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)
SUMMER 2015
Thursday, June 4, Burnside 920, 13:00-14:00
Junehyuk Jung (KAIST)
Title TBA
WINTER 2015
Monday, January 5, Burnside 920, 13:00-14:00
Jerome Vetois (Universite de Nice Sophia Antipolis)
Compactness and blow-up phenomena for sign-changing solutions of scalar
curvature-type equations
Friday, January 9, Burnside 920, 13:00-14:00
Xiangwen Zhang (Columbia)
ABP estimate on Riemannian manifolds and spacetime Minkowski
formulae
Monday, January 12, Burnside 920, 13:00-14:00
Armen Shirikyan (Cergy-Pontoise)
Controllability and mixing for nonlinear differential equations
Monday, January 19, Burnside 920, 13:00-14:00
Jesse Gell-Redman (Johns Hopkins)
Geometric analysis on singular and non-compact spaces
Abstract:
The geometric objects which arise naturally in mathematics are
frequently and in important cases not smooth. Instead, many have
structured ends which look for example like cones, horns, or families of
these; a paradigmatic example is the Riemann moduli space of surfaces of
genus $g > 1$ with the Weil-Petersson metric, which near its singular
locus is approximately Riemannian products of families of horns. This
talk concerns geometric analysis on such spaces, especially the analysis
of naturally arising differential operators like the Hodge-Laplacian, the
Dirac operator, and the D'Alembertian (wave operator). The analysis of
such operators is substantially more complex in the non-smooth setting,
but we will present tools from microlocal analysis which provide both a
clear picture of and a resolution for many problems. We will focus in
particular on recent progress in index theory and spectral theory.
Friday, January 23, Burnside 920, 13:00-14:00
Yaiza Canzani (Harvard and IAS)
Geometry and topology of the nodal sets of Schrodinger eigenfunctions
Abstract:
In this talk I will present some new results on the structure of the
zero sets of Schrodinger eigenfunctions on compact Riemannian manifolds.
I will first explain how wiggly the zero sets can be by studying the number
of intersections with a fixed curve as the eigenvalue grows to infinity.
Then, I will discuss some results on the topology of the zero sets when the
eigenfunctions are randomized.
This talk is based on joint works with John Toth and Peter Sarnak.
Monday, January 26, Burnside 920, 13:00-14:00
Marcello Porta (Zurich)
Effective dynamics of weakly interacting fermionic systems
Abstract:
Systems composed by a large number of particles are often impossible to
describe starting from the fundamental laws of motion. For this reason,
physicists introduced
effective models, much simpler to study than the original many-body systems,
that at the
same time are expected to capture their main features if the number of
particles is large
enough. Examples are: the Boltzmann equation, for the dynamics of classical
particles in the
low density regime, or Thomas-Fermi theory, for the ground state of
fermionic quantum
systems in the mean-field scaling.
In this talk I will discuss a rigorous derivation of the time-dependent
Hartree-Fock equation,
an effective evolution equation for a system of interacting fermionic
particles in the meanfield
scaling. I will consider both pure states (zero temperature) and mixed
states (positive
temperature). With respect to the well understood bosonic case, here the
main difference is
that fermionic mean-field is naturally coupled with a semiclassical scaling.
Monday, February 2, Burnside 920, 13:00-14:00
Anna Lisa Panati (McGill)
Energy conservation, counting statistics and return to equilibrium
Abstract:
We study a microscopic Hamiltonian model describing a finite level
quantum system S
coupled to an infinitely extended thermal reservoir R. Initially, the system
S is in an arbitrary state
while the reservoir is in thermal equilibrium at inverse temperature \beta.
