Nikola
Sadovek
Gromov-Hausdorff distance
Abstract
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24. October
Today
28. October
Tue W43
Lasse
Merkens
HU
Renormalization group flows from defects in N = 1 minimal models
Abstract.
Leveraging the structure of non-invertible symmetries, we construct a family of renormalization group flows connecting N = 1 superconformal minimal models: SM(p, kp + I) → SM(p, kp − I). The triggering operator is G−1/2ϕ(1,2k+1). A key element of our argument is that the topological defect lines of the bosonic coset theory persist in the fermionic case. These flows represent a supersymmetric generalization of the Virasoro flows discovered by Tanaka and Nakayama and include the previously known unitary flows (Pogossyan, k = 1, I = 2) as a special case. Furthermore, we demonstrate the completeness of this family; any flow between models SM(p, q) and SM(p, q′) can be obtained by composing these fundamental flows.
Tim
Stiebert
HU Berlin
29. October
Wed W43
Ludger
Overbeck
Universität Gießen
Bayesian Estimation with MCMC Methods for Stochastic Processes with Hidden States
Abstract.
Abstract: Markov Modulated Stochastic Processes (MMSP) are a more flexible class of Stochastic Processes which capture phase changes arising in economies by allowing jumps in drift and volatility, linked to hidden states of a Markov chain. These models have been used to model option prices, renewable energy markets as well as for risk quantification. While Bayesian inference methods exists for simpler regime-switching models, we aim to extend it to more complex MMSPs. Our approach involves applying Bayesian estimation techniques to recover the hidden states and the parameters associated with each state of the Markov Chain. We propose Markov Chain Monte Carlo algorithms to perform Bayesian inference for MM-SPs. This will allow for a more data-driven analysis of asset returns with regime shifts and jumps. In the first part of the talk we review well-known estimation techniques for the CIR-process which is the solution of dXt = (a+ bXt)dt+ σ X+_t dWt based on the paper Estimation in the CIR-Process (O. & Rydén. Scand, Econometric Theory. 1997). Finally we want to extend this to a model with hidden variables, namely to dXt = a(Zt) + b(Zt)Xt dt + σ(Zt) X+_s dWs where Z is a continuous-time Markov chain. This is a special case of a general regime switching stochastic process. dXt = β(Zt, Xt) dt + σ(Zt, Xt) dWζ(Zt). We consider two special cases ... For parameter estimation we present a new version of the EM (Expectation Maximizer)-approach which was in a similar way used in the paper On the estimation of regime-switching Lévy models (Chevalier & Goutte, Stud. Nonlinear Dyn. E. 2017). Finally, we discuss the potential modification of the EM-algorithm, if we consider conditional least square minimization instead of likelihood maximisation in the M-step of the EM-algorithm.
Hanna
Stange
Universität Münster
Non-local transport distance for point processes
Abstract.
We introduce a non-local transport distance on the space of point processes and analyse the induced geometry. We show — among other things — that the Ornstein–Uhlenbeck semigroup is the gradient flow of the specific relative entropy, functional inequalities like a Talagrand inequality, and exponential convergence of the Ornstein–Uhlenbeck flow to the Poisson point process. Towards the end, we discuss ongoing work on the extension of the framework adapted to Papangelou point processes. Based on joint work with Martin Huesmann and Matthias Erbar.
Debjit
Pal
Leibniz Universität Hannover
Strong generalized holomorphic principal bundles
Abstract.
We explore a classical problem within the framework of generalized complex (GC) geometry, a structure introduced by Hitchin and further developed by Gualtieri and Cavalcanti - namely, the development of an appropriate bundle theory in this setting. In this talk, we present the theory of strong generalized holomorphic (SGH) principal bundles, along with their connections and curvatures. These bundles interpolate between holomorphic and flat symplectic bundles. This is a joint work with Mainak Poddar.
Kirill
Khoruzhii
ZIB
Fast Algorithms for Structured Matrix Multiplication via Flip Graphs
Pawel
Borowka
Jagiellonian University
Some questions about abelian surfaces
Abstract.
At the end of 19th century, Humbert characterised the locus of principally polarised abelian surfaces that contain elliptic curves. This locus has infinitely many irreducible components, called Humbert surfaces. The components can be indexed by natural numbers that are exponents of complementary elliptic curves. We would like to describe irreducible components for non-principally polarised abelian surfaces. In the talk, after a brief overview of principally polarised case, I will show some results based on a joint paper with R. Auffarth. I will restate some questions posed in the article and if time permits I will talk about a possible way to answer them.
