Seminar Talks

Here is a list of seminars that are relevant for our members:

Berlin Probability Colloquium, every other Wednesdays 4pm+

Berliner Oberseminar Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar), Wednesdays 3pm

Research Seminar Stochastic Analysis & Finance, every other Thursday 4pm+

Research Seminar Rough Analysis and Stochastic Dynamics at TU, Thursdays 11am+

Research Seminar Stochastics at FU, Mondays 10am+

Analysis Seminar Potsdam, Fridays 11am+

Forschungsseminar Mathematische Statistik, Wednesdays 10am+

Seminar Interacting Random Systems, Wednesdays 11:30

Algebraic and Combinatorial Perspectives in the Mathematical Sciences, Fridays 3pm+ (online)

Oberseminar Analysis-Probability, Tuesdays 3pm+

Upcoming talks are also posted in the monthly newsletter.

Seminars from Winter Term 2025/26
Past talks from this term can be found at the bottom of this page.

Upcoming Talks

Vladimir Spokoiny (WIAS)

Estimation of a smooth functional for inverse problems

Forschungsseminar Mathematische Statistik at WIAS Berlin, Erhard-Schmidt lecture room, 10:00 AM

Abstract: Since the seminal paper by Ibragimov and Khasmisnkii (1980) it is well known that the plug-in approach is sub-optimal in estimating a nonlinear functional like the squared norm of the signal. A kind of bias correction is necessary to achieve root-n optimality. Series of recent papers by Koltchinskii with coauthors revisited this problem from modern prospective with a high or even dimensional parameter space and a complex structure of the functional to be estimated. This talk discusses the problem of estimation of a smooth functional in the inverse problem setup given by an objective function L(θ).

A different view is offered. Namely, the functional φ(θ) is included in the parameter list as the target value, while the parameter θ is treated as a nuisance parameter. The structural relation x = φ(θ) is replaced by the structural penalty (λ|x − φ(θ))2. The resulting estimator is obtained as a third-order correction (xˆ, θˆ) of the full-dimensional penalized MLE (x ̃, θ ̃) = arg inf(x,θ) L(θ) + λ|x − φ(θ)|2/2. The approach enables us to obtain an accurate expansion with an explicit leading term and self-consistent remainder and provides sharp risk bounds for this estimator. In particular, we present sufficient conditions for root-n consistency of the procedure.

Keefer Rowan (EPFL)

Sharp pathwise nonuniqueness for additive SDEs

Berlin Probability Colloquium at TU Berlin, room MA-043, 5:15 PM

Abstract: We construct a family of random velocity fields demonstrating the sharpness of the classical Zvonkin–Veretennikov–Davie strong well-posedness by noise regime. We consider stochastic differential equations driven by Brownian noise with drift u and show that for any α < 0, there exists a velocity field u ∈ Lt∞ Cxα that admits a unique weak solution but does not satisfy pathwise uniqueness (and hence has no strong solutions). This contrasts with the case α ≥ 0, for which the existence of a unique strong solution is guaranteed. The velocity field construction is random, and the proof essentially uses cen tral limit theorem scaling through the Berry–Esseen theorem. We also give natural extensions to non-Brownian driving noises, including nonuniqueness for arbitrary driving noises with certain H¨older regularities and an analo gous sharpness of the strong well-posedness by noise regime for fractional Brownian motions.

Fabio Bugini (TU Berlin)

Rough Stochastic Kalman-Bucy Filter

Research Seminar Rough Analysis and Stochastic Dynamics at TU Berlin, room MA-748, 11:00 AM

Abstract: In this talk, we adopt a rough path perspective on the classical Kalman-Bucy filtering problem with conditionally linear dynamics and correlated noise. By treating the observation process as a deterministic rough path, the signal dynamics are formulated as Rough Stochastic Differential Equations (RSDEs) with linear coefficients, in the sense of Friz, Hocquet, and Lê. We show that under a Gaussian initial condition, the distribution of the rough signal process remains Gaussian, and we characterize its mean and covariance as solutions to deterministic Rough Differential Equations (RDEs). In particular, the covariance satisfies a linear-quadratic Riccati RDE, for which we establish global well-posedness and non-explosion results that are of independent interest and, to the best of our knowledge, the first for this class of equations. Finally, we show that, when randomised, the RDEs for the mean and the covariance recover the classical Kalman-Bucy filtering equations. Joint work with P.K. Friz, K. Lê, and H. Zhang (arXiv:2509.11825).