Assuming that the coupled
system S + R is mixing with respect to the joint thermal state, we study
the Full Counting Statistics
(FCS) of the energy transfers S \to R and R \to S in the process of return
to equilibrium. The first FCS
is an atomic probability measure P_{S,\lambda,t} concentrated on
the set of energy differences sp(HS)−sp(HS)
(HS is the Hamiltonian of S, t is time at which the measurement of the
energy transfer is performed,
and \lambda is the coupling constant describing the strength of the
interaction between S and R). The second
FCS P_{R,\lambda,t} is typically a continuous probability measure whose
support is the whole real line. We
study the large time limit t \to\infty of these two measures followed
by the weak coupling limit \lambda\to 0
and prove that the limiting measures coincide. This result strengthens
the first law of thermodynamics
for open quantum systems. The proofs are based on modular theory of operator
algebras and quantum
transfer operator representation of FCS. (joint work with V. Jaksic,
J. Panangaden, C-A. Pillet)
Friday, February 13, Burnside 920, 13:00-14:00
Frederic Naud (Avignon)
Nodal lines and domains for Eisenstein series on surfaces
Abstract:
Eisenstein series are the natural analog of “plane waves” for hyperbolic
manifolds of infinite
volume. These non-L^2
eigenfunctions of the Laplacian parametrize the continuous spectrum. In
this talk we will discuss the structure of nodal sets and domains for
surfaces. Upper and lower
bounds on the number of intersections of nodal lines with “generic” real
analytic curves will be
given, together with similar bounds on the number of nodal domains inside
the convex core. The
results are based on equidistribution theorems for restriction of Eisenstein
series to curves that bear
some similarity with the so-called “QER” results for compact manifolds.
Thursday, February 19, 13:30-14:30, Concordia, Library
building, Room LB 921-04
Scott Rodney (Cape Breton university)
Degenerate elliptic equations with rough coefficients: recent regularity
results and H=W
Abstract:
During this talk we will discuss the derivation of a local Harnack inequality
for weak solutions to degenerate elliptic quasi-linear equations with rough
coefficients and also how this leads to Holder continuity of solutions.
Following this, I will describe some related problems involving degenerate
Sobolev spaces and H=W.
Friday, February 20, Burnside 920, 13:00-14:00
Patrick Munroe (McGill)
Moments of Eisenstein series on convex co-compact hyperbolic manifolds
Abstract:
On infinite-volume hyperbolic manifolds, the Eisenstein series
are non-L^2 eigenfunctions of the Laplacian which parametrize the
continuous spectrum. In this talk, we will discuss the moments of
Eisenstein series at high-energy on convex co-compact manifolds, i.e., on
infinite-volume hyperbolic manifolds without cusps. More precisely, a
new result about the vanishing of the odd moments will be presented and
an explicit limit for the fourth moment on surfaces will be given.
Monday, February 23, Burnside 920, 13:00-14:00
Tomasz Kaczynski (Sherbrooke)
Towards a formal tie between combinatorial and classical vector field
dynamics
Abstract:
The Forman’s discrete Morse theory is an analogy of the classical
Morse theory with, so far, only informal ties. Our goal is to
establish a formal tie on the level of induced dynamics. Following the
Forman’s 1998 paper on “Combinatorial vector fields and dynamical
systems”, we start with a possibly non-gradient combinatorial vector
field. We construct a flow-like upper semi-continuous acyclic-valued
mapping whose dynamics is equivalent to the dynamics of the Forman’s
combinatorial vector field, in the sense that isolated invariant sets
and index pairs are in one-to-one correspondence.
Working seminar in Geometric Analysis
Wednesday, February 25, Burnside 920, 13:30-14:30
Yi Wang (IAS and Johns Hopkins)
Isoperimetric inequalities and $Q$-curvature in
conformal geometry and CR geometry
Abstract:
In this talk, we will discuss the connection between
isoperimetric inequalities and Branson's $Q$-curvature on conformally
flat manifolds. This is the higher dimensional analog of the classical
Fiala-Huber's isoperimetric inequality for surfaces. Also, we notice
that the same phenomenon extends to the sub-Riemannian case, with
modified Paneitz operator and $Q$-curvature on CR-manifolds. We will
talk about recent progress in this direction.
