Spectral geometry in the clouds

Spectral geometry in the clouds
Intergalactic seminar on spectral theory and geometric analysis

Fall 2023

September
September 11	Cyril Letrouit Maximal multiplicity of Laplacian eigenvalues in negatively curved surfaces Video
September 18	Michela Egidi Complex analysis, thick sets, and spectral inequalities Video
September 25	Yves Colin de Verdière On the spectrum of the Poincaré operator in ellipsoids Video
October
October 2	Sam Farrington On the geometric stability of Weyl's law and some applications to asymptotic spectral shape optimisation Video
October 9	Jonathan Rohleder Inequalities between Neumann and Dirichlet Laplacian eigenvalues on planar domains Video
October 16	Antoine Métras Dirac eigenvalue optimization Video
October 23	Wadim Gerner Optimal Metrics and Domains for the first Curl eigenvalue
October 30	Ana Menezes Eigenvalue problems and free boundary minimal surfaces in spherical caps
November
November 6, 8, 10	GEMSTONE mini-course Dorin Bucur Shape optimization of spectral functionals
November 13	Sara Farinelli Peijel's nodal domain theorem in spaces with synthetic Ricci curvature lower bounds Video
November 20	Samuel Lin Spectral Multiplicity and Nodal Domains of Torus-invariant Metrics Video
November 27	Dan Mangoubi On the inner radius of nodal domains
December
December 4	Matthew Kwan Exponentially many graphs are determined by their spectrum Video
December 11	Denis Grebenkov Probabilistic and numerical insights onto the spectral properties of the Dirichlet-to-Neumann operator

Winter 2023

January
January 16	Nikolay Filonov Polya's conjecture for Euclidean balls Video
January 23	Badreddine Benhellal Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions Video
January 30	Break
February
February 6	Romain Petrides A variational method for functionals depending on eigenvalues Video
February 13	Peter McGrath Free Boundary Minimal Annuli Immersed in the 3-Ball Video
February 20	Maxime Fortier Bourque Linear programming bounds for hyperbolic surfaces Video
February 27	Laura Monk Towards an optimal spectral gap result for random compact hyperbolic surfaces Video
March
March 6	Yaiza Canzani Counting closed geodesics and improving Weyl’s law for predominant sets of metrics Video
March 13	Francesca Bianchi The first eigenvalue of fractional Dirichlet-Laplacian for planar sets with topological constraints Video
March 20	Blake Keeler Off-diagonal spectral cluster asymptotics On Zoll manifolds Video
March 27, 29, 31	GEMSTONE mini-course 3 Geometry and spectrum of random hyperbolic surfaces
April
April 3	Ilaria Fragalà Riesz inequality for polygons: symmetry and symmetry breaking Video
April 10	Luc Hillairet Spectral tools for geometric degeneration Video
April 17	Jake Fillman Spectral properties of operators on aperiodic graphs
April 24	Michela Egidi Complex analysis, thick sets, and spectral inequalities

Fall 2022

December
December 12	Mikhail Dubashinskiy Growth and divisor of complexified horocycle eigenfunctions Slides
December 5	Mickael Nahon Sharp stability of higher order Dirichlet eigenvalues Video
November
November 28	María del Mar González Nogueras Third order boundary eigenvalue problems Video
November 21	Frédéric Naud Spectrum of random covers of hyperbolic surfaces and GOE/GUE statistics Video
November 14	Marco Michetti Maximization of Neumann eigenvalues under diameter constraint Video
November 7	Clara Lucia Aldana Dominguez On Quasi-isospectral potentials Video
October
October 31	Anke Pohl Fractal Weyl bounds Video
October 24	Polyxeni Spilioti Twisted Ruelle zeta function on locally symmetric spaces, the Fried’s conjecture and further applications Video
October 17	Alexei Stepanenko Computing eigenvalues of the Laplacian on rough domains Video
October 10	Mostafa Sabri Quantum ergodicity for periodic graphs Video
October 3	Bram Petri How do you efficiently chop a hyperbolic surface in two? Video
September
September 26	Semyon Dyatlov Ruelle zeta at zero for nearly hyperbolic 3-manifolds Video
September 19	Break
September 12	Maxime Ingremeau How Lagrangian states evolve into random waves Video
September 5	Egor Shelukhin Coarse nodal count and topological persistence