Benjamin Massat (Université de Toulouse)

Quantification of limit theorem for Hawkes processes

Research Seminar Stochastic Analysis & Finance at TU Berlin, room MA-043, 4:15 PM

Abstract: Hawkes processes are a popular model for self-exciting phenomena, from earthquakes to finance. In this talk, I will first present them in a simple way, using a Poisson imbedding construction. I will then review what is known about their long-time behavior, through limit theorems for both linear and non-linear cases. The focus will be on three regimes that appear when the process has a long memory and the branching ratio gets close to or above one: the Nearly Unstable, the Weakly Critical, and the Supercritical Nearly Unstable Hawkes processes. These regimes have been studied qualitatively, but quantitative convergence results have been missing. I will explain how we obtain explicit convergence rates, relying on a coupling with a Brownian sheet, Fourier analysis, and a careful approximation of the absolute value function.

Idris Karoubi (Sorbonne Université, Paris)

Mean-field control of non exchangeable systems

Research Seminar Stochastic Analysis & Finance at TU Berlin, room MA-043, 5:15 PM

Abstract: We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal probability laws. We prove the well-posedness of such systems and define the control problem together with its related value function. We next prove a law invariance property for the value function which allows us to work on the set of collections of probability laws. We show that the value function satisfies a dynamic programming principle (DPP) on the flow of collections of probability measures. We also derive a chain rule for a class of regular functions along the flows of collections of marginal laws of diffusion processes. Combining the DPP and the chain rule, we prove that the value function is a viscosity solution of a Bellman dynamic programming equation in a L²-set of Wasserstein space-valued functions.

This talk is based on a joint work with A. De Crescenzo, M. Fuhrman and H. Pham.

Julian Kern (FU Berlin)

Semimartingales forced onto a manifold by a large drift

Research Seminar Stochastics at FU Berlin, SR 115, Arminallee 3, 10 AM

Holger Dette (Ruhr-Universität Bochum)

Multiple change point detection in functional data with applications to biomechanical fatigue data

Forschungsseminar Mathematische Statistik at WIAS Berlin, Erhard-Schmidt lecture room, 10:00 AM

Abstract: Injuries to the lower extremity joints are often debilitating, particularly for professional athletes. Understanding the onset of stressful conditions on these joints is therefore important in order to ensure prevention of injuries as well as individualised training for enhanced athletic performance. We study the biomechanical joint angles from the hip, knee and ankle for runners who are experiencing fatigue. The data is cyclic in nature and densely collected by body worn sensors, which makes it ideal to work with in the functional data analysis (FDA) framework.

We develop a new method for multiple change point detection for functional data, which improves the state of the art with respect to at least two novel aspects. First, the curves are compared with respect to their maximum absolute deviation, which leads to a better interpretation of local changes in the functional data compared to classical $L^2$-approaches. Secondly, as slight aberrations are to be often expected in a human movement data, our method will not detect arbitrarily small changes but hunts for relevant changes, where maximum absolute deviation between the curves exceeds a specified threshold, say $\Delta >0$. We recover multiple changes in a long functional time series of biomechanical knee angle data, which are larger than the desired threshold $\Delta$, allowing us to identify changes purely due to fatigue. In this work, we analyse data from both controlled indoor as well as from an uncontrolled outdoor (marathon) setting.

