Lukas
KĂĽhne
Bielefeld University
When alcoved polytopes add
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02. April
Today
03. April
Tomorrow
08. April
Tue W14
Jannis
Halbey
ZIB
Frank-Wolfe for strongly convex sets
Abstract.
The Frank-Wolfe method is a classical first-order algorithm for constrained optimization that avoids projections by relying on linear minimization oracles. While extensively studied over polytopes, its behavior over strongly convex domains remains less understood, especially near the boundary. In this talk, we will explore the challenges of optimizing over such sets, with a particular focus on the difficulty of finding optima located on the boundary. Using the simple example of projections onto the L2-ball, we will provide geometric insights into convergence behavior of Frank-Wolfe. This example illustrates fundamental limitations of the method in boundary regimes and motivates further analysis of step size strategies and alternative update directions.
09. April
Wed W14
Sebastian
Knebel
ZIB
Koopman von Neumann mechanics
16. April
Wed W15
Seta
Rakotoamandimby
enpc
Minimization on the sphere and cut selection for the Capra-cutting plane method
Michael
Tsopanopoulos
WIAS
Higher regularity for elliptic systems with mixed boundary conditions
Abstract
Manuel
Kauers
JKU Linz
D-Finite Functions
Abstract.
A function is called D-finite if it satisfies a linear differential equations with polynomial coefficients. Such functions play a role in many different areas, including combinatorics, number theory, and mathematical physics. Computer algebra provides many algorithms for dealing with D-finite functions. Of particular importance are operations that preserve D-finiteness. In the talk, we will give an overview over some of these techniques.
22. April
Tue W16
Vincent
Bouchard
University of Alberta
W-constraints for the ancestor potential of (r,s)-theta classes
Abstract.
Witten’s conjecture, which was proved by Kontsevich, states that the generating series for intersection numbers on the moduli space of curves is a tau-function for the KdV integrable hierarchy. It can be reformulated as the statement that the ancestor potential of the trivial cohomological field theory is the unique solution to a system of differential constraints that form a representation of the Virasoro algebra. In this talk I will present a new generalization of this celebrated result. The object of study becomes the ancestor potential of an interesting set of cohomology classes on the moduli space of curves, called (r,s) theta classes, which form a non-semisimple cohomological field theory. (Here, r is a positive integer and s is a positive integer between 1 and r-1.) The (r,s) theta classes are constructed as the top Chern classes of the Chiodo classes, and can be understood as a higher generalization of the Norbury classes. We show that the ancestor potential is the solution of a system of differential constraints that form a representation of a W-algebra. However, the differential constraints form an Airy structure (and thus uniquely fix the ancestor potential) only in the cases s=1 and s=r-1. An equivalent way of stating this result is that we determine loop equations satisfied by the correlators for all (r,s), but only when s=1 or s=r-1 are the loop equations uniquely solved by (shifted) topological recursion. This talk is based on work in progress with N. K. Chidambaram, A. Giacchetto and S. Shadrin and previous work by many people such as https://arxiv.org/abs/2412.09120, https://arxiv.org/abs/2408.02608, https://arxiv.org/abs/2205.15621, https://arxiv.org/abs/1812.08738, to name a few.
Lina
Zhao
City University of Hong Kong
23. April
Wed W16
Yusuke
Kimura
FUJITSU
Multi-node quantum circuit simulation with decision diagram in HPC
Danai
Deligeorgaki
KTH
Colored multiset Eulerian polynomials
Abstract.
The central objects in this talk are the descent polynomials of colored permutations on multisets, referred to as colored multiset Eulerian polynomials. These polynomials generalize the colored Eulerian polynomials that appear frequently in algebraic combinatorics and are known to admit desirable distributional properties, including real-rootedness, log-concavity, unimodality and the alternatingly increasing property. In joint work with Bin Han and Liam Solus, symmetric colored multiset Eulerian polynomials are identified and used to prove sufficient conditions for a colored multiset Eulerian polynomial to satisfy the self-interlacing property. This property implies that the polynomial obtains all of the aforementioned distributional properties as well as others, including bi-gamma-positivity. To derive these results, multivariate generalizations of a generating function identity due to MacMahon are deduced. The results are applied to a pair of questions, both previously studied in several special cases, that are seen to admit more general answers when framed in the context of colored multiset Eulerian polynomials. The first question pertains to s-Eulerian polynomials, and the second to interpretations of gamma-coefficients. We will see some of these results in detail, depending on the pace of the talk. We may also discuss some connections between multiset permutations and polytopes from algebraic statistics.
29. April
Tue W17
Thomas
Creutzig
Erlangen Universität
30. April
Wed W17
Rossella
Giorgio
TU Wien
Anastasia
Giorgi
University of Calgary
Kevin
KĂĽhn
Goethe University Frankfurt
07. May
Wed W18
Rossella
Giorgio
TU Wien
13. May
Tue W19
Leonid
Chekhov
Michigan State University
Symplectic groupoid and cluster algebras
Abstract.
