Upcoming seminars

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

• 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),
  Wednesday 10 September at 14:30, Room TBD

  Title: 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 TBD

  Title TBD

  Abstract TBD

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

  Title TBD

  Abstract TBD

Past seminars (2025-2026)

• Nothing yet