notions and explaining some of the known results, I will consider the "generic" case, in which \(b_1(F)\) is as small as possible. I will describe ways to extract information on the cohomology jump loci, the lower central series quotients, and the Chen ranks of the fundamental group of the Milnor fiber in this situation.
Jürgen
Sprekels
WIAS
Necessary and sufficient optimality conditions in the sparse optimal control of
singular Allen--Cahn systems
with dynamic boundary conditions
Marian
Aprodu
University of Bucharest
Resonance, syzygies, and rank-3 Ulrich bundles on the del Pezzo threefold \(V_5\)
Abstract.
This is a joint work with Yeongrak Kim. We investigate a geometric criterion for a smooth curve of genus 14 and degree 18 to be described as the zero locus of a section in an Ulrich bundle of rank 3 on a del Pezzo threefold \(V_5\). The main challenge is to read off the Pfaffian quadrics defining \(V_5\) from geometric properties of the curve. We find that this problem is related to the existence of a special rank-two vector bundle on the curve, with trivial resonance. From an explicit calculation of the Betti table, we also deduce the uniqueness of the del Pezzo threefold.
Paul
Mücksch
Combinatorial models of fibrations for hyperplane arrangements and oriented matroids
Abstract.
The complement of an arrangement of hyperplanes in a complex vector space is a much studied interesting topological space. A fundamental problem is to decide when this space is aspherical, i.e. its universal covering space is contractible. For special classes of arrangements, such as the braid arrangements or more generally supersolvable arrangements, this can be achieved by utilizing fibrations which connect complements of arrangements of different rank. Another prominent space associated to an arrangement is its Milnor fiber -- the typical fiber of the evaluation map of the defining polynomial of the arrangement on its complement which is a smooth fibration by Milnor's famous result. This is a much more subtle topological invariant and it is still an open problem to understand its homology or even its first Betti number in conjunction with the combinatorial structure of the arrangement. I will present a new combinatorial approach to study such fibrations for arrangements which can be defined over the reals via oriented matroids. This is partly joint work with Masahiko Yoshinaga (Osaka University).
23. May
Thu W21
Ilia
Zharkov
KSU
Approximation of the diagonal and A-infinity structures on polytopes
Abstract.
Given a convex polytope P and a choice of a linear function on it one can define the multiplication on its cellular cochains by a cellular approximation of the diagonal in P^2. This is not associative (except for simplices and cubes) and gives rise to so called higher A-infinity products. I will describe a one-parameter family of permuto-associahedra based on a q-version of the Reiner-Ziegler realization. As q tends to zero, the family tends to the dual permutahedron. Restricted to a single permutation chamber, this inscribes the associahedron in the simplex similar to the Loday realization and allows one to give a geometric explanation of the A-infinity relations among the products. This is a part of a joint project with Gabe Kerr in the context of mirror symmetry. But in the talk we will restrict our attention to the combinatorics of the (fiber) polytopes.
24. May
Fri W21
Yan
Alves Radtke
Signotopes: Pseudoconfigurations and Extensions
Alessio
Figalli
ETH Zürich
Exploring Stability in Geometric and Functional Inequalities
Abstract.
In the realms of analysis and geometry, geometric and functional inequalities are of paramount significance, influencing a variety of problems. Traditionally, the focus has been on determining precise constants and identifying minimizers. More recently, there has been a growing interest in investigating the stability of these inequalities. The central question we aim to explore is: "If a function nearly achieves equality in a known functional inequality, can we demonstrate, in a quantitative way, its proximity to a minimizer?" In this talk I will overview this beautiful topic and discuss some recent results.
27. May
Mon W22
Michael
Zaks
Inst. of Physics, HU Berlin
Continua of equilibrium states in globally coupled ensembles
28. May
Tue W22
Andrea
Walther
HU Berlin
Backpropagation and Nonsmooth Optimization for Machine Learning
Abstract.
Backpropagation is the major workhorse for many machine learning algorithms. In this presentation, we will examine the theory behind backpropagation as provided by the technique of algorithmic differentiation. Subsequently, we will discuss how this classic derivative information can be used for nonsmooth optimization. Examples from reail will illustrate the application of the proposed nonsmooth optimization algorithm.
