Shelby
Cox
MPI MiS Leipzig
Weighted tropical Fermat-Weber points
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23. January
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24. January
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Julian
Marx
Beiträge zum Zählen von Bäumen auf Punktmengen
Ekin
Ergen
Online Makespan Scheduling Under Scenarios
Carla
Cederbaum
U Tübingen
Coordinates are messy in general (relativity)
28. January
Tue W04
Daniel
Roggenkamp
MiS Leipzig
Rozansky-Witten models as extended defect TQFTs
Abstract.
Very few examples of extended topological quantum field theories are known explicitly. In this talk I will discuss a very explicit construction of the extended TQFTs associated to Rozanksy-Witten models with affine target spaces. I will furthermore explain how to incorporate defects into the extended TQFTs. This can be used for instance to derive the Hilbert spaces of affine Rozansky-Witten models associated to surfaces with arbitrary insertions of defect networks.
Laurent
Coté
Bonn
Fukaya categories of conical symplectic resolutions
Abstract.
Conical symplectic resolutions are a rather loosely defined class of hyperkähler varieties arising from canonical constructions in representation theory. Important examples include hypertoric varieties, Nakajima quiver varieties and Hitchin spaces. Assuming as little background as possible in symplectic geometry, I will introduce a categorical invariant called the Fukaya category, which is defined using methods of global analysis. When specialized to conical symplectic resolutions, the Fukaya category turns out to be intimately related to a category of longstanding interest in geometric representation theory, called Category O. This talk will report on joint work with (subsets of) Benjamin Gammage, Justin Hilburn, Christopher Kuo, David Nadler and Vivek Shende.
29. January
Wed W04
Coherent Transport of Semiconductor Spin-Qubits: Modeling, Simulation and Optimal Control
Abstract
Helena
Kremp
TU/WIAS Berlin
Mihály
Kovács
PPKE ITK Budapest
30. January
Thu W04
Constantin
Ickstadt
Uni Frankfurt
Alexandros
Saplaouras
ETH Zürich
The Itô Integral for Nonlinear Lévy Processes: Insights into the G-Lévy Framework
Abstract.
Nonlinear Lévy processes, as established within the general framework by A. Neufeld and M. Nutz, offer a versatile foundation without restrictions on the characteristic triplets. Building on this foundational work, we focus specifically on G-Lévy processes, a concept introduced by S. Peng. Adopting Peng's approach, we construct the Itô integral with respect to G-Lévy processes and examine its associated properties. Alongside, we delve into results concerning the uniqueness of fully nonlinear integro-partial differential equations and briefly discuss the technical challenges.
Stefan
Weber
Leibniz Universität Hannover
Robust Portfolio Selection Under Recovery Average Value at Risk
Abstract.
We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical Average Value at Risk shows that portfolio selection under its recovery version allows financial institutions to better control the recovery of liabilities while still allowing for tractable computations. The talk is based on joint work with Cosimo Munari, Justin Plückebaum and Lutz Wilhelmy.
04. February
Tue W05
Raffaele
Vitolo
University of Salento
Bi-Hamiltonian geometry of WDVV equations: general results
Abstract.
It is known (work by Ferapontov and Mokhov) that a system of N-dimensional WDVV equations can be written as a pair of N-2 commuting quasilinear systems (first-order WDVV systems). In recent years, particular examples of such systems were shown to possess two compatible Hamiltonian operators, of the first and third order. It was also shown that all $3$-dimensional first-order WDVV systems possess such bi-Hamiltonian formalism. We prove that, for arbitrary N, if one first-order WDVV system has the above bi-Hamiltonian formalism, than all other commuting systems do. The proof needs some interesting results on the structure of the WDVV equations that will be discussed as well. (Joint work with S. Opanasenko).
Mattia
Cavicchi
Dijon
05. February
Wed W05
Gioni
Mexi
ZIB
Demystifying Pseudo-Boolean Conflict Analysis through a MIP Lens
Abstract.
For almost two decades, mixed integer programming (MIP) solvers have used graph-based conflict analysis to learn from local infeasibilities during branch-and-bound search. In this talk, we discuss improvements for MIP conflict analysis by instead using reasoning based on cuts, inspired by the development of conflict-driven solvers for pseudo-Boolean optimization. Phrased in MIP terminology, this type of conflict analysis can be understood as a sequence of linear combinations, integer roundings, and cut generation. We leverage this MIP perspective to design a new conflict analysis algorithm based on mixed integer rounding cuts, which theoretically dominates the state-of-the-art method in pseudo-Boolean optimization using Chvátal-Gomory cuts. Furthermore, we discuss how to extend this cut-based conflict analysis from pure binary programs to mixed binary programs and-in limited form-to general MIP with also integer-valued variables. Our experimental results indicate that the new algorithm improves the default performance of SCIP in terms of running time, number of nodes in the search tree, and the number of instances solved.
