Probabilistic methods in geometry, topology and spectral theory : CRM workshops, probabilistic methods in spectral Geometry PDE, August 22-26, 2016, probabilistic methods in topology, November 14-18, 2016, Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada
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Bibliographic Information
Probabilistic methods in geometry, topology and spectral theory : CRM workshops, probabilistic methods in spectral Geometry PDE, August 22-26, 2016, probabilistic methods in topology, November 14-18, 2016, Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada
（Contemporary mathematics, 739 . Centre de Recherches Mathématiques proceedings）
American Mathematical Society , Centre de Recherches Mathématiques, c2019
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Probabilistic methods
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Includes bibliographical references
Description and Table of Contents
Description
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 Mathematiques, Universite de Montreal, Montreal, 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 Schrodinger 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.
Table of Contents
L. Chen and N. Shu, A geometric treatment of log-correlated Gaussian free fields
S. Eswarathasan, Tangent nodal sets for random spherical harmonics
J. Friedman, Formal zeta function expansions and the frequency of Ramanujan graphs
D. Jakobson, T. Langsetmo, I. Rivin, and L. Turner, Rank and Bollobas-Riordan polynomials: Coefficient measures and zeros
V. Konakov, S. Menozzi, and S. Molchanov, The Brownian motion on $\mathrm{Aff}(\mathbb{R})$ and quasi-local theorems
N. Laaksonen, Quantum limits of Eisenstein series in $\mathbb{H}^3$
F. Macia and G. Riviere, Observability amd quantum limits for the Schrodinger equation on $\mathbb{S}^d$
M. Rossi, Random nodal lengths and Wiener chaos
L. Silberman and A. Venkatesh, Entropy bounds and quantum unique ergodity for Hecke eigenfunctions on division algebras.
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