Berlin Math Seminars

Thu, 15. Oct at 11:00

Room IMOS 2003

Andrea V. Hurtado-Quiceno RPTU Kaiserslautern

Hypocoercive Langevin Dynamics on the Lie Groups SE(2) and SE(3)

Abstract.

We consider Langevin-type diffusions on Lie groups of rigid motions, where the dynamics couple position and orientation and the noise acts only in a subset of directions, leading to degenerate Kolmogorov generators. While hypocoercivity for related models in Euclidean settings is well understood, our aim is to develop an intrinsic formulation on the underlying Lie group and to identify the mechanisms responsible for exponential convergence to equilibrium. Starting from the planar motion group SE(2), we express the generator in terms of invariant vector fields and decompose it into its symmetric and antisymmetric parts. The natural projection onto the kernel of the symmetric part separates the microscopic and macroscopic dynamics, while averaging over the rotational subgroup leads to an effective elliptic operator in the spatial variables. This allows us to verify the microscopic and macroscopic coercivity properties required by an abstract hypocoercivity framework and to obtain exponential convergence to equilibrium. Building on this approach, we investigate the three-dimensional case SE(3), where the geometry and the corresponding operator structure become more involved. The results for SE(3) are currently in progress.

Stochastics

Thu, 15. Oct at 14:00

SR 115, Arnimallee 3

Nicolas Perkowski

Organisatorial meeting: Overview and distribution of talks

Stochastic Analysis

Thu, 15. Oct at 16:15

HU Berlin, Instit...

Frederico Cannerozzi Universität Bielefeld

cancelled

Singular Mean-Field Control via singular Mean-Field Games

Abstract.

Mean-field control (MFC) and mean-field games (MFGs) provide two different descriptions of large interacting populations: in MFC, a central planner optimizes the collective performance of the system, while in MFGs each representative player optimizes individually against a given population distribution, which is then determined through a consistency condition. In general, the corresponding optimal controls and equilibria need not coincide. A much tighter connection is known for potential mean-field games: an MFG equilibrium can be obtained by solving an associated auxiliary mean-field control problem. This naturally suggests the reverse question: can a mean-field control problem be solved by means of an auxiliary potential mean-field game? We discuss this approach in two settings of mean-field control with singular controls, where the associated potential MFG can provide a tractable route to the original MFC problem. In a stationary Ornstein-Uhlenbeck model with two-sided singular controls, we obtain a two-way correspondence between the MFC problem and an associated potential MFG. In a finite-horizon framework with general dependence on the state distribution, we show that equilibria of the associated potential MFG yield optimal controls for the MFC problem, and illustrate the approach through a mean-field monotone follower problem.

Stochastic Analysis

Thu, 15. Oct at 17:15

HU Berlin, Instit...

Ziyu Huang Humboldt Universität

Classical Solutions to HJB Equations for Mean Field Type Control Problems: An FBSDE Approach

Abstract.

Mean field type control problems lead to Hamilton–Jacobi–Bellman (HJB) equations on the space of probability measures. In this talk, we will present a probabilistic approach to constructing classical solutions through forward-backward stochastic differential equations (FBSDEs), allowing for degenerate and unbounded diffusion coefficients. Starting with linear dynamics, we will explain how convexity ensures the global well-posedness of the associated FBSDE system, and how variational equations establish the regularity of the value function needed for the HJB equation. We will then extend the framework to jump-diffusion models, where the associated HJB equation is an integro-partial differential equation. Finally, we will consider the case where a backward equation forms part of the state.

Stochastic Analysis

Thu, 15. Oct at 17:15

HU Berlin, Instit...

Ziyi Huang Humboldt University of Berlin

cancelled

Mean -Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study

Abstract.

We study continuous-time mean-variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes yet the coefficients of these processes are unknown. Based on the recently developed reinforcement learning (RL) theory for diffusion processes, we present a general data-driven RL algorithm that learns the pre-committed investment strategy directly without attempting to learn or estimate the market coefficients. For multi-stock Black-Scholes markets without factors, we further devise a baseline algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of Sharpe ratio. For performance enhancement and practical implementation, we modify the baseline algorithm and carry out an extensive empirical study to compare their performance, in terms of a host of common metrics, with a large number of widely used portfolio allocation strategies on S&P 500 constituents. The results demonstrate that the proposed continuous-time RL strategy is consistently among the best especially in a volatile bear market, and decisively outperforms the model-based continuous-time counterparts by significant margins.

