Silvia
De Toffoli
IUSS Pavia
Kovalevskaya Lecture
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04. July
Today
06. July
Sun W26
08. July
Tue W27
Julia
Schaeffer
HU Berlin
Subrabalan
Murugesan
Heriot-Watt University
A geometric recipe for constructing coordinates on the moduli space of flat connections
Abstract.
The moduli space M(C, G) of flat G-connections on a Riemann surface C is an object that appears in various places in physics, especially in the context of supersymmetric gauge theories. It was shown that one could construct a particularly nice set of coordinates on M(C, G) provided C is equipped with some additional structure known as a spectral network W. This construction uses a technique called W-abelianisation. W-abelianisation, and the inverse map W-nonabelianisation, define a diffeomorphism between the space M(C, G) and a (possibly) simpler space M(ÎŁ, GL(1, C)) where ÎŁ is a branched cover over C. In this talk, I shall give a pedagogical introduction to the abelianisation and nonabelianisation maps that were introduced in [Gaiotto-Moore-Neitzke] and later expanded upon by [Hollands-Neitzke]. This talk should be accessible to anyone comfortable with differential geometry and complex geometry.
09. July
Wed W27
Vincent
Rivoirard
Université Dauphine, Paris
Johannes
Bäumler
UCLA
Ruijie
Yang
University of Kansas
p-adic zeta function and Hodge theory
Abstract.
In 1988, Igusa proposed a mysterious conjecture, in the spirit of Weil's conjecture, which predicts certain arithmetic quantities of a given polynomial (poles of the p-adic zeta function) are in fact topological/geometric, i.e. they must induce roots of the Bernstein-Sato polynomial and monodromy eigenvalues on the cohomology of Milnor fibers. This conjecture is widely open, but for hyperplane arrangements, Budur-Mustațǎ-Teitler proposed the n/d-conjecture in 2009 and showed that it will imply Igusa's conjecture in this case. In this talk, I will report a recent work of mine with Dougal Davis, where we prove the n/d-conjecture, finishing the previous work of Saito, Walther, Budur, Yuzvinsky, Veys, Bath, Shi-Zuo and many others. The proof uses Hodge theory in an essential way, especially Schmid's nilpotent orbit theorem and its consequences.
Antoine
Deza
McMaster University
Is the squared inverse of the distance between kissing polytopes always an integer?
Abstract.
A lattice $(d,k)$-polytope is the convex hull of a set of points in dimension $d$ whose coordinates are integers ranging from $0$ to $k$. We investigate the smallest possible distance between two disjoint lattice $(d,k)$-polytopes. A pair of such polytopes are called kissing polytopes. This question arises in various contexts where the minimal distance between such polytopes appears in complexity bounds for optimization algorithms. We provide nearly matching lower and upper bounds for this distance and propose an algebraic model. Our formulation yields explicit formulas in dimensions $2$ and $3$, and allows for the computation of previously intractable values. We also discuss related results, such as the Alon–Vu bounds for flat simplices — that is, the minimum distance between a vertex of a lattice $(d,1)$-simplex and the affine space spanned by the remaining vertices. Finally, we observe that all the known squared distances between kissing polytopes are inverses of integers, and we ask whether this observation holds in general. Based on joint-work with Shmuel Onn (Technion), Sebastian Pokutta (Zuse Institute Berlin and TU Berlin), and Lionel Pournin (Université Paris 13).
10. July
Thu W27
Thierry
Gallay
Grenoble Alpes University, France
Axisymmetric vortex rings at high Reynolds number
Abstract
Daniel
Matthes
TU MĂĽnchen
A mediocre two-component variant of the famous result on equilibration in scalar Fokker-Planck equations
Abstract
Sadok
Kallel
American University of Sharjah, UAE, and Laboratoire Painlevé, Université de Lille, France
Configuration spaces and the chromatic polynomial
Abstract.
We study the chromatic configuration space associated to a simple finite graph. This is the complement of the so-called graphic subspace arrangement associated to the graph. Using poset topology, we show that the Poincaré polynomial of the chromatic configuration space is the reciprocal of the chromatic polynomial of the graph (with signs). As an important application, we deduce the homology of spaces of configurations consisting of n>1 moving objects in a euclidean space, distinct or not, each avoiding a given subset of r>0 fixed obstacles.
11. July
Fri W27
Andrea
Walther
HU Berlin
On optimality conditions for nonsmooth functions
14. July
Mon W28
Joachim
Naumann
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.
16. July
Wed W28
Claudia
Strauch
Universität Heidelberg
Frank
Seifried
U Trier
17. July
Thu W28
Alice
Marveggio
Hausdorff Center for Mathematics Universität Bonn
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.
29. July
Tue W30
Aaron
Lewin
HU Berlin