Mohab
Safey El Din
Sorbonne
Computing all minimizers of Morse funcitons over a compact set through point evaluations and polynomial approximations
Abstract.
Consider a Morse function $f: C → R$ defined on the n-dimensional cube $C = [-1, 1]^n$ that admits multiple local minimizers. We address the problem of computing all local minimizers when $f$ is only accessible through noisy evaluations. Specifically, $f$ is given by an evaluation program Gamma that takes a precision parameter and returns approximations within that precision of the true function values. We present an algorithm that computes all local minimizers of $f$ on $C$. Given the evaluation program Gamma, precision parameters, and explicit regularity parameters as input, our algorithm returns finitely many rational points in $C$. These points have the property that balls of radius epsilon centered at them contain and separate all local minimizers of $f$. The method combines polynomial approximation theory with computer algebra techniques for solving polynomial systems. Under probabilistic assumptions concerning the selection of evaluation points, we establish bit complexity estimates when all regularity parameters are known. Our approach constructs polynomial approximants from the noisy evaluations, then leverages algebraic methods to identify the minimizers. We have implemented this algorithm in the Julia package Globtim. This is joint work with Georgy Scholten (Harrington Group, Center for Systems Biology Dresden) and Emmanuel Trélat (Laboratoire Jacques-Louis Lions, Sorbonne Université).
30. October
Thu W43
Georg
Hofstätter
TU Wien
Localizations of valuations and Alesker's irreducibility theorem
Abstract.
We introduce a new localization technique for translation-invariant valuations on convex bodies, that is functionals satisfying a finite inclusion-exclusion principle. We then apply it to show that smooth valuations are representable by integration over the normal cycle. With this representation, we reprove Alesker's famous irreducibility theorem. This is joint work with J. Knoerr.
03. November
Mon W44
Roman
Popovych
Silesian University in Opava, Czech Republic
Symmetries of heat equation and beyond
04. November
Tue W44
Xavier
Blot
Unversiteit van Amsterdam
On the DR-DZ equivalence, and beyond
Abstract.
Witten’s conjecture, proved by Kontsevich, predicted that the Gromov–Witten invariants of a point are governed by the KdV hierarchy. In this talk, I will explain how the DR–DZ equivalence extends this result by constructing the Dubrovin–Zhang (DZ) hierarchy, which governs the Gromov–Witten invariants of any smooth projective variety (and more generally, any cohomological field theory). I will also discuss the equivalence between the DZ and Double Ramification (DR) hierarchies, and, if time allows, their equivalence to new hierarchies associated with the Chiodo class. This is based on joint works with Danilo Lewanski, Adrien Sauvaget and Sergey Shadrin.
Stefan
Sauter
Uni Zürich
05. November
Wed W44
Daebeom
Choi
University of Pennsylvania
Extremal effective curves and non-semiample line bundles on the moduli space of curves.
Abstract.
In this work, we develop a new method for establishing extremality in the closed cone of curves on the moduli space of curves and determine the extremality of many boundary 1-strata. As a consequence, by using a general criterion for non-semiampleness that extends Keel's argument, we demonstrate that a substantial portion of the cone of nef divisors on the moduli space of pointed curves is not semiample. As an application, we construct the first explicit example of a non-contractible extremal ray of the closed cone of effective curves on the moduli space of n-pointed curves of genus 3. Moreover, we show that this extremal ray is contractible in characteristic p. Our method relies on two main ingredients: (1) the construction of a new collection of nef divisors, and (2) the identification of a tractable inductive structure on the Picard group, arising from Knudsen's construction of the moduli space.
Florian
Frick
Carnegie Mellon University
Zeros by symmetry: Chebyshev systems, cubature, and convex geometry
Abstract.