Arithmetic Geometry

Tue, 20. Oct at 13:15

Room 3.007, Rudow...

Giuseppe Ancona Strasburg

Math. Statistics

Wed, 21. Oct at 10:00

ESH, Anton-Wilhel...

Kolyan Ray Imperial College London

Bayesian regression models with dense confounding variables

Abstract.

Inferring causal relationships from observational data can be invalidated by the existence of confounding variables. We consider nonparametric Bayesian inference in regression models with additive errors under a dense confounding assumption, i.e. that every confounding variable affects many covariates. We show that by using suitable priors, which are equivalent to marginalizing out the confounders in a certain sense, such confounding can be corrected for. Our approach is illustrated via Gaussian process and spike and slab priors, for which we provide accompanying theoretical guarantees via posterior convergence rates. This is joint work with Luke Travis

Discrete Math

Wed, 21. Oct at 16:30

IMoS 3003

Ilia Itenberg Institut de Mathématiques de Jussieu

Topology of real tropical hypersurfaces

Abstract.

Real algebraic varieties seem to be quite distant from combinatorial geometry. However, it is possible to construct real algebraic hypersurfaces in projective spaces (and, more generally, in toric varieties) in a completely combinatorial fashion: one can patchwork them from pieces which essentially are hyperplanes. This procedure, called the combinatorial patchworking, is a particular case of the Viro method of construction of real algebraic varieties with prescribed topology. The combinatorial patchworking is one of the sources of tropical geometry, and the results of this construction can be seen as real tropical hypersurfaces. We will discuss the combinatorial patchworking and several results concerning the topology of real tropical hypersurfaces.

Langenbach

Thu, 22. Oct

WIAS, Erhard-Schm...

Clara Thierbach HU Berlin

A variational characterization of a Gibbs measure related to the Aviles-Giga functional

Abstract

Villa Seminar

Thu, 22. Oct at 14:00

FU Berlin, Villa ...

Bashar Hamade

MATH+ Friday

Fri, 23. Oct at 14:15

Stefanie Petermichl U Würzburg

Optimization

Mon, 26. Oct at 15:00

Rudower Chaussee ...

Raphael Kuess HU Berlin

Math. Physics

Tue, 27. Oct at 11:15

1.023 (BMS Room, ...

Alexander Bobenko TU Berlin

Group Theory

Tue, 27. Oct at 14:00

MA 366

Peter Buergisser Berlin

Arithmetic Geometry

Wed, 28. Oct

Room 3.007, Rudow...

Olivier de Gaay Fortman Imperial College

Math. Statistics

Wed, 28. Oct at 10:00

ESH, Anton-Wilhel...

Nicolas Verzelen INRAE, Université Montpellier

Random Systems

Wed, 28. Oct at 11:30

WIAS-406

Lars Schroeder University of Twente

The Geometry of Hierarchical Navigation

Abstract.

Many applications use multi-layered hierarchical data structures for fast approximate nearest-neighbor search in high-dimensional vector spaces. However, the geometric conditions that ensure accurate and efficient greedy navigation remain poorly understood. In this talk, we study the efficiency of greedy navigation on a hierarchy of proximity graphs constructed from n data points on the $d$-dimensional torus. We identify a deterministic coverage condition under which, given any query $q$, greedy search returns a point within $(1+\epsilon)$-factor of the distance to the closest point. This coverage property holds with high probability when the data is distributed as a homogeneous Poisson process, a Hermitian determinantal process, or a bounded-density Cox process, as long as $d=o(\log n/\log\log n)$. Additionally, we obtain logarithmic expected hop count for the number of greedy hops in fixed dimension. Joint work with Shankar Bhamidi, Souvik Dhara and Clara Stegehuis.

Discrete Math

Wed, 28. Oct at 16:30

IMoS 3003

Eugenia Saorín Gómez

Orthogonal projections, linearization and sausages: a geometric approach to Cheeger sets

Abstract

Villa Seminar

Thu, 29. Oct at 14:00

FU Berlin, Villa ...

Cesar Ceballos

Stochastic Analysis

Thu, 29. Oct at 16:15

HU Berlin, Instit...

Carlo Sgarra Università degli Studi di Bari Aldo Moro

Semi-static variance-optimal hedging with self-exciting jumps

Abstract.

