Canzani Yaiza, Chen Linan, Jakobson Dmitry (eds.) Probabilistic Methods in Geometry, Topology and Spectral Theory

American Mathematical Society, 2019. — 197 p. — (Contemporary Mathematics 739). — ISBN: 978-1-4704-4145-6; 978-1-4704-5599-6.This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22–26, 2016 and Probabilistic Methods in Topology, held from November 14–18, 2016 at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada.
Probabilistic methods have played an increasingly important role in many areas of mathematics, from the study of random groups and random simplicial complexes in topology, to the theory of random Schrödinger operators in mathematical physics.
The workshop on Probabilistic Methods in Spectral Geometry and PDE brought together some of the leading researchers in quantum chaos, semi-classical theory, ergodic theory and dynamical systems, partial differential equations, probability, random matrix theory, mathematical physics, conformal field theory, and random graph theory. Its emphasis was on the use of ideas and methods from probability in different areas, such as quantum chaos (study of spectra and eigenstates of chaotic systems at high energy); geometry of random metrics and related problems in quantum gravity; solutions of partial differential equations with random initial conditions.
The workshop Probabilistic Methods in Topology brought together researchers working on random simplicial complexes and geometry of spaces of triangulations (with connections to manifold learning); topological statistics, and geometric probability; theory of random groups and their properties; random knots; and other problems.
This volume covers recent developments in several active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.Readership
Graduate students and research mathematicians interested in probability theory and its applications to various areas of mathematics.Linan Chen and Na Shu – A geometric treatment of log-correlated Gaussian free fields
Suresh Eswarathasan – Tangent nodal sets for random spherical harmonics
Joel Friedman – Formal Zeta function expansions and the frequency of Ramanujan graphs
Dmitry Jakobson, Tomas Langsetmo, Igor Rivin and Lise Turner – Rank and Bollobás-Riordan polynomials: Coefficient measures and zeros
V. Konakov, S. Menozzi and S. Molchanov – The Brownian motion on
and quasi-local theorems
Niko Laaksonen – Quantum limits of Eisenstein series in
Fabricio Macià and Gabriel Rivière – Observability and quantum limits for the Schrödinger equation on
Maurizia Rossi – Random nodal lengths and Wiener chaos
Lior Silberman and Akshay Venkatesh – Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division alge