Seminar Talks

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.

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.

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.

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.

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.

Nikolaos Zygouras (University of Warwick)

TBA

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

Abstract: TBA

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, 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.

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).

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.

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.

Elena Magnanini (WIAS Berlin)

TBA

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

Abstract: TBA

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).

Vladimir Spokoiny (WIAS)

TBA

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

Abstract: TBA

Benjamin Massat (Université de Toulouse)

TBA

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

Abstract: TBA

Idris Karoubi (Sorbonne Université, Paris)

TBA

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

Abstract: TBA

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.

Eva-Maria Hekkelman (MPI Bonn)

TBA

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

Abstract: TBA

Martin Heida (WIAS)

TBA

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

Abstract: TBA

Ismaël Bailleul (Université de Bretagne Occidentale)

"Mean field type singular SPDEs"

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

Abstract: I will explain how to set up a variant of the first order paracontrolled calculus to prove local in time well-posedness for some mean field type (gPAM)-like equation, and prove propagation of chaos for an associated system of interacting fields.

Riccarda Rossi (University of Brescia)

TBA

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

Abstract: TBA

Paolo Pigato (University of Rome)

TBA

Abstract: TBA

Chiara Rossato (ETH Zurich)

TBA

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

Abstract: TBA

Recent Talks

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.

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