The symplectic groupoid is a set of pairs (B,A) with A unipotent upper-triangular matrices and B in GLn being such that the matrix A~ = BABT is itself unipotent upper triangular. It turned out recently that the problem of description of such pairs can be explicitly solved in terms of Fock--Goncharov--Shen cluster variables; moreover, for B satisfying the standard semiclassical Lie--Poisson algebra, the matrices B, A, and A~ satisfy the closed Poisson algebra relations expressible in the r-matrix form. Since works of J.Nelson, T.Regge and B.Dubrovin, it was known that entries of A can be identified with geodesic functions on Riemann surfaces with holes. In our approach, we are able to construct a complete set of geodesic functions for a closed Riemann surface. We have a complete description for genus two; I'm also about to discuss moduli spaces of higher genera. Based on my joint papers with MIsha Shapiro and our students.
14. May
Wed W19
Pierluigi
Colli
UniversitĂ Pavia, Italy
Andrea
Signori
Politecnico di Milano, Italy
16. May
Fri W19
Paolo
Rossi
Padova
Moduli spaces of curves and the classification of integrable systems
Abstract.
I will present several results and conjectures on the classification of different classes of integrable systems of evolutionary PDEs, up to the appropriate transformation groups. These include Hamiltonian systems, tau symmetric systems and systems of conservation laws. I will then explain in what sense we expect that integrable systems arising from intersection theory on the moduli space of stable curves are universal objects with respect to these classifications. In the rank one case I will present strong evidence in support of these claims. This is joint work with A. Buryak.
Danilo
Lewanski
Trieste
On the DR/DZ equivalence
Abstract.
There are two main recipes to associate to a Cohomological Field Theory (CohFT) an integrable hierarchy of hamiltonian PDEs: the first one was introduced by Dubrovin and Zhang (DZ, 2001), the second by Buryak (DR, 2015). It is interesting to notice that the latter relies on the geometric properties of the Double Ramification cycle — hence the name DR — to work. As soon as the second recipe was introduced, it was conjectured that the two had to be equivalent in some sense, and it was checked in a few examples. In the forthcoming years several papers by Buryak, Dubrovin, Guerè, Rossi and others followed, checking more examples of CohFTs, making the conjecture more precise, proving the conjecture in low genera, and eventually turning the statement of the conjecture in a purely intersection theoretic statement on the moduli spaces of stable curves. Lately, the conjecture was proved in its intersection theoretic form, employing virtual localisation techniques. (j.w.w. Blot, Rossi, Shadrin).
Reinier
Kramer
Milano Bicocca
Leaky Hurwitz numbers and topological recursion
Abstract.
Leaky Hurwitz numbers were introduced by Cavalieri-Markwig-Ranganathan by extending the branching morphism from the logarithmic double ramification cycle to its pluricanonical counterpart. These numbers also have a natural interpretation in terms of tropical geometry and yield (non-hypergeometric) KP tau functions. I will explain how to think about these numbers, and how we can extend the recent works of Alexandrov-Bychkov-Dunin-Barkowski-Kazarian-Shadrin to prove (at least blobbed) topological recursion. Along the way, I will interpret the cut-and-join operator as a hamiltonian whose flow generates the spectral curve. This is joint work in progress with M. A. Hahn.
21. May
Wed W20
Franziska
Eberle
MATH+ Junior Research Group Leader
Demand Strip Packing
23. May
Fri W20
Artur
Avila
U ZĂĽrich
04. June
Wed W22
11. June
Wed W23
Martin
Brokate
WIAS and TU MĂĽnchen
18. June
Wed W24
Christophe
Roux
ZIB
Bounding geometric penalties in Riemannian optimization
Abstract.
Riemannian optimization refers to the optimization of functions defined over Riemannian manifolds. Such problems arise when the constraints of Euclidean optimization problems can be viewed as Riemannian manifolds, such as the symmetric positive-definite cone, the sphere, or the set of orthogonal linear layers for a neural network. This Riemannian formulation enables us to leverage the geometric structure of such problems by viewing them as unconstrained problems on a manifold. The convergence rates of Riemannian optimization algorithms often rely on geometric quantities depending on the sectional curvature and the distance between iterates and an optimizer. Numerous previous works bound the latter only by assumption, resulting in incomplete analysis and unquantified rates. In this talk, I will discuss how to remove this limitation for multiple algorithms and as a result quantify their rates of convergence.
02. July
Wed W26
Benjamin
Gess
TU Berlin and MPI Leipzig
04. July
Fri W26
Silvia
De Toffoli
IUSS Pavia
Kovalevskaya Lecture
06. July
Sun W26
09. July
Wed W27
Amru
Hussein
Universität Kassel
16. July
Wed W28
Alice
Marveggio
Hausdorff Center for Mathematics Universität Bonn