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 […]
Multi-scale Mathematical Modelling and Coarse-grain Computational Chemistry
The M^3 + C^3 semester programme concerns molecular and materials modelling from atomistic to continuum scales. Our aim in the programme is to bring together theoreticians and practitioners, from all of applied mathematics, statistics, engineering, physics and computational chemistry, to work on the development of a systematic account of available coarse-grain and multi-scale techniques, with […]
Computational aspects of partition functions
Partition functions arise as fundamental quantities in physics, mathematics, statistics, computer science and many engineering disciplines. They are often notoriously hard to compute since they typically involve summations over an exponential number of terms. Different computational approaches have been developed in various mathematical disciplines to bound or estimate these important quantities. The aim of this […]
Analytic and Geometric Aspects of Probability on Graphs
Interplay between the probability theory and geometric group theory yielded many spectacular results enriching both areas. Asymptotic properties of various models coming from statistical physics and probabilities were connected to the geometry and combinatorics of the underlying discrete algebraic structure (for instance a group, a graph, a group action). The study started with simple random […]
Geometric Mechanics, Variational and Stochastic Methods
The basic goal of this program is to advance research in geometric as well as stochastic methods in mechanics, control theory, and imaging, taking into account recent developments also in connected areas, such as infinite dimensional Lie groups and representation theory, quantum gauge field theory, infinite dimensional analysis. Applications ranging from mathematical physics to modeling […]