The aim of this talk is to investigate a quadratic, i.e., variance-optimal, semi-static hedging problem in an incomplete market model where the underlying log-asset price is driven by a diffusion process with stochastic volatility and a self-exciting jump process of Hawkes type. More precisely, we aim at hedging a claim at time T > 0 by using a portfolio of available contingent claims, so to minimize the variance of the residual hedging error at time T. In order to improve the replication of the claim, we look for a hybrid hedging strategy of semi-static type, in which some assets are continuously rebalanced (the dynamic hedging component) and for some other assets a buy-and-hold strategy (the static component) is performed. We discuss in detail a specific example in which the approach proposed is applied, i.e., a variance swap hedged by means of European options, and we provide a numerical illustration of the results obtained. (In cooperation with G. Callegaro, P. Di Tella and B. Ongarato, to appear on Mathematics of Operations Reasearch)

Stochastic Analysis

Thu, 29. Oct at 16:15

HU Berlin, Instit...

Philipp Schmocker ETH

Stochastic Analysis

Thu, 29. Oct at 17:15

HU Berlin, Instit...

Christoph Czichowsky LSE

Math. Physics

Tue, 03. Nov at 11:15

1.023 (BMS Room, ...

Nitin Kumar Chidambaram UNED Madrid

Refining Witten-Kontsevich

Abstract.

The moduli space of metric Möbius graphs, which are non-orientable ribbon graphs, has one component homeomorphic to the moduli space of Riemann surfaces and another component homeomorphic to the moduli space of Klein surfaces. I'll discuss a lattice point count on this moduli space, weighted by a polynomial in b known as the measure of non-orientability. This "refined" lattice point count satisfies a refined version of Norbury's recursion for the count of lattice points on the moduli space of curves. Consequently, we obtain a recursion for the volumes of these moduli spaces that reduces to the Witten-Kontsevich recursion when b=0.

Arithmetic Geometry

Tue, 03. Nov at 13:15

Room 3.007, Rudow...

Charles Vial Bielefeld

Math. Statistics

Wed, 04. Nov at 10:00

HVP 11 a, R.313

Mark Podolski Universität Luxemburg

Langenbach

Wed, 04. Nov at 14:15

R. 405/406

Martin Kružík Czech Academy of Sciences Prague, CZ

Villa Seminar

Thu, 05. Nov at 14:00

FU Berlin, Villa ...

Alex Lassota

Optimization

Thu, 05. Nov at 15:15

Rudower Chaussee ...

Patrick Heimbach Oden Institute for Computational Engineering and Sciences, University of Texas at Austin

Differentiable programming for hybrid Earth system modeling

Abstract.

Despite the revolution in autonomous in-situ and satellite remote sensing, much of the ocean remains poorly sampled observationally in terms of its spatio-temporal evolution. Inverse methods seek to combine the incomplete knowledge reservoirs from sparse observations and numerical models that require the provision of uncertain inputs to produce optimal state and parameter estimates of the system considered. In its various renderings, methods of optimal estimation and control or data assimilation are being used to learn uncertain parameters (calibration problem) in models or to produce optimal initial states for prediction (extrapolation problem). State estimates serve as optimal reconstructions to improve system understanding (interpolation problem). Rigorously applied, these methods also enable characterization of uncertainty that arise from different sources (model, observations, forcings). Scientific machine learning methods rely on similar mathematical concepts that underpin optimal estimation and may be successful when the system is heavily sampled. In this presentation I explore some of the concepts in the context of ocean modeling, in particular the concept of differentiable programming. I provide a subjective perspective on opportunities and challenges with a view toward hybrid data assimilation and machine learning to enable online or full-model learning. These ideas are being implemented in the context of general-purpose automatic differentiation applied to a new ocean model written in the Julia programming language.

MATH+ Friday

Fri, 06. Nov at 14:15

Silvia De Toffoli IUSS Pavia

Mathematics After AI

Math. Physics

Tue, 10. Nov at 11:15

1.023 (BMS Room, ...

Davide Scazzuso HU Berlin

A novel open/closed duality on toric Calabi--Yau threefolds

Abstract.

The study of A-model topological string theory on toric Calabi--Yau threefolds X occupies a distinguished position at the crossroads of physics and mathematics, as it provides a tractable framework for string theory in which quantum string amplitudes can be defined rigorously and computed exactly. In this talk, I will discuss the open-closed A-model on X in the presence of Aganagic--Vafa special Lagrangian A-branes, as well as the closed A-model on X in the presence of Ramond--Ramond fluxes induced by toric B-branes. I will establish an open-closed duality theorem that explicitly relates the amplitudes arising in these two setups, thereby demonstrating that the two A-model configurations provide dual descriptions of the same underlying physical and enumerative problem. If time permits, I will further comment on the conjectural interpretation of the duality in terms of the geometric engineering of surface and line defects in four-dimensional N=2 gauge theory.