Quan Shi (AMSS Chinese Academy of Sciences)

Two phase transitions for catalytic branching Markov chains

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

Abstract: Consider a continuous-time branching Markov chain (Zt,t≥0) on a locally finite graph G rooted at o. Each particle moves according to an irreducible Markov process ξ and branches at a rate that depends on their location: the branching rate is

λrt ≥0 at the root and λ≥0 elsewhere. The offspring distribution is supercritical with mean m>1, has no extinction and finite second moment. We characterize the recurrence/transience phase transition for this catalytic branching Markov chain. Furthermore, under suitable assumptions we prove a second phase transition concerning the asymptotic behaviour of the relative empirical density,

(Zt(G))−1Zt, where Zt is the empirical measure of the particles and Zt(G) is the total population size. If (m−1)(λ0−λ)>γesc, where

γesc is the escape probability that ξ never returns to the root, then (Zt(G))−1Zt converges almost surely to a deterministic probability measure. If (m−1)(λ0−λ)∈(0,γesc], then (Zt(G))−1Zt converges almost surely to zero. When the graph is the integer lattice G=Zd and ξ is the simple random walk, our results confirm several conjectures of Mailler and Schapira [Ann. Appl. Probab. 2026], which studied this model via a different approach.

Based on a joint work in progress with Xinxin Chen (Bejing Normal Unversity), Nina Gantert (Technical University of Munich) and Haojie Hou (Beijing Institute of Technology).

Marco Inversi (MPI Leipzig)

TBA

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

Abstract: TBA

Aleks Kissinger (University of Oxford)

TBA

Algebraic and Combinatorial Perspectives in the Mathematical Sciences via Zoom, 3:00 PM

Abstract: TBA

TBA

Berlin Probability Colloquium at TU Berlin, room MA-043, 4:15 PM

Willem van Zuijlen (WIAS, FU Berlin)

Discrete Anderson Hamiltonians with correlated Gaussian potentials

Abstract: TBA

Chiara Rossato (ETH Zurich)

TBA

Research Seminar Stochastic Analysis & Finance at TU Berlin, room MA-043, 5:15 PM

Abstract: TBA

Bao Quoc Tang (Universität Graz)

TBA

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

Abstract: TBA

Recent Talks

Yuchen Sun (HU Berlin) & Carlos Villanueva Mariz (FU Berlin)

Stochastic control for singular diffusions: viscosity solutions & BSDEs

Research Seminar Stochastics at FU Berlin, SR 115, Arminallee 3, 10 AM

Jannis Dause (TU Berlin)

Controlled fields, rough stochastic calculus, and Itô-Wentzell-Alekseev-Gröbner identities

Research Seminar Rough Analysis and Stochastic Dynamics at TU Berlin, room MA-748, 11:00 AM

Abstract: We introduce a calculus of space–time controlled functions for rough stochastic systems, providing a unified composition rule for evaluating random fields along rough semimartingales. This framework yields a rough stochastic Itô–Wentzell formula under natural and verifiable regularity assumptions. Motivated by recent work of Hude et al. (2024) and, independently, Del Moral and Singh (2022), which established forward–backward perturbation identities for diffusion processes, we show how Itô–Alekseev–Gröbner and backward Itô–Wentzell type representations arise naturally within a rough stochastic framework. This is joint work with Peter K. Friz, Arnulf Jentzen and Jian Song.

Stefanie Schindler (WIAS)

Time-asymptotic self-similarity of the damped Euler equations in parabolic scaling variables

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

Abstract: In this talk, we study the long-time behavior of solutions to the compressible Euler equations with frictional damping on the whole space, assuming nonzero direction-dependent values for the density at spatial infinity. By introducing parabolic scaling variables, we reformulate the system and derive a relative entropy inequality. This framework allows us to show that the density converges to a self-similar solution of the porous medium equation, while the limiting momentum is governed by Darcy’s law. We also obtain convergence rates that explicitly depend on the flatness of the limiting profile. The main part of the analysis focuses on weak solutions in the one-dimensional case, and we further extend the results to energy-variational solutions in the multidimensional setting.

This research is joint work with Thomas Eiter (WIAS).

