Categorified Enumerative Geometry and Representation Theory
This one-week workshop aims to foster exchange of ideas between mathematicians working on the various aspects of enumerative geometry and related representation theory, as well as to bring together both world experts and aspiring young researchers working in the area(s). Speakers Noah Arbesfeld (Imperial College London) Dori Bejleri (Harvard University) Ben Davison (University of Edinburgh) […]
Stochastic Dynamical Models in Mathematical Finance, Econometrics, and Actuarial Sciences
This program focuses on three important areas where stochastic dynamical models play a major role, namely, mathematical finance, econometrics, and actuarial sciences. Stochastic dynamical models are of major importance in mathematical finance where, for example, the quality of the non-arbitrage pricing and hedging instruments for derivative products that this theory produces depends strongly on the […]
Enumerative geometry of moduli spaces of sheaves in low dimension
This semester-long program will be focused on the enumerative invariants of moduli spaces of sheaves in low dimensions. The main examples of the moduli spaces we will consider are the moduli spaces of sheaves on surfaces and Calabi-Yau 3-folds, the moduli spaces of vector and Higgs bundles on curves, and quiver varieties. The program will […]
Enjoying Probability and Fluids in Lausanne
The workshop aims at bringing together some of the most talented young researchers working on modern analytic and probabilistic aspects of fluid dynamics. The focus will be on Euler, Navier-Stokes equations and related models. Topics that might be addressed include non-uniqueness, blow-up, bifurcation, invariant measures, ergodicity, mixing. Invited speakers: Roberta Bianchini (CNR Rome) Elia Brué (Università Bocconi […]
Entanglement Scaling and Criticality with Tensor Networks
The description of critical phenomena in terms of the renormalization group forms the cornerstone of our modern understanding of strongly-correlated systems. It leads to effective Hamiltonians that can be studied using numerical methods such as Monte Carlo, and the success of those methods relies heavily on scaling ideas for the interpretation of the data. Based […]
Weak turbulence in general relativity
In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. One way to introduce confinement to the equations is by imposing a negative value for the cosmological constant. In this setting, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime […]
Adaptive Sampling for Constrained Optimization under Uncertainty
Stochastic optimization problems with deterministic constraints commonly appear in machine learning, finance, and engineering applications. This talk presents an improved adaptive solution strategy for this important class of problems. The aim is to decrease the computational cost while maintaining an optimal convergence rate. The guiding principle is to adjust the batch size (or sample size) […]
Universal optimality in distributed computing and its connections to diverse areas of theoretical computer science
The modern computation and information processing systems shaping our world have become massively distributed, and a fundamental understanding of distributed algorithmics has never been more important. At the same time, despite 40 years of intense study, we often do not have an adequate understanding of the fundamental barriers that rule out the existence of ultra-fast […]
Dynamics, Transfer Operators, and Spectra
The transfer operator is one of the basic tools of ergodic theory of smooth “chaotic” dynamics. Its discrete spectrum gives rise to the Ruelle-Pollicott resonances, which embody fundamental statistical properties of the dynamics. This semester-long program brings together three communities who share an interest in transfer operator methods (also in the presence of singularities): mathematicians […]
Dynamics with Structures
The theory of dynamical systems, which in barest terms is the study of maps from a set to itself, permeates mathematics and science. It is used in diverse contexts, from proving the existence of solutions of equations to the modelling of complex natural phenomena. In more recent years dynamical methods have proven to be remarkably […]