I’ll present a unified, equivariant-topological framework that controls the zero distribution of real-valued functions obtained by composing a fixed equivariant map with linear (or affine) functionals. This yields upper bounds on the topology of regions where multivariate trigonometric polynomials remain sign-constant, generalizing classical results. As special cases, we derive new restrictions on zero sets in Chebyshev spaces. Finally, I’ll show how these constraints translate into existence results for efficient cubature formulas for these functions. Joint work with Francesca Cantor, Julia D'Amico, Eric Myzelev
06. November
Thu W44
Xiaohao
Ji
On an a priori bound for the Kuramoto–Sivashinsky equation
Rahul
Pandharipande
ETH Zürich
Florian
Frick
Sam
Cohen
University of Oxford
07. November
Fri W44
Ko
Sanders
Leibniz Universität Hannover
Gabriele
Steidl
TU Berlin
Adapting Noise to Data: Generative Flows from 1D Processes
10. November
Mon W45
Rahul
Pandharipande
ETH Zürich
11. November
Tue W45
Taro
Kimura
Université Bourgogne Europe
Non-perturbative Schwinger-Dyson equation for DT/PT vertices
Abstract.
Non-perturbative Schwinger-Dyson (SD) equation is a discrete analog of the loop equation appearing in matrix models and related models. It was initially discussed for the gauge theory partition function and, as in the case of the matrix models, it has a close relation to the underlying infinite-dimensional symmetry of the system. In this talk, I'd like to discuss the non-perturbative SD equation for the higher-dimensional gauge theory partition function, interpreted as the generating function of the DT and PT invariants (DT/PT vertices) for CY3 and CY4 varieties, and address its underlying quantum algebraic structure, which is a consequence of geometric representation theory of the corresponding algebra.
Stefan
Sauter
Uni Zürich
Georgi
Mitzov
HU Berlin
12. November
Wed W45
Thomas
Kneib
Universität Göttingen
Demystifying Spatial Confounding
Abstract.
Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random effects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can lead to significant bias in covariate effect estimates. The problem is complex and has been the topic of extensive research with sometimes puzzling and seemingly contradictory results. We will give an introduction to spatial confounding and discuss some suggested solutions for dealing with it, including the formalisation as a structural equation model and spatial+, where spatial variation in the covariate of interest is regresssed away first and remaining residuals are then used to identify the relevant effect. In the second part of the presentation, we develop a broad theoretical framework that brings mathematical clarity to the mechanisms of spatial confounding, relying on an explicit analytical expression for the resulting bias. We see that the problem is directly linked to spatial smoothing and identify exactly how the size and occurrence of bias relate to the features of the spatial model as well as the underlying confounding scenario. Using our results, we can explain subtle and counter-intuitive behaviours. Finally, we propose a general approach for dealing with spatial confounding bias in practice, applicable for any spatial model specification. When a covariate has non-spatial information, we show that a general form of the so-called spatial+ method can be used to eliminate bias. When no such information is present, the situation is more challenging but, under the assumption of unconfounded high frequencies, we develop a procedure in which multiple capped versions of spatial+ are applied to assess the bias in this case. We illustrate our approach with an application to air temperature in Germany.
Sophia-Marie
Mellis
Universität Bielefeld
Nathan
Pflueger
Amherst College
Leonard
Kreutz
TU München
Γ-expansion of the Cahn--Hilliard functional with Dirichlet boundary conditions
Abstract
Bobo
Hua
Fudan Univeristy
14. November
Fri W45
Bin
Zhang
Sichuan University
18. November
Tue W46
Piotr
Sulkowski
Warsaw University
Wall-crossing, Schur indices and symmetric quivers
Abstract.
I will show that symmetric quivers encode various observables of 4d N=2 theories related to wall-crossing phenomena. The observables in question include (wild) Donaldson-Thomas invariants, as well as Schur indices, which at the same time are known to reproduce characters of 2d conformal field theories. Furthermore, symmetric quivers of our interest encode 3d N=2 theories, therefore all these relations can be interpreted as a web of dualities between 2d, 3d, and 4d systems.
Georgi
Mitzov
HU Berlin
19. November
Wed W46
Alain
Celisse
Paris
David
Rügamer
LMU Munich
Lutz
Recke
Humboldt-Universität zu Berlin
An H-convergence-based implicit function theorem and homogenization of nonlinear non-smooth elliptic systems
Abstract
Jinrong
Hu
TU Vienna
21. November
Fri W46
Tamás
Hausel
ISTA
Anatomy of big algebras
24. November
Mon W47
Lutz
Recke
HU Berlin
Strange formulas in homogenization theory
25. November
Tue W47
Gaëtan
Borot
HU Berlin
Panorama of matrix models and topological recursion I
Abstract.