Elena Magnanini (WIAS Berlin)

Non-Standard Fluctuations of the edge density in the edge-triangle Model

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

Abstract: Exponential Random Graph Models extend the classical (dense) Erdős–Rényi random graph by incorporating higher-order structural features through a Hamiltonian formalism inspired by statistical mechanics. Among these, the edge-triangle model is a basic but non trivial example, where the competition between edge and triangle terms leads to a rich phase structure. In this talk we will give an overview of known limit theorems and concentration results for subgraph densities, with particular emphasis on an open problem: a non-standard CLT for the edge density. The conjecture will be supported by a mean-field analysis, which allows for explicit computations and suggests a different fluctuation scaling, while also providing some insight into related open questions.

This talk is based on joint works with A. Bianchi, F. Collet, and G. Passuello.

Felix Medwed (Universität Potsdam)

The signature group for paths of higher variation as an inverse limit

Analysis Seminar Potsdam Campus Golm, Building 9, Room 2.22 and via Zoom, 11:00 AM

Abstract: E. Le Donne and R. Züst (2021) showed that the space of signatures of rectifiable paths is a geodesic metric tree. We extend their result originally formulated in terms of curve length to the setting of p-variation for p > 1. This extension relies on results of Boedihardjo, Geng, Lyons, and Yang (2016) concerning signatures of weakly geometric rough paths, which provide the appropriate analytical control in the p-variation framework. The key components of the original construction are reinterpreted using the language of metric groups, allowing us to define and work with the signature group adapted to p-variation.

Within this framework, we revisit the lifting procedure introduced by Le Donne and Züst - namely, the construction of a canonical lift of a path into a suitable group structure - and show that the main result, concerning the existence and properties of such lifts, continues to hold when length is replaced by p-variation.

Nicola Gnecco (Imperial College London)

Extremes of Structural Causal Models

Forschungsseminar Mathematische Statistik at WIAS Berlin, Erhard-Schmidt lecture room, 10:00 AM

Abstract: The behaviour of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for the observational distribution and under extremal interventions. We show that under suitable regularity conditions on the structure functions, the extremal behavior is described by a multivariate Pareto distribution, which can be represented as a new SCM on an extremal graph. Importantly, the latter is a sub-graph of the graph in the original SCM, which means that causal links can disappear in the tails. We further introduce a directed version of extremal graphical models and show that an extremal SCM satisfies the corresponding Markov properties. Based on a new test of extremal conditional independence, we propose two algorithms for learning the extremal causal structure from data. The first is an extremal version of the PC-algorithm, and the second is a pruning algorithm that removes edges from the original graph to consistently recover the extremal graph. The methods are illustrated on river data with known causal ground truth.

Willem van Zuijlen (WIAS Berlin, FU Berlin)

Discrete Anderson Hamiltonians with correlated Gaussian potentials

Research Seminar Stochastics at FU Berlin, SR 115, Arminallee 3, 10 AM

Jan Mandrysch (Universität Wien)

How to measure quantum fields? Implementing a causal measurement scheme

Analysis Seminar Potsdam Campus Golm, Building 9, Room 2.22 and via Zoom, 1:00 PM

Abstract: While measurement processes in standard quantum mechanics are well understood, the extension of these ideas to quantum field theory (QFT) remains a key challenge. In particular, ensuring that measurements respect fundamental principles such as relativistic causality is crucial. A persistent issue concerning measurements in QFT is, though, that the usual axioms for QFT alone are insufficient to prevent superluminal signaling. In this talk, I will discuss a recent proposal by Fewster and Verch for a local, covariant and causal measurement framework in algebraic QFT. In particular, I will discuss completeness of the framework and motivate its underlying assumptions focussing on the concrete setting of a free scalar field and Gaussian measurements. We conclude that the Fewster-Verch approach is suitable to model typical measurements in QFT.

