Seminar Talks

Abstract: Stochastic convex optimization is a well understood problem when the learner has access to first-order feedback. However, when the learner can only access noisy function evaluations instead of the gradients, a logarithmic gap between upper and lower bounds has remained even in dimension one.

In this talk, we will consider this problem of stochastic convex Derivative-Free Stochastic Convex Optimization in One Dimensionoptimization with zeroth-order feedback, present the tools that can be used instead of gradient and introduce a new adaptive algorithm which closes this logarithmic gap.

Azadeh Parvaneh (Bielefeld University)

Large Deviation Principle for Friendship Biases in Galton-Watson Trees

Seminar "Interacting Random Systems" at WIAS Berlin, Room 405-406, 11:30 AM

Abstract: The friendship bias of a vertex is defined as the difference between the average degree of its neighbours and its own degree; for isolated vertices, this bias is considered to be zero. According to the sign of the friendship bias, vertices can naturally be classified as "negative", "neutral", or "positive". The friendship paradox says that the average friendship bias is non-negative for all finite undirected graphs, whether simple graphs or multigraphs. However, the combined number of neutral and positive vertices can be significantly smaller than the number of negative vertices. For instance, in a complete graph on a large number of vertices with a single edge removed, only the two endpoints of the removed edge are positive, while all other vertices are negative. The fractions of different vertex types can also vary across graphs and reflect aspects of the geometry of a graph. The typical behaviour of these fractions has been studied for sparse random graphs that are locally tree-like, as well as for finite and infinite Galton-Watson trees. In this talk, we analyse the atypical behaviour of the fractions of vertex types along a random downward path in an infinite Galton-Watson tree by deriving a large deviation principle as the branching depth grows. The rate function is characterised through a variational problem involving relative entropy under a linear constraint. We discuss its properties in the case of binary branching.

Based on joint work with Frank den Hollander.

Tom ter Elst (Department of Mathematics, University of Auckland, New Zealand)

The variational solution of the Dirichlet problem for elliptic operators with complex lower-order coefficients

Langenbach-Seminar at WIAS Berlin, Erhard-Schmidt lecture room, 2:15 PM

Abstract: can be found here

Lukas Wessels (Université Côte d’Azur, Nice)

On Mean Field Games and Mean Field Control in Infinite Dimensions

Berlin Probability Colloquium at IMoS (TU Berlin), 4:15 PM

Abstract: Mean field games (MFGs) and mean field control (MFC) provide a mathematical framework for modeling large controlled interacting particle systems, with applications ranging from financial mathematics to biological neural networks. In the first part of this talk, I will give an accessible introduction to MFGs and MFC. I will then show how the infinite-dimensional case arises naturally in applications, highlight its specific analytical challenges, and provide an overview of my recent results.

In the second part of the talk, I will detail how we address these challenges in recent joint work with A. Święch, where we investigate an MFG posed in a Hilbert space and driven by degenerate noise. We study the associated MFG system consisting of a Hamilton–Jacobi–Bellman (HJB) equation for the value function coupled with a nonlinear Fokker–Planck (FP) equation for the distribution of the particles, both governed by a degenerate Kolmogorov operator. This degeneracy introduces significant analytical challenges. In particular, the HJB equation is treated in the viscosity sense, while the FP equation is interpreted in a suitable weak formulation. Proving the uniqueness of solutions to the FP equation becomes particularly delicate. Under appropriate structural assumptions, we establish the well-posedness of the MFG system.

[1] A. Święch and L. Wessels, Mean field games in Hilbert spaces with degenerate diffusion: a viscosity solution approach, preprint, arXiv:2605.12690 (2026)

Alejandro Ramirez (NYU)

A universality property of the one-sided ballistic deposition model near the time axis

Berlin Probability Colloquium at IMoS (TU Berlin), 5:15 PM

Abstract: Ballistic deposition is a model of interface growth introduced by Vold in 1959, which has remained largely mathematically intractable. It is defined as a process of vertically falling blocks that stick to the top, the right or the left of growing columns. We introduce a variant, the one-sided ballistic deposition model, in which vertically falling blocks can only stick to the top or the upper right corner of growing columns. We establish that in dimension d=2, strong KPZ universality holds near the time axis, proving that the fluctuations of the height function there are given by the Tracy-Widom GUE distribution. The proof is based on a graphical construction of the process in terms of a last passage percolation model. This talk is based on a joint work with Pablo Groisman, Santiago Saglietti and Sebastián Zaninovich.