Friday, February 27, Burnside 920, 13:00-14:00
M. Karpukhin (McGill)
Upper bounds for the first Laplace eigenvalue on non-orientable surfaces
and real algebraic geometry
Abstract:
One of the important questions of spectral geometry is to determine the
supremum of the first Laplace eigenvalue over the space of Riemannian
metrics of unit volume on a fixed surface M. The celebrated inequality of
Yang and Yau guarantees finiteness of this quantity for orientable surfaces.
In the present talk we prove the analog of Yang-Yau inequality for
non-orientable surfaces. The proof uses interesting concepts of real
algebraic geometry.
Monday, March 16, Burnside 920, 13:00-14:00
Victor Kalvin (Concordia)
Moduli spaces of meromorphic functions and determinant of Laplacian
Abstract:
The Hurwitz space is the moduli space of pairs (X,f), where X is a compact
Riemann surface and f is a meromorphic function on X. We consider the
Laplace operator on the flat non-compact singular Riemannian manifold
(X, |df|^2). We define a regularized relative determinant of the Laplace
operator and obtain an explicit expression for the determinant in terms of
the basic objects on the underlying Riemann surface (the prime form,
theta-functions, the canonical meromorphic bidifferential) and the divisor
of the meromorphic differential df. In this talk I will mainly speak about
a surgery formula of the type of Burghelea-Friedlander-Kappeler for the
relative determinant of the Laplace operator on singular flat surfaces with
conical and Euclidean ends. This formula allows to close the
conical/Euclidean ends and thus reduces the proof of explicit expression
for the relative determinant to the proof of a similar expression for the
zeta-regularized determinant of Laplace operator on the (compact) manifold
with closed ends. We believe the surgery formula is also of independent
interest. The talk is based on a joint work with Alexey Kokotov and Luc
Hillairet.
Friday, March 20, Burnside 920, 13:00-14:00
Jun Kitagawa (Toronto)
Generated Jacobian equations and regularity: optimal transport,
geometric optics, and beyond
Abstract:
Equations of Monge-Ampere type arise in numerous contexts, and solutions
often exhibit very subtle qualitative and quantitative properties; this is
owing to the highly nonlinear nature of the equation, and its degenerate
ellipticity. Motivated by an example from geometric optics I will talk about
the class of Generated Jacobian Equations, recently introduced by Trudinger.
This class encompasses, for example, optimal transport, the Minkowski
problem, and the classical Monge-Amp{\`e}re equation. I will present a new
regularity result for weak solutions of these equations, which is new even
in the case of equations arising from near-field reflector problems in
geometric optics. This talk is based on joint works with N. Guillen.
Monday, March 23, 14:00-15:00,
UdeM/CRM, Room 4336
Beatrice-Helen Vritsiou (U. of Michigan)
On the Bourgain-Milman inequality: a proof that uses only tools from
Convex Geometry
Abstract:
The classical Blaschke-Santaló inequality states that the volume product
vol(K)vol(K^o) of symmetric convex bodies K, or, more generally, convex
bodies K with barycentre at the origin, is (uniquely) maximised by ellipsoids
(here vol denotes Lebesgue measure and K^o is the polar body of K). The
Bourgain-Milman inequality, proved by Bourgain and Milman in 1987, is an
(asymptotic) inverse to the Blaschke-Santalo inequality: it tells us that
vol(K)vol(K^o) >= a^n vol(E)vol(E^o) >= (b/n)^n for every n-dimensional
convex body K that contains the origin in its interior, where E is any
n-dimensional symmetric ellipsoid and a, b are constants independent of the
dimension n. We will present an alternative proof of the Bourgain-Milman
inequality that uses only convex-geometric tools, and in particular methods
developed for the study of isotropic convex bodies.
This is joint work with A. Giannopoulos and G. Paouris.