Arithmetic Geometry

Tue, 10. Nov at 13:15

Room 3.007, Rudow...

Gregorio Baldi Jussieau

Group Theory

Tue, 10. Nov at 14:00

MA 366

Dominic Bunnett Berlin

Math. Statistics

Wed, 11. Nov at 10:00

ESH, Anton-Wilhel...

Simon Weißmann Universität Mannheim

Optimization

Thu, 12. Nov at 15:15

Rudower Chaussee ...

Rohit Pochampalli HU Berlin

Stochastic Analysis

Thu, 12. Nov at 17:15

HU Berlin, Instit...

Federica Masiero University of Milano-Bicocca

Math. Physics

Tue, 17. Nov at 11:15

1.023 (BMS Room, ...

Ivan Dneprov University of Mons

Group Theory

Tue, 17. Nov at 14:00

MA 366

Óscar Fenández Ayala Braunschweig

Math. Statistics

Wed, 18. Nov at 10:00

ESH, Anton-Wilhel...

Botond Szabo Bocconi University

Random Systems

Wed, 18. Nov at 11:30

WIAS-406

Vinicio Rodrigues Moreira UFMG Brazil

Random Systems

Wed, 18. Nov at 11:30

WIAS-406

Vinicio Rodrigues Moreira UFMG Brazil

Langenbach

Wed, 18. Nov at 14:15

WIAS, Erhard-Schm...

Gianna Götzmann U Augsburg

Perturbed minimizing movements of time-dependent functionals on metric spaces

Abstract

Math. Physics

Thu, 19. Nov at 14:00

1.023 (BMS Room, ...

Nathanaël Berestycki Universität Wien

Near-critical dimers and sine-Gordon model

Abstract.

We consider the dimer model with Temperleyan boundary conditions on the square lattice (or more generally isoradial superpositions). When the edge weights are critical it is well known since the work of Kenyon that in the scaling limit, the associated height function is conformally invariant and is described by the Gaussian free field (aka massless free boson). We consider here a massive perturbation of this model, where the edge weights deviate slightly from their critical values. I will discuss a recent result, obtained jointly with Scott Mason and Lucas Rey, in which we showed that the associated height function is described in the scaling limit by the sine-Gordon model at its free fermion point. In parallel, geometric interfaces naturally associated via Temperley's bijection were previously shown (in joint work with Levi Haunschmid-Sibitz) to converge to a massive variant of SLE (Schramm--Loewner Evolution) introduced by Makarov and Smirnov. We will strive to present these ideas in a non-technical manner; in particular no probability background should be needed.

Arithmetic Geometry

Tue, 24. Nov at 13:15

Room 3.007, Rudow...

Javier Fresán Jussieau

Math. Statistics

Wed, 25. Nov at 10:00

ESH, Anton-Wilhel...

Christoph von Tycowicz Zuse Institute Berlin (ZIB)

Symmetry-preserving geodesic regression on Lie Groups for longitudinal medical imaging

Abstract.

Many medical imaging tasks require statistical modeling of continuous transformations, including longitudinal anatomical shape change and articulated skeletal motion. These transformations naturally live on Lie groups, where meaningful statistical analysis should respect group symmetries to remain invariant to arbitrary coordinate choices and reference frames. In this talk, I will present a geodesic regression framework on Lie groups for longitudinal imaging data. Common approaches rely on Riemannian metrics, but many Lie groups do not admit a metric fully compatible with the group structure. This mismatch breaks symmetry and leads to unstable regression estimates. We therefore introduce a non-metric, bi-invariant estimator that is equivariant under both left and right group actions. We evaluate the method on synthetic data and on an open-access clinical dataset of longitudinal knee joint configurations acquired for osteoarthritis research. The proposed approach yields stable trajectories and reproducible statistical conclusions, while state-of-the-art Riemannian methods exhibit sensitivity and instability. These results highlight the practical advantages of symmetry-preserving statistical modeling in longitudinal medical imaging studies.

Random Systems

Wed, 25. Nov at 11:30

WIAS-406

Ulrik Thinggaard Hansen University of Innsbruck

Discrete Math

Wed, 25. Nov at 16:30

IMoS 3003

Yan Alves Radtke

Fast Counting of Cyclic Polytope Triangulations

Stochastic Analysis

Thu, 26. Nov at 16:15

HU Berlin, Instit...