Andrea V. Hurtado-Quiceno (RPTU Kaiserslautern)

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

Seminar "Rough Analysis an dStochastic Dynamics" at TU Berlin, IMoS room 2003, 11:00 AM

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.

Federico Cannerozzi (Bielefeld)

Singular Mean-Field Control via singular Mean-Field Games

Research Seminar Stochastic Analysis & Finance at HU Berlin, Rudower Chaussee 25, Room 1.115, 4:15 PM

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.

Ziyu Huang (HU Berlin)

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

Research Seminar Stochastic Analysis & Finance at HU Berlin, Rudower Chaussee 25, Room 1.115, 5:15 PM

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.

Kolyan Ray (Imperial College London)

Bayesian regression models with dense confounding variables

Research Seminar Mathematical Statistics at WIAS Berlin, Erhard-Schmidt lecture room, 10 AM

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.

Clara Thierbach (HU Berlin)

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

Langenbach-Seminar at WIAS Berlin, Erhard-Schmidt lecture room, 2:15 PM

Abstract: The Aviles-Giga functional is one of the most prominent models arising in the variational modelling of pattern formation in materials. It has applications ranging, e.g., from blistering phenomena in thin films to liquid crystals. In this talk, we will discuss a characterization of the associated Gibbs measure in the sense of statistical mechanics. For that, we build on ideas that were developed by N. Barashkov and M. Gubinelli in [1] in the context of the Φ^4_d model.

[1] N. Barashkov and M. Gubinelli. A variational method for ϕ^4_3. Duke Mathematical Journal, 169(17), November 2020

Nicolas Verzelen (INRAE)

TBA

Research Seminar Mathematical Statistics at WIAS Berlin, Erhard-Schmidt lecture room, 10 AM

Abstract: TBA

Lars Schröder (University of Twente)

TBA

Seminar "Interacting Random Systems" at WIAS Berlin, Room 405-406, 11:30 AM

Abstract: TBA

Yifan Jiang (Imperial College London)

Local-Global Convergence and Optimal Control on Graphings

Berlin Probability Colloquium at IMoS (TU Berlin), 4:15 PM

Abstract: We develop a general framework for optimization and stochastic control problems on large sparse graphs, where a control is assigned to each vertex and the objective aggregates local cost functionals depending on neighboring vertices. A central question is how such problems behave as the graph grows. It turns out that locally convergent sparse graphs can have divergent optimal values. Instead, we identify local-global convergence as the appropriate notion, with graphings serving as the limiting objects. For a broad class of graph optimization problems, we prove the convergence of optimal values to their graphing counterparts and derive first-order optimality conditions for the limiting problem. Furthermore, we extend the theory to dynamic decentralized stochastic control problems and establish a stochastic maximum principle for the corresponding graphing control problem. This talk is based on a joint work with Eyal Neuman and Sturmius Tuschmann.

René Aïd (Université Paris-Dauphine)

TBA

Berlin Probability Colloquium at IMoS (TU Berlin), 5:15 PM

Abstract: TBA

Philipp Schmocker (ETH Zürich)

TBA

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.

Abstract: TBA

Recent Talks

Herbert Koch (Universität Bonn)

Smoothed scattering: Randomized initial data and the deterministic case

Oberseminar Analysis-Probability at MPI Leipzig, E1 05 (Leibniz-Saal), 3:15 PM

Abstract: In this joint word with Nicolas Burq, Nicola Visciglia and Nikolay Tzvetkov we consider two different cases for scattering and prove that the scattering operator minus the identity is more regular than the initial data. For randomized initial data we use the lens transform to transform the problem to a finite interval. In the deterministic case for the nonlinear Schrödinger equation and the Korteweg-de Vries equation with nonlinearity |u|^p u, p >4 we use a local smoothing estimate and a maximal estimate to gain up to one derivative for the difference above.