This is crash course which aims at explaning various aspects of: random matrix ensembles and Coulomb gases, loop equations, spectral curves, topological recursion, maps, free probability, how they fit together and pose some open problems.
26. November
Wed W47
Alessandro
Palummo
Politecnico Milano
Physics-informed Functional Principal Component Analysis of Large-scale Datasets
Abstract.
Physics-informed statistical learning is an emerging area of spatial and functional data analysis that integrates observational data with prior physical knowledge encoded by partial differential equations (PDEs). We propose an iterative Majorization–Minimization scheme for functional Principal Component Analysis of random fields in a general Hilbert space, formulated under the practically relevant assumption of partial observability of the data. By combining differential penalties with finite element discretizations, our approach recovers smooth principal component functions while preserving the geometric features of the spatial domain. The resulting estimation procedure involves solving a smoothing problem, which may become computationally demanding for large-scale datasets. After establishing the well-posedness of this smoothing problem under mild assumptions on the PDE parameters, we develop an efficient iterative algorithm for its solution. This framework enables the practical analysis of massive functional datasets at the population level, ranging from physics-informed fPCA to functional clustering, with applications to environmental and neuroimaging data.
Margherita
Lelli-Chiesa
Universita Roma Tre
Illia
Karabash
Institut für Angewandte Mathematik, Universität Bonn
Random boundary conditions for open resonators and the Laplace--Beltrami--Weyl asymptotics
Abstract
28. November
Fri W47
Jan
Mandrysch
IQOQI Wien
02. December
Tue W48
Nikolay
Barashkov
MiS Leipzig
03. December
Wed W48
Fanny
Seyzilles
Cambridge
Emanuele
Delucchi
SUPSI
04. December
Thu W48
Kristoffer
Andersson
University of Verona
Alex
Tse
University College London
05. December
Fri W48
Chuangzhong
Li
Shandong University of Science and Technology
Julia
Böttcher
LSE
09. December
Tue W49
Gaëtan
Borot
HU Berlin
Panorama of matrix models and topological recursion II
Abstract.
This is crash course which aims at explaning various aspects of: random matrix ensembles and Coulomb gases, loop equations, spectral curves, topological recursion, maps, free probability, how they fit together and pose some open problems.
10. December
Wed W49
Vladimir
Spokoiny
WIAS
12. December
Fri W49
Barbara
Niethammer
U Bonn
16. December
Tue W50
Gaëtan
Borot
HU Berlin
Panorama of matrix models and topological recursion III
Abstract.
This is crash course which aims at explaning various aspects of: random matrix ensembles and Coulomb gases, loop equations, spectral curves, topological recursion, maps, free probability, how they fit together and pose some open problems.
17. December
Wed W50
Cesare
Miglioli
University of Pittsburgh
Incomplete U-Statistics of Equireplicate Designs: Berry-Esseen Bound and Efficient Construction.
Abstract.
U-statistics are a fundamental class of estimators that generalize the sample mean and underpin much of nonparametric statistics. Although extensively studied in both statistics and probability, key challenges remain. These include their inherently high computational cost—addressed partly through incomplete U-statistics—and their non-standard asymptotic behavior in the degenerate case, which typically requires resampling methods for hypothesis testing. This talk presents a novel perspective on U-statistics, grounded in hypergraph theory and combinatorial designs. Our approach bypasses the traditional Hoeffding decomposition, which is the the main analytical tool in this literature but is highly sensitive to degeneracy. By fully characterizing the dependence structure of a U-statistic, we derive a new Berry–Esseen bound that applies to all incomplete U-statistics based on deterministic designs, yielding conditions under which Gaussian limiting distributions can be established even in the degenerate case and when the order diverges. Moreover, we introduce efficient algorithms to construct incomplete U-statistics of equireplicate designs, a subclass of deterministic designs that, in certain cases, enable to achieve minimum variance. To illustrate the power of this novel framework, we apply it to kernel-based testing, focusing on the widely used two-sample Maximum Mean Discrepancy (MMD) test. Our approach leads to a permutation-free variant of the MMD test that delivers substantial computational gains while retaining statistical validity.
