Seminar Talks

Abstract: In this talk, we will present a selection of recent theoretical results on high-dimensional inference for the drift component of diffusion models. Such models have found numerous applications in areas including mathematical finance and biology among others. The primary focus will be on drift estimation for high-dimensional Ornstein--Uhlenbeck processes, although we will also discuss extensions to more general linear and nonlinear diffusion models. In particular, we will present Lasso-type estimators for sparse drift matrices, establish their statistical guarantees, and discuss consistent support recovery property. In the second part of the talk, we will consider drift estimation under low-rank constraints, a framework closely related to the concept of cointegration in continuous time.

The presentation is based on joint work with Gabriela Ciołek, Dmytro Marushkevych, and Francisco Pina.

Martin Kružík (Czech Academy of Sciences Prague, CZ)

The effects of pressure loads in the dimension reduction of elasticity models

Langenbach-Seminar at WIAS Berlin, Room 405-406, 2:15 PM

Abstract: We study the dimensional reduction from three to two dimensions in hy perelastic materials subject to a live load, modeled as a constant pressure force. Our results demonstrate that this loading has a significant impact in higher-order scaling regimes, namely those associated with von K´arm´an-type theories, where a nontrivial interplay arises between the elastic energy and the pressure term. In contrast, we rigorously show that in lower-order bend ing regimes, as described by Kirchhoff-type theories, the pressure load does not influence the minimizers. Finally, after identifying the corresponding Γ-limit, we conjecture that a similar independence from the pressure term persists in the most flexible membrane regimes. This is a joint work with F. Riva (Prague).

Kexing Ying (EPFL)

Non-explosion of rough differential equations with applications to stochastic flows

Seminar "Rough Analysis and Stochastic Dynamics" at TU Berlin, IMoS 2003, 1:30 PM

Abstract: We study rough differential equations (RDEs) with unbounded coefficients and provide sharp conditions for non-explosion. This allows us to show the existence of a global continuous solution flow for stochastic differential equations (SDEs). Already in the additive noise case, this question is subtle and in fact, noise induced path-wise explosion can be observed for a class of rotating SDEs implying the lack of a continuous solution flow. This result is then extended to the branched rough path setting allowing us to cover the case of SDEs driven by fractional Brownian motion with Hurst parameter H>1/4.

Julian Kern (FU Berlin)

Transformers and large language models

Research Seminar Stochastics at FU Berlin, Arnimallee 3, SR 024, 2 PM

Simon Weißmann (Universität Mannheim)

Stochastic Optimization and Regularization for Inverse Problems

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

Abstract: In this talk, I will investigate two perspectives on the interaction between regularization and stochastic optimization. In the first part, I will present stochastic gradient methods with decaying Tikhonov regularization and show that a suitably balanced vanishing regularization schedule can stabilize the optimization dynamics while preserving convergence to a solution of the original unregularized problem. In the second part, I will turn to data-driven variational regularization, formulated as a stochastic bilevel optimization problem. In this setting, each upper-level evaluation requires a computationally expensive and typically inexact lower-level solve. This naturally motivates the use of multilevel Monte Carlo methods, whose efficiency depends critically on the coupling between successive lower-level approximations.

Gabriele Steidl (TU Berlin)

TBA

Berlin Probability Colloquium at TU Berlin, IMoS 0005, 5:15 PM

Abstract: TBA

Bernhard Eisvogel (FU Berlin)

Pretraining, scaling, in-context learning

Research Seminar Stochastics at FU Berlin, Arnimallee 3, SR 024, 2 PM

Federica Masiero (Università degli Studi di Milano-Bicocca)

TBA

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

Abstract: TBA

Botond Szabo (Bocconi)