Felix Medwed (U Potsdam)

Recovering the Length of a Path from its Signature

Seminar "Rough Analysis an dStochastic Dynamics" at TU Berlin, IMoS room 2003, 11:00 AM

Abstract: A central question in rough path theory is how geometric information about a path is reflected in its signature, the formal series of its iterated path integrals. In their seminal work, B. Hambly and T. Lyons (2010) showed that, for bounded variation paths in finite-dimensional spaces, the signature transformation determines the path up to a natural notion of equivalence, called tree-like equivalence. Moreover, every such equivalence class contains a unique representative that has no redundant backtracking, named the tree-reduced path. This result was later generalised by H. Boedihardjo, X. Geng, T. Lyons and D. Yang to weakly geometric rough paths in arbitrary real Banach spaces. In the same work, B. Hambly and T. Lyons proved, under additional regularity assumptions and for suitable tensor norms, that the length of the tree-reduced path can be recovered from the asymptotic behaviour of its normalised signature. Subsequently, J. Chang, T. Lyons and H. Ni (2018) established the corresponding limit to exist also for general bounded variation paths over arbitrary Banach spaces and conjectured the same recovery to hold for the choice of reasonable tensor algebra norms. This problem is now commonly referred to as the length conjecture and H. Boedihardjo and X. Geng (2022) later gave a more precise formulation as well as proving the conjecture for a class of planar tree-reduced paths using sl₂-developments. The main difficulty of the conjecture lies in establishing a suitable lower estimate for the normalised signature. Our approach, while inspired by the underlying initial strategy of H. Boedihardjo and X. Geng, differs in that we relate natural powers of polygonal approximations back to the signature, and identify a family of continuous functionals that allow for controlled growth. In this talk, I will explain the core ideas behind this approach and show how, together with the existence result of Chang–Lyons–Ni, they give the required lower bound. This allows us to prove the length conjecture in the general setting.

Martin Bordemann (Université de Haute Alsace)

Multiplication of differential operators in terms of connections using Lie-Rinehart algebras

Algebraic and Combinatorial Perspectives in the Mathematical Sciences via Zoom, 3 PM

Abstract: The multiplication of two differential operators in an open set of R^n is explicitly known in terms of their standard symbols: This is a motivating point for the theory of deformation quantization. On a differentiable manifold equipped with a connection ∇ in the tangent bundle the same formula --where partial derivatives are replaced with symmetrized covariant derivatives-- will be wrong in general, and one has to correct it by terms containing torsion and curvature and their covariant derivatives. In the talk, based on our work with my PhD student Hamilton Menezes de Araujo 2021, we shall give an `explicit formula' of the corrected formula in the more algebraic framework of Lie-Rinehart algebras L (G.S.Rinehart, 1963, which are now being used in the study of singular foliations) over a commutative unital K-algebra A (where the ground ring K should contain the rational numbers as a subring). Similar results have been obtained independently by M.Al-Kaabi, K.Ebrahimi-Fard, D.Manchon, and H.Munthe-Kaas (2022) and X.Bekaert, N.Kowalzig, and P.Saracco (2022). L generalizes the Lie algebra of vector fields (more generally a Lie algebroid) and A the algebra of smooth functions in differential geometry. The enveloping algebra of L over A introduced by Rinehart plays the rôle of the differential operator algebra. The arising combinatorial problems can conveniently be treated in terms of the fibrewise shuffle comultiplication in the free algebra generated by L over A and the associated convolution products. The torsion and curvature terms arise in a morphism of Lie-Rinehart algebras Z from the free Lie algebra generated by L over A equipped with a Lie-Rinehart bracket isomorphic to the one on M.Kapranov's `free path Lie algebroid' (2007) to L which are related to the (infinitesimal) holonomy of the connection. Z is obtained by a simple explicit linear recursion.

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