Spring and summer 2022

July
July 11	Melanie Rupflin Almost harmonic maps from higher genus surfaces Video
July 4	Nadine Große Boundary value problems on domain with cusps Video
June
June 27	Nunzia Gavitone An eigenvalue problem for the Laplace operator in doubly connected domains Video
June 20	Andrea Mondino Optimal transport and quantitative geometric inequalities Video
June 13	Dennis Kriventsov Stability for Faber-Krahn inequalities and the ACF formula Video
June 6	Jiaoyang Huang Extreme eigenvalues of random \(d\)-regular graphs Video
May
May 30	Romain Petrides Minimizing combinations of Laplace eigenvalues and applications Video
May 23	Dorin Bucur Maximization of Neumann eigenvalues Video
May 16	Yves Colin de Verdière Attractors for internal or inertial waves Video
May 9	Beniamin Bogosel On the polygonal Faber-Krahn inequality Video
May 2	Pedro Freitas Pólya-type inequalities on spheres and hemispheres Video

Winter 2022

April
April 25	GEMSTONE mini-course Mikhail Karpukhin and Daniel Stern Harmonic maps, minimal surfaces, and shape optimization in spectral geometry
April 18	Break
April 11	Jean Lagacé Variations on the Weyl law for the Steklov problem on surfaces Video
April 4	Bruno Colbois Upper bounds for Steklov eigenvalues Video
March
March 28	Mikhail Cherdantsev Stochastic homogenisation of high-contrast media Video
March 21	Young researchers in spectral geometry IV
March 14	James Bonifacio Bootstrap bounds on closed hyperbolic surfaces Video
March 7	Nelia Charalambous The form spectrum of open manifolds Video
February
February 28	Ilaria Lucardesi On the maximization of the first (non trivial) Neumann eigenvalue of the Laplacian under perimeter constraint
February 21	Malo Jézéquel Semiclassical measures for higher dimensional quantum cat maps Video
February 14	Maxime Fortier Bourque The multiplicity of \(\lambda_1\) in genus 3 Video
February 7	Francesco Ferraresso Neumann and intermediate biharmonic eigenvalue problems on sigularly perturbed domains Video
January
January 31	Alessandro Savo Isoperimetric inequalities for the lowest Aharonov-Bohm eigenvalue of the Neumann and Steklov problems Video
January 24	Gregory Berkolaiko Towards Morse theory of dispersion relations Video
January 17	Oleksiy Klurman Boundary-adapted arithmetic random waves and spectral semi-correlations Video

Fall 2021

December
December 13	Yann Chaubet Closed geodesics with prescribed intersection numbers Video
December 6	Jean-Claude Cuenin Schrödinger operators with complex potentials: Beyond the Laptev-Safronov conjecture Video
November
November 29	David Sher Nodal counts for the Dirichlet-to-Neumann operator Video
November 22	Michael Magee The maximal spectral gap of a hyperbolic surface
November 15	Ben Sharp Łojasiewicz-type inequalities for the H-functional near simple bubble trees Video
November 8	Sabine Boegli On the discrete eigenvalues of Schrödinger operators with complex potentials Video
November 1	Jonathan Rohleder Note the change of time this week: 9h PST -- 12h EST -- 16h GMT -- 17h CET A new approach to the hot spots conjecture Video
October
October 25	Valentin Blomer Eigenvalue statistics of flat tori Video
October 18	Daniel Stern Note the change of time this week: 8h PST -- 11h EST -- 16h BST -- 17h CEST Steklov-maximizing metrics on surfaces with many boundary components Video
October 11	Break
October 4	Philippe Charron Pleijel's theorem for Schrödinger operators Video
September
September 27	Gabriel Rivière Poincaré series and linking of Legendrian knots Video
September 20	Martin Vogel Spectral asymptotics of noisy non-selfadjoint operators Video
September 13	Young researchers in spectral geometry III 3 short talks
September 6	Nalini Anantharaman Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization Video
August
August 30	Jürgen Jost Spectra of graphs and hypergraphs Video
August 23	Wencai Liu Small denominators and large numerators of quasiperiodic Schroedinger operators Video

Spring and summer 2021

August
August 2, 9 and 16: break
July
July 26	Victor Ivrii Pointwise Spectral Asymptotics out of the Diagonal Video
July 19	Yannick Sire Eigenfunction and cluster estimates for Schrodinger operators on manifolds Video
July 12	Derek Kielty Degeneration of the spectral gap with negative Robin parameter Video
July 5	Steve Zelditch Eigenfunction restriction problems Video
June
June 28	Ari Laptev Spectral inequalities for Jacobi matrices following Hundertmark and Simon Video
June 21	Paolo Luzzini On the spectral asymptotics for the buckling problem Video
June 14	Javier Gómez-Serrano Computer-assisted proofs and counterexamples in spectral geometry Video
June 7	Mikhail Karpukhin Stability of isoperimetric eigenvalue inequalities Video
May
May 31	Maciej Zworski Spectral theory of internal waves in fluids Video
May 24	Genqian Liu Geometric invariants of spectrum of the Navier-Lame operator Video
May 17	Alexandre Girouard Free boundary minimal surfaces and large Steklov eigenvalues Video
May 10	Ram Band Neumann domains on manifolds and graphs Video
May 3	Jared Wunsch Semiclassical analysis and the convergence of the finite element method Video

