Réunion d'hiver SMC 2026
Montréal, 11 - 14 décembre 2026
Géométrie spectrale
Org: Maxime Fortier Bourque (Université de Montréal), Alexandre Girouard (Université Laval) et Lawford Hatcher (Université de Montréal)
[PDF]
Org: Maxime Fortier Bourque (Université de Montréal), Alexandre Girouard (Université Laval) et Lawford Hatcher (Université de Montréal)
[PDF]
- SAMUEL AUDET BEAUMONT, Université Laval
- THOMAS BECK, Fordham University
- JARED BRONSKI, University of Illinois Urbana-Champaign
- DMITRY FAIFMAN, Université de Montréal
- JOSEF GREILHUBER, Massachusetts Institute of Technology
- THOMAS HÉLIÈRE, Université Laval
- DMITRY JAKOBSON, McGill
Small eigenvalues of degenerating Riemann surfaces [PDF]
- THOMAS BECK, Fordham University
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It is known that the small eigenvalues of the Laplacian of a Riemann surface close to the boundary of the modular
space can be well approximated by the eigenvalues of the discrete Laplacian on a certain graph coming from the pair
of pants decomposition of the surface. We provide a complete description of the sets of eigenvalues of
the weighted graph Laplacian for all graphs on four vertices that correspond to a valid pair of pants decomposition of a
surface of genus 3.
- HANNA KIM, University of North Carolina
- RICHARD LAUGESEN, University of Illinois
- NILIMA NIGAM, Simon Fraser University
- KSHITIJ PATIL, Simon Fraser University
- FRÉDÉRIC ROCHON, Université du Québec à Montréal
- EGOR SHELUKHIN, Université de Montréal
- DAVID SHER, DePaul University
- ROMAIN SPECIEL, Stanford University
- ALINA STANCU, Concordia University
- JOHN TOTH, McGill University
- DENIS VINOKUROV, Université de Montréal
- GUOFANG WEI, UC Sabta Barbara
A Sharp Diameter-Dependent Lower Bound for the First Nonzero Neumann Eigenvalue of Geodesic Triangles in Space Forms [PDF]
- RICHARD LAUGESEN, University of Illinois
-
We prove a sharp lower bound for the first nonzero Neumann eigenvalue of geodesic triangles of given diameter in two-dimensional space forms. The bound is given by the first positive radial Neumann eigenvalue of a one dimensional model; it is approached by degenerating isosceles triangles. When \(K>0\) and \(D=\pi/(2\sqrt K)\), equality is attained precisely by birectangular triangles. We also prove a hot-spots theorem for non-acute spherical triangles of diameter at most \(\pi/2\), and establish antisymmetry and eigenvalue monotonicity for isosceles spherical triangles of diameter \(\pi/2\). This is a joint work with Shoo Seto and Yusen Xia.