## Computational mathematics for model reduction and predictive modelling in molecular and complex systems

The workshop will address computational and theoretical issues in stochastic modeling and model reduction in molecular and complex systems. In particular, the program will include topics ranging from quantum to mesoscale modelling, with focus on uncertainty quantification, machine learning and approximate inference method, methods using both quantum and classical models, semiclassical limits and their computational aspect. Furthermore, the interplay between mathematical analysis, modeling and statistical physics and trade-offs between statistical (data-driven) learning and physicochemical modelling will be part of the discussions. The workshop aims at bringing together mathematicians and domain scientists interested in applications such as systems with excited states, empirical potentials, kinetic Monte Carlo methods and accelerated simulation methods determined from molecular dynamics, data assimilation and inference for predictive modeling of complex molecular systems.

Part of the Semester : Multi-scale Mathematical Modelling and Coarse-grain Computational Chemistry

By: Markos **Katsoulakis**, University of Massachusetts Amherst Benedikt **Leimkuhler**, University of Edinburgh Petr **Pelchac**, University of Delaware Anders **Szepessy**, KTH Royal Institute of Technology

## Invariant Random Subgroups in groups acting on rooted trees

An invariant random subgroup (IRS) of a countable group is a conjugation invariant probability distribution on the space of subgroups. There have been a number of recent papers studying IRS’s in various types of groups: lattices in Lie groups, the group of finitary permutations of a countable set, free groups, lamplighters and more.

In this talk we will consider IRS’s in groups acting of rooted trees, in particular the group of finitary automorphisms of a d-ary rooted tree. We exploit the action of these groups on the boundary of the tree to understand fixed point sets of ergodic IRS’s. We show that in the fixed point free case IRS’s behave like the ones in lattices in Lie groups, but if there are fixed points they resemble the ones in the finitary permutation group. Joint work with Ferenc Bencs.

By: László Márton Tóth (EPFL)

## Intrinsic wavelet smoothing of curves and surfaces of Hermitian positive definite matrices

Statistics Seminar

By: Prof. Rainer von Sachs, UC Louvain