Tom Klose (University of Oxford)

A Rough Functional Breuer–Major Theorem

Research Seminar Rough Analysis and Stochastic Dynamics at TU Berlin, room MA-748, 11:00 AM

Abstract: We extend the functional Breuer–Major theorem by Nourdin and Nualart (2020) to the space of rough paths. The proof of tightness combines the multiplication formula for iterated Malliavin divergences, due to Furlan and Gubinelli (2019), with Meyer's inequality and a Kolmogorov-type criterion for the r-variation of cadlag rough paths, due to Chevyrev et al. (2022). Since martingale techniques do not apply, we obtain the convergence of the finite-dimensional distributions through a bespoke version of Slutsky's lemma: First, we overcome the lack of hypercontractivity by an iterated integration-by-parts scheme which reduces the remaining analysis to finite Wiener chaos; crucially, this argument relies on Malliavin differentiability of the nonlinearity but not on chaos decay and, as a consequence, encompasses the centred absolute value function. Second, in the spirit of the law of large numbers, we show that the diagonal of the second-order process converges to an explicit symmetric correction term. Finally, we compute all the moments of the remaining process and, through a fine combinatorial analysis, show that they converge to those of the Stratonovich Brownian rough path perturbed by an antisymmetric area correction, as computed by a suitable amendment of Fawcett's theorem. All of these steps benefit from a major combinatorial reduction that is implied by the original argument of Breuer and Major (1983). This is joint work with Henri Elad Altman (Paris XIII) and Nicolas Perkowski (FU Berlin).

Eddi Aamari (ENS-PSL Paris) & Arthur Stephanovich (ENSAE-CREST Paris)

Regularity of the score and convergence rates of generative diffusion models

Forschungsseminar Mathematische Statistik at WIAS Berlin, Erhard-Schmidt lecture room, & ZOOM, 10:00 AM

Abstract: We show that diffusion-based generative models adapt to the smoothness of the target distribution: the score function inherits the target’s regularity. Leveraging this adaptivity, we obtain a concise proof that diffusion models achieve minimax-optimal rates for density estimation.

Nikolaos Zygouras (University of Warwick)

The critical 2-d Stochastic Heat Flow and some of its properties

Oberseminar Analysis-Probability at MPI, E2 10 (Leon-Lichtenstein), 3:15 PM

Abstract: The critical 2-d Stochastic Heat Flow arises as a non-trivial solution of the Stochastic Heat Equation (SHE) and its discretisation via directed polymers at the critical dimension 2 and at a phase transition point. It is a log-correlated field, which is neither Gaussian nor a Gaussian Multiplicative Chaos. We will review the phase transition of the 2-d SHE, describe the main points of the construction of the Critical 2-d SHF and outline some of its features (e.g. singularity, regularity, moments, support etc.) Most of the talk will be based on joint works with Francesco Caravenna and Rongfeng Sun but contributions of other researchers will be presented.

Malte Kampschulte (Charles University Prague)

Variational methods for problems with inertia and their limits

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

Abstract: For static and quasi-static problems, (iterated) minimization has long been one of the most important tools to prove existence of solutions. The main advantage of these variational approaches is that they able to deal with complicated nonlinearities and nonconvexities in a rather natural fashion, directly relying on the description of a problem in terms of its physical energy. In contrast, for dynamic problems, i.e. those involving inertia, such variational approaches so far have been much less used in practical existence proofs.

The aim of this talk is to present our recent and not so recent attempts at bridging this gap, using a ”time-delayed” approach which uses energetical descriptions and minimization as both a modelling approach, as well as a way of showing existence of solutions. This will be illustrated in with a number of problems from recent publications, involving solids, fluids and their interaction. Furthermore we will see how the same ideas can be used to study limit systems of parameter-dependent families of such problems in a similarly general fashion.

This is based on joint works with, among others, B. Benešová, D. Breit, A. Češík, G. Gravina, M. Kružík and S. Schwarzacher.