Monday, March 30, 13:30-14:30, Concordia, Library
building, Room LB 921-04
Vitali Milman (Tel Aviv)
Some algebraic related structures on families of convex sets
Friday, April 10, Burnside 920, 13:00-14:00
Ray McLenaghan (Waterloo)
Huygens' principle and Hadamard's problem of diffusion of waves
Abstract:
Huygens' principle is satisfied by a second order linear hyperbolic partial
differential equation if the solution at any point of every Cauchy initial
value problem depends only on the data in an arbitrarily small neighbourhood
of the intersection of the retrograde characteristic conoid from the point
with the initial surface. The ordinary wave equation in an even number of
independent variables greater than or equal to four has this property while
the
wave equation in an odd number of variables does not. In 1923 Hadamard
posed the problem, which remains unsolved, of determining up to
equivalence all equations which possess the Huygens property. The lecture
will describe the history and current status of attempts to solve the problem
with emphasis on the physically interesting case of four independent
variables. It will include a description of an apparently new non-trivial
Huygens equation.
Friday, April 24, 13:30-14:30, Concordia, LB 921-4
Ataollah Askari-Hemmat
On shearlets of L^2(Q_p^2)
Abstract:
Friday, May 1, Burnside 920, 13:00-14:00
Luc Hillairet (Univ. d'Orleans)
On the wave propagation in generalized polygons
Abstract:
We study the wave propagation on flat surfaces with conical singularities
that generalize polygons. We give a new construction of the wave propagator
near the intersection of the direct front and the diffracted front and
relate it with the class
of singular FIO that was introduced by Melrose-Uhlmann.
We apply this result to the computation of the contribution to the
wave-trace of
any kind of periodic orbit. (joint work with A. Ford and A. Hassell).
Propagation des ondes dans les polygones généralisés
Résumé:
On étudie la propagation des ondes sur les surfaces euclidiennes à
singularités coniques
qui généralisent les polygones. On donne une nouvelle construction du
propagateur au voisinage
de l'intersection des fronts direct et diffracté et on l'interprète dans
la classe des OIF singuliers
introduite par Melrose-Uhlmann. On utilise ce résultat pour calculer la
contribution à la formule
de trace de n'importe quel type d'orbite périodique. (collaboration avec
A. Ford et A. Hassell).
Monday, May 4, Burnside 920, 13:00-14:00
Jacopo de Simoi (Toronto)
An integrable billiard close to an ellipse of small eccentricity is an
ellipse
Abstract:
In 1927 G. Birkhoff conjectured that if a billiard in a strictly convex smooth
domain is integrable, the domain has to be an ellipse (or a circle). The
conjecture is still wide open, and presents remarkable relations with open
questions in inverse spectral theory and spectral rigidity.
In the talk we show that a version of Birkhoff's conjecture is true for small
perturbations of ellipses of small eccentricity.
This is joint work with A. Avila and V. Kaloshin
Friday, May 8, Burnside 920, 13:00-14:00
Alessandro Savo (University of Rome - La Sapienza)
Constant heat flow, Serrin problem and the isoparametric property
Abstract: On a compact domain in a Riemannian manifold, we study
the solution of the heat equation having constant unit initial conditions
and Dirichlet boundary conditions.
The aim of this talk is to discuss the geometry of domains for which,
at any fixed value of time, the normal derivative of the solution (heat
flow) is a constant function on the boundary.
We express this fact by saying that such domains have the "
constant flow property",
or that they are "perfect heat diffusers". In constant curvature spaces
known examples
of such domains are given by geodesic balls and, more generally,
by domains whose boundary is connected and isoparametric.
The question is: are they all like that?
In the talk, we first relate this property with the well-know Serrin problem.
Then, we give a precise characterization in terms of the second
fundamental form
of the boundary and the isoparametric property.
Wednesday, May 13, Burnside 1205, 13:30-14:30
Mike Wilson (Vermont)
Almost-orthogonality: almost as good as orthogonality
Abstract.
Friday, May 15, Univ. de Montreal, Pav. Andre Aisenstadt,
Room 5448, 14:00-15:00
Rick Laugesen (UIUC)
Steklov spectral inequalities through quasiconformal mapping
Abstract:
Eigenvalues of the Steklov or Dirichlet-to-Neumann operator represent
frequencies of vibration of a free membrane whose mass is concentrated at
the boundary. They arise also in sloshing problems.
