Gaëtan
Borot
HU Berlin
Limits in topological recursion
Search by speaker
Filter institution
Filter content
07. January
Tue W01
TĂĽrkĂĽ Ă–zlĂĽm
Çelik
MPI of Molecular Cell Biology and Genetics, Dresden
08. January
Wed W01
Johannes
Schmidt-Hieber
University of Twente
Statistical stimation using zeroth-order optimization
Abstract.
In this talk, we study statistical properties of zeroth-order optimization schemes, which do not have access to the gradient of the loss and rely solely on evaluating the loss function. Such methods are often considered to be suboptimal for high-dimensional problems, as their convergence rates to the minimizer of the objective function are typically slower than those of gradient-based methods. This performance gap becomes more pronounced as the number of parameters increases. Considering the linear model, we show that reusing the same data point for multiple zeroth-order updates can overcome the gap in the estimation rates. Additionally, we demonstrate that zeroth-order optimization methods can achieve the optimal estimation rate when only queries from the linear regression model are available. Special attention will be given to the non-standard minimax lower bound in the query model. This is joint work with Thijs Bos, Niklas Dexheimer and Wouter Koolen.
09. January
Thu W01
Roxana
Radulescu
Utrecht University
10. January
Fri W01
Ilya
Chevyrev
U Edinburgh/TU Berlin
Rough Analysis
Ilya
Cheyrev
U Edinburgh
14. January
Tue W02
Gaëtan
Borot
HU Berlin
Limits in topological recursion
Abstract.
I will discuss the subtle aspects of the behavior of topological recursion (= seen as the construction of W-algebra modules from branched covers of curves) along families of spectral curves. To do so, I will review basics of singularities of plane curves and discuss (maximal) equigeneric families.
TĂĽrkĂĽ Ă–zlĂĽm
Çelik
MPI of Molecular Cell Biology and Genetics, Dresden
15. January
Wed W02
Xiaorui
Zuo
National University of Singapore
Cryptos have rough volatility and correlated jumps
Antonia
Chmiela
ZIB
Patrik
Knopf
Universität Regensburg
The Cahn-Hilliard equation with dynamic boundary conditions and its application to two-phase flows
Abstract
Randolf
Altmeyer
Imperial College London
Ben
Hambly
U of Oxford
16. January
Thu W02
Hana
Kourimska
Universität Potsdam
Amoebas: at the intersection of discrete, differential, and algebraic geometry
Abstract.
Amoebas are mathematical objects introduced in algebraic geometry at the end of the last century. Formally, they are defined as an image of a zero set of a polynomial under the so-called log-absolute map: for each point in the zero set, you take the absolute value of each of its coordinates, and then the (real) logarithm of it, and you end up with a set in the Euclidean space. While this may sound discouraging, it turns out one can tell (and learn) a lot about amoebas also without an extensive knowledge in algebraic geometry. In my talk I will tell you about these types of properties, and also shed light on where amoebas can be applied, and how differential geometry can help in approximating the area of amoebas. This is joint work with Timo de Wolff.
21. January
Tue W03
Olivier
Marchal
Univ. St-Etienne
Isomonodromic deformations, quantization and exact WKB
Abstract.
In this talk, I will review the theory of isomonodromic deformations of meromorphic connections on gl2 and the underlying symplectic structure. In particular, I will explain how to obtain explicit formulas for the Hamiltonian systems and the Lax pairs. Next, I will explain how one can formally reconstruct these results using the quantization of the classical spectral curve using topological recursion. Finally, I will explain the current challenges and results to upgrade this formal reconstruction to an analytic one focusing on the genus zero case where one can use Borel resummation of WKB solutions. The talk is supposed not to require any knowledge in integrable systems, topological recursion of Borel resummation.
22. January
Wed W03
Olivia
Röhrig
ZIB
Jan-Frederik
Pietschmann
Universität Augsburg
Gradient flows on metric graphs with reservoirs
Abstract
Anja
Schlömerkemper
Universität Würzburg
Fabian
Lenzen
TU Berlin
Topological Data Analysis: Algebra and Computation
23. January
Thu W03
Shelby
Cox
MPI MiS Leipzig
24. January
Fri W03
Carla
Cederbaum
U TĂĽbingen
Coordinates are messy in general (relativity)
28. January
Tue W04
Daniel
Roggenkamp
MiS Leipzig
29. January
Wed W04
Coherent Transport of Semiconductor Spin-Qubits: Modeling, Simulation and Optimal Control
Abstract
Mihály
Kovács
PPKE ITK Budapest
30. January
Thu W04
Constantin
Ickstadt
Uni Frankfurt
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 PlĂĽckebaum 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).
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
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
André
Schlichting
WWU MĂĽnster
Fred Espen
Benth
U of Oslo
13. February
Thu W06
Marc
Zimmermann
Uni Köln
19. February
Wed W07
Konrad
Mundiger
ZIB
10. March
Mon W10
Marius
Zeinhofer
ETH, ZĂĽrich, 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