Robust Gaussian process regression: posterior contraction

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

Abstract: Gaussian processes form a popular and flexible class of prior distributions with principled uncertainty quantification, but the Gaussian likelihood on which they rely makes them highly sensitive to outliers and contaminated observations. We study Gaussian process regression when among the n observations, m of these are possibly contaminated. A generic framework to obtain posterior contraction rates in this setting is considered, from a frequentist perspective as the sample size n and the number of corrupted observations m grow. We adopt a generalised Bayes approach in which the log-likelihood is replaced by a robustified version; we discuss various choices thereof, such as one recently proposed by Altamirano et al. (2024) that preserves conjugacy. We investigate the minimax rate of estimation under adversarial contamination in terms of the Sobolev smoothness of the regression function and m. The question of building adaptive procedures to both Sobolev smoothness and m is investigated, and we show that a polynomial loss for adaptation must be paid in general. We instantiate our results for Matern Gaussian process and deep ReLU network priors. Numerical experiments for existing and new robust algorithms are provided, illustrating the practical applicability of our results.

Vinicio Rodrigues Moreira (UFMG Brazil)

TBA

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

Abstract: TBA

Gianna Götzmann (U Augsburg)

Perturbed minimizing movements of time-dependent functionals on metric spaces

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

Abstract: Minimizing movement schemes are a fundamental tool for approximating evolution equations that have a gradient-flow structure with respect to an energy. Motivated by homogenization problems involving, for instance, geo metries that evolve in time, we consider Γ-converging perturbations of time dependent driving energies. We study the convergence of the corresponding minimizing movement scheme and provide sufficient conditions under which limits of the scheme are (time-dependent) curves of maximal slope for the limit energy. We further exhibit examples showing that, in general, such a stability property may fail, with the limit motion depending on the rela tion between the time-discretization parameter τ and the perturbation pa rameter ε. This is joint work with Jan-Frederik Pietschmann and Antonio Tribuzio.

Dave Jacobi (FU Berlin)

Reasoning models and reinforcement learning

Research Seminar Stochastics at FU Berlin, Arnimallee 3, SR 024, 2 PM

Christoph von Tycowicz (Zuse Institut Berlin (ZIB))

Symmetry-preserving Geodesic Regression on Lie Groups for Longitudinal Medical Imaging

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

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.

Ulrik Thinggaard Hansen (University of Innsbruck)

TBA

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

Abstract: TBA

Ana Damnjanovic (FU Berlin)

Information geometry and gradient methods

Research Seminar Stochastics at FU Berlin, Arnimallee 3, SR 024, 2 PM

Jung-Wook Kim (CERN)

TBA

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

Abstract: TBA

Purba Das (King's College)

TBA

Abstract: PDEs model real world systems and build the basis of many downstream applications in optimization, control or uncertainty quantification. To ensure alignment, non-observable model parameters are identified that reconstruct observed data from the real system. The quality of this model fitting procedure depends highly on a-priori knowledge and the quality of data. In this talk we look at how these interact, and present three results in this realm and an outlook on ongoing work.

A theoretical study exhibits identifiability of the turning coefficient in a run-and-tumble model for bacterial chemotaxis. Reconstructing this microscopic quantity from experiments that only see the macroscopic bacteria density poses a challenge that we overcome by a delicate construction of an experimental data collection strategy.

Second, we propose a new perspective and methodology for experimental design when no such construction is available. Relaxing the search from an optimal to a sufficient design allows us to down-sample experiments according to their sensitivity, an idea borrowed from randomized linear algebra. This keeps the parameter identifiable with high probability.

Third, we reconciliate two formulations of gradient-based model fitting for the Fokker–Planck equation, arising from the PDE and particle formulation. Discretization yields gradient estimators that converge at the same rate in the number of particles.

We conclude with work in progress on particle-based sampling methods and on uncertainty quantification for equations learned from data.