Immanuel Zachhuber (FU Berlin)

Elliptic operators with distributional coefficients

Research Seminar Stochastics at FU Berlin, SR 115, Arminallee 3, 10 AM

Elvin Isufi (TU Delft)

Relational Learning with Covariance Information

Algebraic and Combinatorial Perspectives in the Mathematical Sciences via Zoom, 3:00 PM

Abstract: Covariance information is commonly used in machine learning to reveal data interdependencies such as network topology inference (e.g., graphical lasso) and dimensionality reduction (e.g., Principal Component Analysis (PCA)). However, such information is often only the first step in a machine learning pipeline that is performed separately from the task. Because of finite-data estimation errors, we end up working with a sample covariance matrix that leads to uncertainties in its spectrum. For example, PCA is notoriously unstable to covariance estimation errors, i.e., small data perturbations might lead to large changes in principal directions. To address this, coVariance Neural Networks (VNNs) were introduced. These networks perform graph convolutions on the sample covariance matrix, an operation that, similarly to PCA, modulates the data principal components, but with enhanced representation power and greater stability against covariance estimation errors. However, in sparse, high-dimensional settings with limited data, covariance estimation is particularly difficult, which hinders VNNs’ performance despite their stability. Sparse VNNs overcome this by using theoretically grounded covariance sparsification, which improves stability, reduces the impact of spurious correlations on performance and improves computation and memory efficiency. The success of VNNs motivates their extension to different settings. SpatioTemporal VNNs, for instance, process multivariate time series by applying graph convolutions on the online estimated covariance and temporal convolutions over time, achieving stability to estimation errors in both covariance and model parameters due to streaming data. Finally, VNNs’ stability promotes fairness in datasets with poorly represented groups. Building on this, Fair VNNs leverage equitable covariance estimates and fairness penalties in the loss function to ensure a more balanced treatment of these groups.

José Antonio Carrillo (University of Oxford)

Primal dual methods for Wasserstein gradient flows

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

Abstract: Many nonlinear evolution equations arising in porous media flow, materials science, and collective behavior can be understood as gradient flows in the space of probability measures. In this talk, we present a new numerical framework that exploits this variational structure by combining ideas from optimal transport with modern operator splitting methods. Our approach is based on the Jordan-Kinderlehrer-Otto (JKO) scheme and the Benamou-Brenier formulation of the Wasserstein distance, which together recast the solution of certain nonlinear, nonlocal PDEs as a sequence of convex optimization problems. We show how these problems can be solved efficiently using a recent primal-dual splitting algorithm with rigorous convergence guarantees. We illustrate the method with numerical examples for nonlinear PDEs and Wasserstein geodesics. We conclude by outlining extensions to more general nonlinear mobilities and transport costs, highlighting the flexibility of the approach and its potential for a wide range of applications.

Pierluigi Colli (Università Pavia)

Well-posedness and optimal velocity control of a Brinkman--Cahn--Hilliard system with curvature effects

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

Abstract: Diffuse-interface models for multiphase flows have attracted considerable interest due to their ability to describe complex interfacial dynamics, including curvature effects, within a unified and energetically consistent framework. In this talk, we present joint results for a Brinkman–Cahn–Hilliard system coupling a sixth-order phase-field evolution with a Brinkman-type momentum equation with variable shear viscosity. The Cahn–Hilliard equation includes a nonconservative source term modeling mass exchange, while the momentum equation involves a forcing term that is not divergence-free. We prove the existence of weak solutions in a divergence-free variational framework and, in the case of constant mobility and shear viscosity, establish uniqueness and continuous dependence on the forcing. We also analyze the Darcy limit and obtain existence results for the corresponding reduced system. Finally, we consider an optimal control problem with distributed velocity control, prove the existence of optimal controls, show the Fr´echet differentiability of the control-to-state operator, and derive first-order necessary optimality conditions via an adjoint system.

