2017-18 Montreal Analysis Seminar

Seminars are usually held on Mondays or Fridays at Concordia, McGill or Universite de Montreal
For suggestions, questions etc. please contact Dmitry Jakobson (jakobson@math.mcgill.ca), Iosif Polterovich (iossif@dms.umontreal.ca) or Alina Stancu (alina.stancu@concordia.ca)

WINTER 2018

Monday, April 23, 13:30-14:30, McGill, Room 920
Sugata Mondal (Indiana University)
Hot spots conjecture for Euclidean triangles.
Abstract: The hot spots conjecture was made by J. Rauch at a conference in 1974. One of the (many) versions of the conjecture says the following. Let D be a domain in a Euclidean space with piece-wise smooth boundary. Then a second Neumann eigenfunction u for D can not attain its global maximum at an interior point of D. The conjecture is known to be false for domains with holes. Positive results are known in many situations due works of K. Burdzy and his collaborators, D. Jerison-N. Nadirashvilli and many others. This talk will be focused on the hot spot conjecture for Euclidean triangles. Obtuse triangles known to satisfy the conjecture, due to works of Burdzy-Banuelos. A class of acute triangles also known to satisfy the conjecture, due to works of Miyamoto and Siudeja. In this talk I will try to explain a proof of the conjecture for all Euclidean triangles. This a joint work with Chris Judge.

Monday, March 19, 13:30-14:30, McGill, Room 920
Thierry Daude (Cergy-Pontoise)
On the anisotropic Calderon problem on singular Riemannian manifolds of Painleve type: the borderline between uniqueness and invisibility.
Abstract: The anisotropic Calderon problem consists in determing the metric of a Riemannian manifold with boundary from the knowledge of its Dirichlet-to-Neumann map. I this talk, I will study this type of problem on Riemannian manifolds equiped with singular metrics, i.e. metrics whose coefficients are in some L^p spaces. In the particular case of Riemannian manifolds having certain separability properties of the geodesic flow (Painlevé property), I shall show what is the borderline between uniqueness and non-uniqueness results in the corresponding anisotropic Calderon problem. This is a joint work with Niky Kamran (McGIll) and Francois Nicoleau (Nantes).

Friday, March 9, 13:30-14:30, Univ. de Montreal, Pav. Andre Aisenstadt, Room 5183
Antoine Henrot (Institut Elie Cartan de Lorraine)
About two shape functionals involving the maximum of the torsion function
Abstract: In this talk we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider $T(\Omega)/(M(\Omega)|\Omega|)$ and $M(\Omega)\lambda_1(\Omega)$, where $\Omega$ is a bounded open set of $\mathbb{R}^N$ with finite Lebesgue measure $|\Omega|$, $M(\Omega)$ denotes the maximum of the torsion function, (solution of $-\Delta u=1$ in $\Omega$, $u=0$ on the boundary), $T(\Omega)=\int_\Omega u$ $ the torsion, and $\lambda_1(\Omega)$ the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.

Friday, March 2, 13:30-14:30, McGill, Room 920
Yulia Bibilo (Concordia)
Isomonodromic deformations and nonlinear equations
Abstract: We consider monodromy preserving deformations of meromorphic linear systems of ordinary differential equations over the Riemann sphere. In particular, we will discuss some results for systems with both resonant and non-resonant irregular singularities and also applications to integrable nonlinear differential equations.

Joint Analysis and Geometric Analysis seminar
Friday, February 16, 13:30-14:30, McGill, Room 920
Loredana Lanzani (Syracuse)
Harmonic Analysis Techniques in Several Complex Variables
Abstract: pdf

Friday, February 9, 13:30-14:30, McGill, Room 920
Jeff Galkowski (Stanford)
Concentration of Eigenfunctions: Sup-norms and Averages
Abstract: In this talk we relate concentration of Laplace eigenfunctions in position and momentum to sup-norms and submanifold averages. In particular, we present a unified picture for sup-norms and submanifold averages which characterizes the concentration of those eigenfunctions with maximal growth. We then exploit this characterization to derive geometric conditions under which such growth cannot occur.

Friday, Januauary 26, 13:30-14:30, McGill, Room 920
Victor Ivrii (Toronto)
Spectral asymptotics for Steklov’s problem in domains with edges
Abstract: We derive sharp eigenvalue asymptotics for Dirichlet-to-Neumann operator in the domain with edges and discuss obstacles for deriving a sharper (two-term) asymptotics.

FALL 2017

Friday, December 1, 13:30-14:30, McGill, Room 920
Mikhail Panine (Quebec City)
On Perturbative Methods in Spectral Geometry

Friday, November 24, 14:30-15:30, Universite de Montreal, Pav. Andre-Aisenstadt, Room 5448
Damir Kinzebulatov (Laval)
Brownian motion with general drift
Abstract: We construct and study the weak solution to stochastic differential equation dX_t=-b(X_t)dt+dW_t, X_0=x, for every x \in R^d, d \geq 3, with b in the class of weakly form-bounded vector fields, containing, as proper subclasses, a sub-critical class [L^d+L^\infty]^d, as well as critical classes such as weak the L^d class, the Kato class, the Campanato-Morrey class, the Chang-Wilson-T. Wolff class. This is joint work with Yu. A. Semenov arxiv:1710.06729

Friday, November 17, 13:30-14:30, McGill, Room 920
Mircea Voda (Toronto)
On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling
Abstract: The spectrum of single-frequency quasiperiodic Schrödinger operators with analytic potentials is known to be a Cantor set. Chulaevsky and Sinai conjectured that the spectrum of multi-frequency quasiperiodic Schrödinger operators is an interval for generic large potentials. I will discuss a proof of the Chulaevsky-Sinai conjecture based on joint work with M. Goldstein and W. Schlag.