Sebastian
Schwarzacher
Uppsala University, Sweden & Charles University Prague, Czech Republic
Time-periodic solutions for fluid-solid interactions
Abstract
06. February
Thu W05
Stefan
Kober
Universite Libre de Bruxelles
11. February
Tue W06
Mikhail
Gorskii
Hamburg Universität
Counting in Calabi-Yau categories
Abstract.
I will discuss a replacement of the notion of homotopy cardinality in the setting of even-dimensional Calabi--Yau categories and their relative generalizations. This includes cases where the usual definition does not apply, such as Z/2-graded dg categories. As a first application, this allows us to define a version of Hall algebras for odd-dimensional Calabi-Yau categories. I will explain its relation to some previously known constructions of Hall algebras. If time permits, I will also discuss another application in the context of invariants of smooth and graded Legendrian links, where we prove a conjecture of Ng-Rutherford-Shende-Sivek relating ruling polynomials with augmentation categories. The talk is based on joint work with Fabian Haiden, arxiv:2409.10154.
12. February
Wed W06
Konrad
Mundiger
ZIB
Neural Networks for Unsupervised Discovery of Plane Colorings
Abstract.
We present a framework that transforms geometric and combinatorial problems into optimization tasks by designing loss functions that vanish precisely when the desired coloring properties are achieved. We employ neural networks trained through gradient descent to minimize these loss functions, allowing for efficient exploration of the solution space. We demonstrate the effectiveness of the method on variants of the Hadwiger-Nelson problem, which asks for plane colorings that avoid monochromatic unit-distance pairs and sketch how the approach can be applied to other problems.
André
Schlichting
Universität Ulm
Breakdown of the mean-field description of interacting systems: Phase transitions, metastability and coarsening
Abstract
Fred Espen
Benth
U of Oslo
Nikola
Sadovek
FU Berlin
Complex analogues of the Tverberg-Vrećica conjecture and central transversal theorems
Abstract.
The Tverberg-Vrećica conjecture is a broad generalization of Tverberg's classical theorem. One of its consequences, the central transversal theorem, extends both the centerpoint theorem and the ham sandwich theorem. In this talk, we will consider complex analogues of these results, where the corresponding transversals are complex affine spaces. The proofs of the complex Tverberg-Vrećica conjecture and its optimal colorful version rely on the non-vanishing of an equivariant Euler class. Furthermore, we obtain new Borsuk--Ulam-type theorems on complex Stiefel manifolds, which are interesting on their own. These theorems yield complex analogues of recent extensions of the ham sandwich theorem for mass assignments and provide a direct proof of the complex central transversal theorem. This talk is based on a joint work with Pablo Soberón.
13. February
Thu W06
Marc
Zimmermann
Uni Köln
19. February
Wed W07
Konrad
Mundiger
ZIB
Neural Networks for Unsupervised Discovery of Plane Colorings
Abstract.
We present a framework that transforms geometric and combinatorial problems into optimization tasks by designing loss functions that vanish precisely when the desired coloring properties are achieved. We employ neural networks trained through gradient descent to minimize these loss functions, allowing for efficient exploration of the solution space. We demonstrate the effectiveness of the method on variants of the Hadwiger-Nelson problem, which asks for plane colorings that avoid monochromatic unit-distance pairs and sketch how the approach can be applied to other problems.
20. February
Thu W07
Giulio
Schimperna
University of Pavia, Italy
Some results on a modified Cahn-Hilliard model with chemotaxis
Abstract
10. March
Mon W10
Marius
Zeinhofer
ETH, Zürich, Switzerland
First Optimize, Then Discretize for Scientific Machine Learning
Abstract.
This talk provides an infinite-dimensional viewpoint on optimization problems encountered in scientific machine learning and discusses the paradigm first optimize, then discretize for their solution. This amounts to first choosing an appropriate infinite-dimensional algorithm which is subsequently discretized in the tangent space of the neural network ansatz. To illustrate this point, we show that recently proposed state-of-the-art algorithms for scientific machine learning applications can be derived within this framework. Finally, we discuss the crucial aspect of scalability of the resulting algorithms.
12. March
Wed W10
Christophe
Roux
ZIB
26. March
Wed W12
Jan
Pauls
Universität Münster
16. April
Wed W15
Manuel
Kauers
JKU Linz