Adrian Celestino (U Münster)

TBA

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

Abstract: TBA

Giulia Liveri (LSE)

TBA

Abstract: TBA

Randolf Altmeyer (Imperial College London)

TBA

Abstract: TBA

Recent Talks

Christoph Czichowsky (LSE)

No-Arbitrage, Superreplication and Utility Maximisation in Propagator Price Impact Models

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

Abstract: Propagator models describe transient price impact by allowing execution prices to depend on the entire history of past trades through a Volterra kernel. While such models capture empirically observed features of market microstructure, they lead to infinite-dimensional and non-Markovian optimisation problems that fall outside the scope of classical arbitrage and duality theory. In this talk, I develop a comprehensive mathematical finance framework for propagator models, including a fundamental theorem of asset pricing, a superreplication theorem with liquidity-adjusted risk measures, and a convex-duality approach to utility maximisation. Despite non-linear preferences and path-dependent price impact, optimal strategies are obtained by solving a suitably constructed dual problem over a family of fictitious frictionless financial markets.

Philipp Schmocker (ETH Zürich)

Smooth structures on spaces of probability measure

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

Abstract: We introduce a categorical framework for higher-order probability theory based on quasi-M-spaces and Frölicher M-spaces. Besides Giry’s and Forr´e’s probability monads, we introduce our own hybrid pushforward probability monad generated by randomizations of a fixed reference measure. These constructions are canonically transported to saturated Frölicher M-spaces, yielding, in the measurable setting, Giry and quasi-probability monads on the corresponding Frölicher spaces. In the smooth setting, the resulting spaces of probability measures carry a natural smooth structure, which can be related to the continuity equation, Otto calculus and Lions’ derivative. This is joint work with Philipp Harms, Peter W. Michor and Josef Teichmann.

Carlos Villanueva Mariz (FU Berlin)

From regression to neural networks

Research Seminar Stochastics at FU Berlin, Arnimallee 3, SR 024, 2 PM

Ziyu Huang (HU Berlin)

An FBSDE Approach to PDEs in Mean Field Problems: from Mean Field Control to Mean Field Game

Seminar "Rough Analysis and Stochastic Dynamics" at TU Berlin, IMoS 2003, 11:00 AM

Abstract: Mean field control problems and mean field games lead to partial differential equations on spaces of probability measures. In this talk, we present a probabilistic approach to constructing classical solutions of the associated Bellman and master equations through forward-backward stochastic differential equations (FBSDEs). Starting with mean field control under linear dynamics and convexity assumptions, we explain how the well-posedness of the optimality system and its variational equations yield the regularity of the value function. We then discuss extensions to jump-diffusion models and to control problems in which a backward equation forms part of the state. Finally, we explain how related FBSDE methods, together with population consistency, apply to master equations in mean field games.

Felix Medwed (U Potsdam)

TBA

Seminar "Rough Analysis and Stochastic Dynamics" at TU Berlin, IMoS 2003, 10:00 AM

Abstract: TBA

René Aïd (Université Paris-Dauphine)

A Stationary Mean-Field Model for Carbon Market Stability Reserve

Berlin Probability Colloquium at TU Berlin, IMoS 0005, 5:15 PM

Abstract: We formulate the design of a market stability reserve as a stationary mean field singular control problem. The allowance balance follows a regime-switching diffusion, while the regulator injects or withdraws allowances through bounded variation controls. The objective trades off the average allowance balance, its stationary dispersion, deviations from a long-run target, and intervention costs. The optimal policy is a regime-dependent band rule characterized by four reflecting thresholds. Its computation reduces to a scalar fixed-point problem combining a coupled variational inequality with the invariant distribution of the reflected process. A calibration to the EU ETS yields thresholds of the same order of magnitude as the existing Market Stability Reserve rule. Comparative statics show that volatility is the main determinant of the intervention band, whereas the frequency and duration of crisis regimes have limited effects. A simpler two threshold policy based on average regime dynamics closely reproduces the optimal regime-dependent policy in terms of liquidity and intervention volumes.

Joint work with Giorgio Ferrari and Federico Cannerozzi (Bielefeld University).