Joint Analysis + Geometric Analysis seminar
Friday, November 10, 13:30-14:30, McGill, Room 920
Dan Pollack (U. Washington)
On the geometry and topology of initial data sets with horizons

Friday, November 3, 13:30-14:30, McGill, Room 920
Niko Laaksonen (McGill)
Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space
Abstract: On hyperbolic manifolds the lengths of primitive closed geodesics (prime geodesics) have many similarities with the usual prime numbers. In particular, they obey an asymptotic distribution analogous to the Prime Number Theorem. The error in this estimation is well-studied in two dimensions. In three dimensions the only unconditional non-trivial estimate is by Sarnak. In this talk we show how to improve on Sarnak's pointwise bound for the error term. We also investigate the second moment of the error term and highlight some of the difficulties compared to the two dimensional case.

Monday, October 16, 13:30-14:30, McGill, Room 920
Frederic Naud (Avignon)
Sharp resonances and large covers of hyperbolic surfaces
Abstract: (joint With D. Jakobson and L. Suares) In this talk we will look at the spectral properties of infinite area hyperbolic surfaces in families of covers. Depending on the structure of the covering groups we establish several asymptotic results on the distribution of resonances in the large degree limit.

Friday, October 6, 13:30-14:30, McGill, Room 920
Kay Kirkpatrick (University of Illinois at Urbana-Champaign)
Free Araki-Woods Factors and a Calculus for Moments in Quantum Groups.
Abstract: We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to almost-periodic free Araki-Woods factors. This is joint work with Michael Brannan.

Spectral Theory seminar
Monday, September 25, 14:00-15:00, UdeM, Room 5340/5380
Lise Turner (McGill)
Distribution of coefficients of rank polynomials for random sparse graphs
Abstract: We study the distribution of coefficients of rank polynomials of random sparse graphs. We first discuss the limiting distribution for general graph sequences that converge in the sense of Benjamini-Schramm. Then we compute the limiting distribution and Newton polygons of the coefficients of the rank polynomial of random d-regular graphs. This is joint work with S. Norin and D. Jakobson

Monday, September 18, 13:00-14:00, McGill, Burnside 920
Alexander Olevskii (Tel Aviv University)
Around uncertainty principle
Abstract: How "small" the support and the spectrum of a function in R^d can be? I'll present an introduction to the subject and discuss new results joint with Fedor Nazarov and with my student T.Amit.

Monday, September 18, 14:00-15:00, Burnside 920
Alex Iosevich (Rochester University)
Finite point configuration in continuous, discrete and arithmetic settings
Abstract: The basic question we ask is, how "large" does a subset of a vector space need to be to ensure that it contains a given geometric configurations, or a positive proportion of congruence classes of a given geometric configuration? This problem is connected with many interesting questions in analysis, number theory and combinatorics, including the sum-product phenomenon, the local smoothing conjecture for the wave equation and various notions of rigidity in classical geometry. We will survey some recent results in a variety of settings and describe the ideas behind them.

Friday, September 15, 13:30-14:30, McGill, Burnside 920
Eli Liflyand (Bar Ilan University)
Asymptotic relations for the Fourier transform of a function of bounded variation
Abstract: Earlier and recent one-dimensional estimates and asymptotic relations for the cosine and sine Fourier transform of a function of bounded variation are refined in such a way that become applicable for obtaining multidimensional asymptotic relations for the Fourier transform of a function with bounded Hardy variation.

Monday, August 28, Univ. de Montreal, 13:30-14:30, Room 5183
Alexei Penskoi (Moscow State University and Higher School of Economics)
An isoperimetric inequality for Laplace eigenvalues on the sphere and the projective plane
Abstract: The ﬁrst subject of this talk is an isoperimetric inequality for the second non-zero eigenvalue of the Laplace-Beltrami operator on the real projective plane (based on a joint paper with N. Nadirashvili). For a metric of area 1 this eigenvalue is not greater than 20\pi. This value could be attained as a limit on a sequence of metrics of area 1 on the projective plane converging to a singular metric on the projective plane and the sphere with standard metrics touching in a point such that the ratio of the areas of the projective plane and the sphere is 3:2. The second subject of this talk is a very recent result (joint paper with M. Karpukhin, N. Nadirashvili and I. Polterovich) about an isoperimetric inequality for Laplace eigenvalues on the sphere. For a metric of area 1 the k-th eigenvalue is not greater than 8\pi k. This value could be attained as a limit on a sequence of metrics of area 1 on the sphere converging to a singular metric on k spheres with standard metrics of equal radius touching in a point.