Paul
Ziegler
Darmstadt
p-adic integration on Artin stacks
Abstract.
After giving an introduction to the technique of p-adic integration, I will explain how this technique can be extended to Artin stacks, and give an application to BPS invariants. This is joint work with M. Groechenig and D. Wyss.
29. May
Wed W22
Tailen
Hsing
University of Michigan
Andreas
Vikelis
Faculty of Mathematics, University of Vienna, Austria
30. May
Thu W22
Lilla
Tothmeresz
ELTE
Relationships between the geometry of graph polytopes and graph structure
Abstract.
The symmetric edge polytope is a lattice polytope associated to a graph, that is actively investigated both because of its beautiful geometry, and because of its connections to the Kuramoto synchronization model of physics. One can also investigate „non-symmetric” edge polytopes, that are assigned to directed graphs instead of undirected ones. Moreover, one can even generalize them to regular (oriented) matroids. For these more general polytopes, many interesting geometric phenomena uncover themselves that are hidden for symmetric edge polytopes. We would like to demonstrate that the geometric properties of (graph and matroid) edge polytopes are connected to deep graph/matroid-theoretic properties. In particular, we show that the co-degree of an edge polytope is equal to the minimal cardinality of a dijoin. Other notions of combinatorial optimization also turn up naturally with respect to edge polytopes. In particular, for an Eulerian directed graph, complements of arborescences rooted at a given vertex give a (unimodular) triangulation of the edge polytope of the cographic matroid. This gives an alternative, geometric proof for the fact that an Eulerian digraph has the same number of arborescences for any choice of root vertex. I will also mention open problems. Based on joint work with Tamás Kálmán.
31. May
Fri W22
Anna
Wienhard
MPI Leipzig
Beyond hyperbolic geometry
04. June
Tue W23
Richard
Rimanyi
University of North Carolina
05. June
Wed W23
Jia-Jie
Zhu
WIAS Berlin
Data-Adaptive Discretization of Inverse Problems
Tristram
Bogart
Los Andes
Rene
Brandenberg
TU München
11. June
Tue W24
Marco
Flores
HU Berlin
12. June
Wed W24
Marc
Hallin
Université Libre de Bruxelles
Tristram
Bogart
Los Andes
13. June
Thu W24
Vladimir
Shikmann
Technische Universität Chemnitz
14. June
Fri W24
Heather
Harrington
MPI Dresden
19. June
Wed W25
A Soft-Correspondence Approach to Shape Analysis
Carl
Lian
Tufts University
Simon
Schmidt
Ruhr-Universität Bochum
25. June
Tue W26
Gari Yamel
Peralta Alvarez
HU Berlin
26. June
Wed W26
Clément
Berenfeld
Universität Potsdam
Martin
Ulirsch
27. June
Thu W26
Karel
Devriendt
MPI-MiS
28. June
Fri W26
María Ángeles
García Ferrero
Universitat de Barcelona
02. July
Tue W27
Remy
van Dobben de Bruyn
Utrecht
03. July
Wed W27
Celine
Duval
Université de Lille
Wasserstein Gradient Flows for Generalised Transport in Bayesian Inversion
Andreas
Vikelis
Faculty of Mathematics, University of Vienna, Austria
Measure-valued solutions for non-associative finite plasticity
Abstract
04. July
Thu W27
Eleonore
Bach
EPFL
05. July
Fri W27
Richard von Mises Lecture
10. July
Wed W28
Anya
Katsevich
MIT, Cambridge, MA
Does gender still matter? Perspectives of scientists in leadership position and early career researchers on academic careers in mathematics.
Caroline
Lasser
Fakultät für Mathematik, TU München
Variational Gaussian approximation for quantum dynamics
Abstract
11. July
Thu W28
Germain
Poullot
Uni Osnabrück
16. July
Tue W29
Jürg
Kramer
HU Berlin
17. July
Wed W29
Likelihood Geometry of Max-Linear Bayesian Networks
18. July
Thu W29
Adélie
Garin
EPFL
24. July
Wed W30
Emil
Wiedemann
Universität Erlangen-Nürnberg