Anastasiia
Hrabovets
Institute of Mathematics, Ukraine
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14. July
Mon W28
Joachim
Naumann
HU Berlin
On weak solutions of the Maxwell equations with temperature dependent density fields
15. July
Tue W28
Rob
Klabbers
HU Berlin
How to freeze elliptic spin Ruijsenaars models
Abstract.
The connection between integrable quantum many body systems and spin chains is formed by `freezing', an idea that goes back to Polychronakos. I will discuss a reformulation of freezing in the language of deformation quantisation, that builds on recent work by Mikhailov and Vanhaecke. I will show that there exists an SL(2,Z) famiy of equilibria on which one can freeze, yielding an infinite family of integrable spin chains. Based on work with Jules Lamers.
Yves
Jäckle
Zuse-Institut Berlin
BerLean
Abstract.
tLean is an interactive theorem prover and programming language. It allows its users to write definitions and proofs from mathematics or computer science in a formal language, so that they may be verified. We'll introduce formalization in Lean with a simple study of linked lists. Then, we'll proceed with a discussion of what it means to verify algorithms in Lean, and how it differs from algorithms that produce proofs. Finally, we'll implement a variant of subgradient descent in Lean and prove a convergence theorem for it.
16. July
Wed W28
Claudia
Strauch
Universität Heidelberg
Statistical analysis of reflected diffusions and random-time reversals in generative modelling
Frank
Seifried
U Trier
17. July
Thu W28
Alice
Marveggio
Hausdorff Center for Mathematics Universität Bonn
Stability of multiphase mean curvature flow beyond circular topology changes
Abstract
Jayden
Wang
Lorentzian polynomials and the incidence geometry of tropical linear spaces
Abstract.
Tropical linear spaces are complicated. Even the most elementary questions about their incidence geometry can be hard. I will give some answers to three types of such questions that are especially important to other recent advancements. The central object is the moduli space of all codimension-1 tropical linear subspaces of a given tropical linear space. The structure of this moduli space is closely related to the structure of spaces of Lorentzian polynomials. I will show how convexity results about tropical linear spaces can be derived and can be used to derive convexity results about Lorentzian polynomials.
Anna
Shalova
TU Eindhoven
Porous medium is the message: variational analysis of toy transformers
Abstract.
We study an aggregation PDE with competing attractive and repulsive forces on a high-dimensional sphere. In particular, we consider the limit of localized repulsion with a constant attraction term. We prove convergence of solutions of such a system to solutions of the aggregation-diffusion equation with the porous-medium-type diffusion. The proof combines variational techniques with the elements of harmonic analysis on a sphere. Specifically, we characterize the square root of the convolution operator in terms of the spherical harmonics, which allows us to overcome difficulties arising due to the convolution on a sphere being non-commutative. The system under study naturally arises as an extension of the toy model of transformers introduced by Geshkovski et al. (2024) and provides some insights on the driving mechanisms behind the modern language models. This is a joint work with Mark Peletier.
22. July
Tue W29
Anastasiia
Hrabovets
Institute of Mathematics, Ukraine
23. July
Wed W29
Michael
Joswig
Open problems for young people
29. July
Tue W30
Aaron
Lewin
HU Berlin
Gamma-convergence and large deviations: Variants of the relative entropy