Upcoming seminars

See the Google Agenda of the seminar, and add the iCal url to your calendar.

• Jonathan Eckstein (Rutgers University),
  Thursday 2 October at 10:30, Room B211

  Monotone Operator Splitting, Projection, and Stochastic Programming

  We begin by describing the basics of monotone set-valued operators, proximal, methods, and operator splitting, with a particular focus on solving stochastic programming problems defined on finite multistage trees. A classic form of operator splitting is (perhaps misleadingly) called “Douglas Rachford” and underlies the now-popular ADMM algorithm. We will survey the basics of that algorithm and how it leads to the progressive hedging (PH) method of Rockafellar and Wets. Projective splitting is a newer approach to operator splitting, and allows derivation of algorithms allowing forms of asynchronous implementation. We consider a specialization of this approach to stochastic programming, producing a method that needs to re-solve only a subset of the scenarios at each iteration. We will also touch on an ongoing project to develop a more strongly asynchronous implementation and apply it to stochastic problems with integer variables

• Charles Bertucci (École polytechnique),
  Thursday 2 October at 10:30, Room B211

  Analysis on the space of probability measures and application to optimal control and large deviations.

   

  I will motivate the study of non-linear partial differential equations on the space of probability measures by presenting some general questions of optimal control and large deviations of mean field problems. I will then explain some general tools of analysis of functions of a measure argument such as derivatives or super-differentials. I will then explain how those tools can be used in the motivating problems.

• Andrew McRae (EPFL/ CERMICS(!)),
  Thursday 13 November at 10:30, Room B211

  Nonconvex optimization landscapes in statistics: benignness, relaxation, and tightness

   

  Nonconvex (continuous) optimization is everywhere. Classically, nonconvexity is problematic due to the possibility of spurious local optima. However, in practice, for many applications, naïve algorithms that find a local optimum give satisfactory solutions. Why is this? In my work, I try to explain theoretically how problem structure coming from statistical applications has a surprising impact on the difficulty of an optimization problem. One possible explanation is that the landscape is benign: that is, all local optima are, in fact, global optima (or at least close enough for the task at hand). When this fails, we can try to make the problem easier by relaxing or overparametrizing it. However, this then raises the questions of (a) how much do we relax (there is then often a tradeoff between the number of variables and how close the problem is to a convex one), and (b) is the relaxation tight? I will illustrate these issues and present some of my recent work in the area of low-rank matrix estimation, specifically low-rank matrix sensing and orthogonal group synchronization. These problems have applications in many areas such as computational microscopy, sensor network localization, robotics, and dynamical systems.

Past seminars (2025-2026)

• Jesús De Loera (UC Davis),
  Friday 5 September at 10:00, Room B211

  What is the Best Way to Slice a Polyhedron?

  For hundreds of years mathematicians have been fascinated with slicing high-dimensional mathematical objects as a way to get knowledge and intuition of higher dimensions. There are many classical results and conjectures (e.g., Bourgain’s conjecture, recently a theorem, on the relation of volume and area of slices). My talk is computational contribution to this subject.

  Given a d-dimensional convex polytope P, what is the “best’’ slice of P by a hyperplane? Here “best’’ can mean many possible things, analytics e.g., a slice with the largest volume? Or combinatorial, e.g., a slice with the largest number of vertices? etc. This touches on classical work by Lagrange, Bourgain, Ball, Koldobsky, Milman, Pournin, and many other mathematicians. Not only we investigate the above optimization theorem but also, as we slice P with hyperplanes, we create many combinatorially different (d-1)-slices, which are also polytopes of course. E.g., for a 3-dimensional regular cube there are 4 combinatorial types of slices (triangles, quadrilaterals, pentagons, hexagons). We investigate: How many different slices are there for a polytope P? How can we count them all? Can we give lower/upper bounds on their number? What are extremal cases?

  I will explain a powerful new geometric model (a moduli space of slices) and algorithmic framework that answers these problems (and others) in polynomial time when dim(P) is fixed. Moreover, we show the problems have hard complexity otherwise.

  This is joint work with Marie-Charlotte Brandenburg (U Bochum) and Chiara Meroni (ETH) and Antonio Torres and Gyivan López (UC Davis)

• Marios Andreou (University of Wisconsin-Madison),
  Tuesday 09 September at 10:30, Room B211

  Harnessing the Conditional Gaussian Nonlinear System Framework for Efficient Adaptive-Lag Online Smoothing and Causal Inference

  This talk presents recent advances in data assimilation and causal inference through the Conditional Gaussian Nonlinear System (CGNS) framework. This is a class of nonlinear stochastic models in which, conditioned on a subset of state variables, the unobserved components follow a Gaussian posterior distribution. This structure enables efficient Bayesian state estimation and sampling via closed-form solutions, making CGNS especially suitable for high-dimensional, multiscale systems with regime shifts and intermittent extreme events. CGNSs have wide applications in uncertainty quantification, modelling complex geophysical phenomena, dealing with high-dimensional systems, and facilitating machine learning.

  We first introduce an adaptive-lag online smoother that leverages the analytical tractability of CGNSs to effectively reduce the computational storage requirements of standard smoothing procedures. Adaptively adjusting the lag by exploiting information-theoretic criteria, this strategy is applicable to turbulent systems with time-varying temporal correlations and performs well in challenging real-world problems such as Lagrangian data assimilation and online parameter estimation.

  Building on this, we present a paradigm-shifting causal inference framework, called Assimilative Causal Inference (ACI), which leverages Bayesian data assimilation to trace causes backward from observed effects by solving an inverse problem rather than quantifying forward influence. It uniquely identifies dynamic causal interactions without requiring observations of candidate causes, accommodates short datasets, and scales efficiently to high dimensions. Crucially, it provides online tracking of causal roles, which may reverse intermittently, and facilitates a mathematically rigorous criterion for the causal influence range, revealing how far effects propagate. ACI opens new avenues for studying complex systems, where transient causal structures are critical. Despite its general setting, within the CGNS framework ACI enables explicit nil-causality principles and analytical characterisations of the associated causal influence ranges for objective temporal attribution and prediction.

  Applications to systems showcasing turbulent dynamics and nonlinear geophysical flows illustrate how CGNSs provide scalable, real-time, and theoretically grounded solutions to online smoothing and causal inference.

• Laure Saint-Raymond (IHES),
  Wednesday 10 September at 14:30, Room B211

  Autour de l’équation de Boltzmann.

  Je présenterai quatre résultats mathématiques marquants de ces cinquante dernières années qui permettent de mieux appréhender ce modèle fondamental de la théorie cinétique des gaz.