Winter 2021

April
April 26	Karl-Mikael Perfekt Infinitely many embedded eigenvalues for the Neumann-Poincaré operator in 3D Video
April 19	Bernard Helffer Semi-classical edge states for the Robin Laplacian (after Helffer-Kachmar) Video
April 12	Svitlana Mayboroda The landscape law for the integrated density of states Video
April 5	Break
March
March 29	Mariel Saez Eigenvalue bounds for the Paneitz operator and its associated boundary operator Video
March 21 and 22	Mini Conference Young researchers in spectral geometry II
March 15	Nilima Nigam The approximation of Laplace Steklov eigenvalues Video
March 8	Graham Cox Nodal deficiency via equipartitions and Dirichlet-to-Neumann maps Video
March 1	Grigori Rozenblum Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case Video
February
February 22	Peter Kuchment Spectral shift via lateral variation Video
February 15	Uzy Smilansky Can one hear a matrix? The determination of a real symmetric matrix from spectral information
February 8	Alessandro Carlotto Free boundary minimal surfaces with connected boundary and arbitrary genus
February 1	Luigi Provenzano Spectral representation of the trace spaces of H² and biharmonic Dirichlet problems for multi-parameter Steklov problems Video
January
January 25	Zeev Rudnick Robin vs Neumann spectra for planar domains
January 18	Pavel Exner Discrete spectrum of Dirichlet Laplacian in spiral-shaped regions Video
January 11	Olaf Post Operator estimates for wildly perturbed manifolds Video

Fall 2020

December
December 14	Marco Marletta A Laplace operator with boundary conditions singular at one point Video
December 7	Simon Larson Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain Video
November
November 30	Édouard Oudet Metric Optimization in Spectral geometry Video
November 23	Peter Sarnak Gap Sets for the Spectra of Cubic Graphs Video
November 16	Katie Gittins Upper bounds for Steklov eigenvalues Video
November 9	Jeffrey Galkowski The interior behavior of Steklov eigenfunctions Video
November 2	Stefano Decio Nodal sets of Steklov eigenfunctions near the boundary Video
October
October 26	Christiane Tretter Spectral problems on star graphs Video
October 19	Antoine Henrot Isodiametric inequalities for eigenvalues Video
October 12	Sugata Mondal Hot spots conjecture for polygonal domains Video
October 5	Richard Laugesen Two balls maximize the third Neumann eigenvalue in hyperbolic space Video Slides
September
September 28	Jeremy Marzuola A local test for global extrema in the dispersion relation for periodic graphs Video
September 21	Davide Buoso The Bilaplacian with Robin boundary conditions Video
September 14	Alix Deleporte Semiclassical analysis of a problem with a circular well Video
September 7	Jean Lagacé Measure theoretic methods in spectral shape optimisation Video
August
August 31	Gerasim Kokarev Comparison principles, minimal surfaces, and eigenvalue inequalities

Spring and summer 2020

August 24	Special seminar on the occasion of Dima Jakobson's 50th birthday
August 3 and 4	Mini Conference: Young researchers in spectral geometry
July
July 27	Julie Rowlett Same-same but different: Polyakov formulas via microlocal analysis and mathematical physics Video
July 20	Asma Hassannezhad Eigenvalue bounds for the mixed Steklov problem Video
July 13	Panagiotis Polymerakis Bottom of spectra and coverings
July 6	Rupert Frank Sharp Weyl Laws in 3d with rough potentials Slides Video
June
June 29	Daniel Stern Min-max harmonic maps and extremal metrics for Laplacian eigenvalues Slides Video
June 22	Stefan Steinerberger Nodal Sets of Eigenfunctions: Progress via Optimal Transport Slides Video
June 15	Cristina Trombetti Sharp Estimates for solutions to Elliptic Equations with Robin boundary conditions Video
June 8	Peter Humphries The random wave conjecture and arithmetic quantum chaos Slides Video
June 1	Xuwen Zhu Spectral properties of reducible spherical conical metrics Video
May
May 25	Iosif Polterovich Lambdas, bubbles, and spheres Slides Video
May 18	Yaiza Canzani \(L^p\)-norms via geodesic beams. Video
May 11	Henrik Matthiesen Asymptotic behaviour of eigenvalues in glueing constructions and new minimal surfaces via shape optimization Notes Video
May 4	Dorin Bucur Stable and unstable spectral inequalities Video
April
April 27	Emilio Lauret On the first Laplace eigenvalue of a homogeneous sphere Slides
April 20	Michael Levitin Inverse Steklov spectral problem for curvilinear polygons Slides