Sebastian
Hensel
Universität Leipzig
A weak-strong uniqueness principle for the Mullins--Sekerka equation
Abstract
18. December
Thu W50
Felix
Höfer
University of Princeton
Martin
Keller-Ressel
Technische Universität Dresden
07. January
Wed W01
George
Hitching
OSLOMET
Secant loci of scrolls over curves
Abstract.
The secant loci associated to a linear system l over a curve C parametrise effective divisors which impose fewer conditions than expected on l. For a rank r bundle E and a space of global sections of E, we define and investigate generalised secant loci, which are determinantal loci on Quot schemes of torsion quotients of E. We extend the Abel-Jacobi map to the context of Quot schemes, and examine the relation between smoothness of generalised secant loci and their associated Brill-Noether loci. In one case, we indicate how formulas of Oprea-Pandharipande and Stark can be used to enumerate the generalised secant locus when it has and attains expected dimension zero.
13. January
Tue W02
Piotr
Sulkowski
University of Warsaw
14. January
Wed W02
Frank
Konietschke
Charité
15. January
Thu W02
Francesca
Primavera
University of California
16. January
Fri W02
Daan
Janssen
University of York
23. January
Fri W03
Malte
Leimbach
MPI Bonn
Janina
Bernardy
MPI Bonn
27. January
Tue W04
Maciej
Dolega
Institute of Mathematics, Polish Academy of Sciences
28. January
Wed W04
Jakob
Runge
Uni Potsdam
29. January
Thu W04
Xiaofei
Sei
University of Toronto
Claudio
Dappiaggi
University of Pavia
Equivalence between local and global Hadamard States with Robin boundary conditions on half-Minkowski spacetime
Abstract.
We construct the fundamental solutions and Hadamard states for a Klein-Gordon field in half-Minkowski spacetime with Robin boundary conditions in arbitrary dimensions using a generalisation of the Robin-to-Dirichlet map. On the one hand this allows us to prove the uniqueness and support properties of the Green operators. On the other hand, we obtain a local representation for the Hadamard parametrix that provides the correct local definition of Hadamard states, capturing `reflected' singularities from the spacetime timelike boundary. This allows us to prove the equivalence of our local Hadamard condition and the global Hadamard condition with a wave-front set described in terms of generalized broken bicharacteristics, obtaining a Radzikowski-like theorem in half-Minkowski spacetime. <br>Joint work with B. Costeri, R. D. Singh and B. Juárez-Aubry -- ArXiv: 2509.26035 [math-ph]
Alessandro
Bondi
École Polytechnique Paris
30. January
Fri W04
Beatrice
Costeri
University of Pavia
11. February
Wed W06
Ho
Yun
EPFL
Linear Monge is All You Need
Abstract.
In this talk, we explore the geometry of the Bures-Wasserstein space for potentially degenerate Gaussian measures on a separable Hilbert space, based on our recent work with Yoav Zemel. A key feature of our approach is its simplicity: relying only on elementary arguments from linear operator theory, we are able to derive explicit results without resorting to Kantorovich duality or Otto's Calculus. We provide a complete characterisation of both the Monge and Kantorovich problems in this context, regardless of the degeneracy of their measures. Furthermore, we show a simple way to construct all possible Wasserstein geodesics connecting two Gaussian measures. Finally, we generalise our results to characterise Wasserstein barycenters of Gaussian measures, borrowing the idea of Procrustes distance from statistical shape analysis
Béatrice
Matteo
University of Geneva
Kernel ridge regression for spherical responses
Abstract.
The aim is to propose a novel nonlinear regression framework for responses taking values on a hypersphere. Rather than performing tangent space regression, where all the sphere responses are lifted to a single tangent space on which the regression is performed, we estimate conditional Frechet means by minimizing squared distances on the nonlinear manifold. Yet, the tangent space serves as a linear predictor space where the regression function takes values. The framework integrates Riemannian geometry techniques with functional data analysis by modelling the regression function using methods from vector-valued reproducing kernel Hilbert space theory. This formulation enables the reduction of the infinite-dimensional estimation problem to a finite-dimensional one via a representer theorem and leads to an estimation algorithm by means of Riemannian gradient descent. Explicit checkable conditions on the data that ensure the existence and uniqueness of the minimizing estimator are given.
Andrea
Poiatti
Universität Wien
12. February
Thu W06
Guido
Gazzani
University of Verona
Beatrice
Ongarato
Technische Universität Dresden