Willem van Zuijlen (WIAS Berlin)

Anderson Hamiltonians with correlated Gaussian potentials

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

Abstract: Anderson Hamiltonians, which are random Schrödinger operators, model the evolution of electrons or quantum states in a disordered system. Philip Warren Anderson (1958) showed that if there is too much disorder in the system, instead of seeing a diffusive behaviour for the electron, they get trapped. A similar localisation effect takes place in the parabolic Anderson model, which is the parabolic problem or Cauchy problem related to the Anderson Hamiltonian. The spectral properties of the Hamiltonian determine this localisation behaviour. Many such models have been studied, but often with a potential field that is i.i.d. We study these Hamiltonians with a correlated Gaussian potential and consider it eigenvalue order statistics.

This is joint work with Giuseppe Cannizzaro and Cyril Labbé.

Marcella Palese (University of Turin)

Invariant variational problems and cohomology

Analysis Seminar Potsdam Campus Golm, Building 9, Room 2.22 and via Zoom, 11:00 AM

Abstract: The interplay of inverse variational problems with invariance properties is exploited. We focus on symmetries of globally defined locally variational field equations and find conditions for the variation of local Noether strong currents to be conserved and variationally equivalent to a global conserved current.

Nihat Ay (Hamburg University of Technology)

Information geometry of the Otto metric

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

Abstract: In this talk, I present a novel extension of information geometry to the setting of Wasserstein geometry and highlight its applications in machine learning. The central structure of information geometry consists of a Riemannian manifold together with a pair of dual affine connections. Classically, this structure arises from a statistical model endowed with the Fisher–Rao metric, the mixture connection, and its dual, the exponential connection. While this framework captures fundamental statistical properties, it does not account for the metric structure of the underlying sample space.

Motivated by this limitation, I propose an extension to the Wasserstein setting. Within this framework, I introduce the dual of the mixture connection with respect to the Otto metric, yielding a novel form of exponential connection. This leads to a new dual structure comprising the mixture connection, the Otto metric as the Riemannian metric, and the newly defined exponential connection.

I derive the geodesic equation associated with this exponential connection and show that it coincides with the Kolmogorov forward equation of a gradient flow, also known as the continuity equation in Wasserstein geometry. Furthermore, I construct the canonical contrast function of the proposed dual structure, which I term the Wasserstein–Kullback–Leibler divergence, and demonstrate how it addresses limitations of the classical Kullback–Leibler divergence.

Rong Tang (Jilin University)

Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures

Algebraic and Combinatorial Perspectives in the Mathematical Sciences via Zoom, 3:00 PM

Abstract: We prove that the post-Lie algebraic structure on the decorated trees which appears spontaneously in Regularity Structures is a post-Lie deformation of a pre-Lie algebra. This post-Lie structure is the conerstone of the algebraic foundations of the theory of Regularity Structures, a theory that solves a large class of subcritical singular stochastic partial differential equations which were out of reach without a proper algebraic structure. This deformation allows to reduce the origin of these structures to a simpler object. We use the formalism of deformation theory in order to understand the nature of this deformation. This leads us to construct the differential graded Lie algebra that governs post-Lie deformations of a pre-Lie algebra, to develop the post-Lie cohomology theory for a pre-Lie algebra, by which we classify infinitesimal post-Lie deformations of a pre-Lie algebra using the second cohomology group. The rigidity of such kind of deformations is also characterized using the second cohomology group. This is a joint work with Yvain Bruned and Yunhe Sheng.

Timo Schorlepp (Courant Institute of Mathematical Sciences)

Precise large deviations for S(P)DEs: theory, numerics, applications

Oberseminar Analysis-Probability at MPI, G3 10 (Lecture hall), 3:15 PM

Abstract: In this talk, I will first review the classical theory of Laplace asymptotics for small-noise diffusions in R^n and extensions to stochastic partial differential equations (SPDEs), with particular emphasis on sharp asymptotics. Going beyond the usual log-asymptotics of large deviation theory, we focus on prefactors and thus Hessian contributions that are essential for accurate probability estimation.

I will then describe how these theoretical results can be turned into a practical computational framework for estimating rare event probabilities without sampling. The approach is designed to scale to high-dimensional state spaces, as required for SPDEs, and involves solving ODE/PDE-constrained optimization problems to identify optimal paths, as well as computing Hessian determinants around minimizers. Modern tools, such as automatic differentiation, make these steps tractable.

