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

Joint Analysis and Geometric Analysis seminar
Friday, February 16, 13:30-14:30, McGill, Room 920 (to be confirmed)
Loredana Lanzani (Syracuse)
Title TBA

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.

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