Yifan Jiang (Imperial College London)

Local-Global Convergence and Optimal Control on Graphings

Berlin Probability Colloquium at TU Berlin, IMoS 0005, 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.

Lars Schröder (University of Twente)

The Geometry of Hierarchical Navigation

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

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+ϵ)-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.

Nicolas Verzelen (INRAE)

Statistical–Computational Trade-offs: Low-Degree Polynomials and Community Recovery

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

Abstract: In many high-dimensional problems, such as planted clique, sparse PCA, clustering and community detection, the signal strength needed by the best known polynomial-time algorithms is much larger than what is information-theoretically necessary. Is this gap intrinsic? Since NP-hardness says nothing about random instances, evidence of hardness must come from other sources: average-case reductions, or lower bounds for broad classes of algorithms.

In the first part, I will introduce the low-degree polynomial framework, starting from testing problems in additive models. In the Gaussian additive model, the χ² divergence and the low-degree advantage admit simple expressions in terms of the overlap between two independent copies of the signal. Comparing them shows how truncating at a low degree discards the rare large overlaps that only exhaustive search can exploit.

In the second part, based on joint work with Alexandra Carpentier and Christophe Giraud, I will consider community recovery in the stochastic block model with more than √n communities. We prove that low-degree polynomials fail below a threshold conjectured by Chin, Mossel, Sohn and Wein, for any graph density, and that this threshold lies below the Kesten–Stigum threshold. We also show that counting suitable motifs succeeds above it in moderately sparse regimes. These motifs are dictated by the lower-bound analysis: cliques, paths, and blow-ups of cycles.

Ryoji Takano (Tokyo Metropolitan University)

Freidlin–Wentzell type large deviation principle for rough differential equations driven by fractional Brownian motion

Seminar "Rough Analysis and Stochastic Dynamics" at TU Berlin, IMoS 2003, 11:00 AM

Abstract: In this talk, we establish a Freidlin—Wentzell type large deviation principle for solutions to rough differential equations driven by fractional Brownian motion. Matsuda and Mayorcas (2025) studied regularization by noise for multiplicative stochastic differential equations driven by fractional Brownian motion. In this setting, Lyons’ continuity theorem cannot be applied, making the derivation of a large deviation principle for the solutions a nontrivial task. One of our contributions is to demonstrate that the weak convergence method is effective even within the framework of rough path theory, where Itô calculus is not applicable. This is joint work with Peter K. Friz (TU Berlin).

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

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.

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.

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.

Gabriel Riffo (TU Berlin)

Universal Varieties for Signatures of Membranes

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

Abstract: Membranes are sufficiently smooth vector-valued functions defined on the unit square, widely used in applications such as interpolation of image data. The signature of a membrane is a collection of nonlinear features that capture its essential geometry. We index these features in the graded Hopf algebra of two-parameter shuffle products and study the algebraic varieties for each graded component. At each truncation level, we obtain the dimension of this variety via a novel Witt-type formula. We propose a Chen–Chow theorem for membranes, which we prove at the second truncation level and conjecture for higher levels, supported by extensive computational evidence from our open-source package SignatureTensors.jl, implemented in the computer algebra system OSCAR.

This is joint work with Carlos Améndola and Leonard Schmitz.

Andrea V. Hurtado-Quiceno (RPTU Kaiserslautern)

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

Seminar "Rough Analysis and Stochastic Dynamics" at TU Berlin, IMoS 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.

Alejandro Ramirez (NYU)

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

Berlin Probability Colloquium at TU Berlin, IMoS 0005, 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.

Lukas Wessels (Université Côte d’Azur, Nice)

On Mean Field Games and Mean Field Control in Infinite Dimensions

Berlin Probability Colloquium at TU Berlin, IMoS 0005, 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)

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

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.

Chloé Rouyer (U Potsdam)

Derivative-Free Stochastic Convex Optimization in One Dimension

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

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.

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 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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