As an application, I will present results for intermittency in the stochastic 1D viscous Burgers equation, as a canonical toy model of fluid turbulence. Time permitting, I will conclude with an outlook on future improvements based on ideas from the functional renormalization group.

Based on joint work with Tobias Grafke, Rainer Grauer, Georg Stadler, Shanyin Tong, in Stat. Comput. 33(6), 137 (2023), arXiv:2502.20114, and arXiv:2512.03841.

Anh Duc Vu (WIAS Berlin)

Generalised graphical representations

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

Abstract: Numerous dynamic spatial models feature interactions between particles that are based on waiting times; the most prominent examples being first passage percolation, where a fluid spreads from a source, and the contact process, where an infection spreads on a graph with the possibility of recovery. However, waiting times are unnatural for certain models. One can argue that people have a daily routine and meet each other on a relatively fixed schedule, rather than a random waiting time after having met someone else. With the help of graphical representations, we develop a framework that moves away from waiting times towards so called contact times. As an application, we present results on a first contact percolation model, where people follow a random daily meeting routine, as well as contact processes with periodic recoveries.

Hannes Meinlschmidt (Friedrich-Alexander-Universität Erlangen-Nürnberg)

Quasilinear parabolic equations in the Bessel scale

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

Abstract: In this talk, I will discuss and analyze scalar quasilinear parabolic equations posed on nonsmooth domains with generally irregular input data. The lat ter refers to merely measurable and bounded coefficients, mixed boundary conditions, possibly inhomogeneous Robin- or Neumann boundary data, and also to nonlinear forcing functions which may act on the gradient of the solution. The driving force for the analysis will be maximal parabolic regu larity of the differential operators in the scale of (duals of) Bessel potential spaces incorporating mixed boundary conditions, with the scale parameter depending on the smoothness of the solution within the quasilinear operator. These depend on permanence principles for the elliptic counterparts which are leveraged from bilinear interpolation. A careful analysis allows to close the loop for the quasilinear equation and thus obtain local-in-time solutions under minimal assumptions. I further mention some sufficient criteria for solutions to exist globally, and how these can be leveraged in the framework of optimal control problems to achieve a satisfying theory for nonsmooth problems with strong nonlinearities.

Björn Bringmann (Princeton University)

On the global well-posedness of the stochastic Yang-Mills-Higgs equations in two dimensions

Oberseminar Analysis-Probability at MPI, E2 10 (Leon-Lichtenstein), 3:15 PM

Abstract: The Yang-Mills-Higgs (YMH) model plays a central role in several areas of mathematics, including analysis, geometry, and probability theory. In this talk, we implement the stochastic quantization procedure for the YMH model in two dimensions. That is, we construct the two-dimensional YMH measure by proving global well-posedness and uniform-in-time bounds for the two-dimensional stochastic YMH equations. As part of our proof, we first discuss covariant stochastic objects and a covariant para-controlled Ansatz. Then, we discuss a decay mechanism for the stochastic YMH equations near unstable Yang-Mills connections. This is joint work with S. Cao, M. Hairer, and W. Zhao.

Xavier Goaoc (Université de Lorraine, Nancy)

Oriented matroids of planar point configurations

Algebraic and Combinatorial Perspectives in the Mathematical Sciences via Zoom, 3:00 PM

Abstract: Oriented matroids are purely combinatorial objects that were devised, independently, by Bland to study the simplex algorithm, by Folkman and Lawrence to study face lattices of polytopes, and by Las Vergnas to study questions in graphs and combinatorics. In this talk, I will discuss the oriented matroids that arise from finite, planar point configurations. We will consider them from the point of views of computational complexity and discrete geometry, with a particular emphasis on their symmetries and typical properties.

Jan Mandrysch (Universität Wien)

How to measure quantum fields? Implementing a causal measurement scheme

Analysis Seminar Potsdam Campus Golm, Building 9, Room 2.22 and via Zoom, 1:00 PM

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