We show the disk maximizes various functionals of the Steklov eigenvalues,
under normalization of the perimeter and a kind of boundary moment. The
results cover the first eigenvalue, spectral zeta function and trace of
the heat kernel. Interestingly, the method employs quasiconformal mapping
to estimate the distortion of the energy functional (Dirichlet integral).
ANALYSIS-RELATED TALKS ELSEWHERE, WINTER 2015
CRM/McGill Applied Mathematics seminar
Monday, February 9, 15:00-16:00, McGill, Burnside 920
Renato Calleja (IIMAS-UNAM)
Construction of quasi-periodic response solutions for forced systems
with strong damping
Abstract:
I will present a method for constructing quasi-periodic response
solutions (i.e. quasi-periodic solutions with the same frequency as the
forcing) for over-damped systems. Our method applies to non-linear wave
equations subject to very strong damping and quasi-periodic external forcing
and to the varactor equation in electronic engineering. The strong damping
leads to very few small divisors which allows to prove the existence by
using a contraction mapping argument requiring very weak non-resonance
conditions on the frequency. This is joint work with A. Celletti, L. Corsi,
and R. de la Llave.
CRM-ISM Colloquium
Thursday, March 5, McGill University, Burnside Hall,
805 Sherbrooke str. West, Room 920
THE TALK IS CANCELLED
Alvaro Pelayo (UC San Diego)
Classical and quantum integrable systems
CRM NIRENBERG LECTURES IN GEOMETRIC ANALYSIS
CRM, March 20-24, Pav. Andre-Aisenstadt, Univ. de Montreal,
Salle / Room 6214
Andre Neves (Imperial College London)
SUMMER 2014
Tuesday, August 26, Burnside 920, 13:15-14:15
Michael Wilson (Vermont)
Almost-orthogonality without discreteness or smoothness
Abstract
Tuesday, August 26, Burnside 920, 14:30-15:30
Alexander Stokolos (Georgia Southern)
Geometric maximal function in harmonic analysis
Abstract: Some interesting examples of maximal functions associated with a differentiation bases of convex sets will considered.
FALL 2014
Please, note that in the Fall 2014, Monday seminars at McGill
will be held in Burnside 306 (3rd floor) between 14:30-15:30
Monday, September 15, 14:30-15:30, Burnside 306
Suresh Eswarathasan (McGill)
Perturbations of the Schrodinger equation on negatively curved surfaces
Abstract: In this talk, we will take small perturbations of the semiclassical
Schrodinger equation on negatively curved surfaces and consider some
of the corresponding long-time quantum evolutions. We will show that,
under certain admissibility conditions on the perturbation, these
solutions become equidistributed in the semiclassical limit for
"typical" perturbations. This is joint work with Gabriel Riviere.
Monday, October 6, 14:30-15:30, Burnside 306
Javad Mashreghi (Laval)
Embedding theorems for the Dirichlet space
Abstract: A finite positive Borel measure $\mu$ on $\mathbb{D}$
is a {\em Carleson measure} for the (classical) Dirichlet space
$\mathcal{D}$ if \[ \|f\|_{L^2(\mu)} \leq C \|f\|_{\mathcal{D}},
\qquad f \in \mathcal{D}.
\]
Equivalently, we can say that $\mathcal{D}$ embeds in $L^2(\mu)$. We will
discuss the geometric characterization of such measures and present a
particular "one-box condition".
Friday, October 10, 15:10-16:10, Burnside 1120 (time changed!)
Boaz Slomka (Concordia, CRM)
Covering numbers of convex sets and their functional extension
Abstract:
In the first part of the talk we will discuss the notions of classical and
fractional covering numbers, mainly in the context of convex bodies. In
particular, we will describe an application to Hadwiger's famous covering
problem.
In the second part of the talk we will focus on the extension of covering
numbers to the realms of functions (mainly log-concave). We will present
some of their properties as well as related inequalities.
Based on joint works with Shiri Artstein-Avidan
Monday, October 27, 14:30-15:30, Burnside 306
Andrei Martinez-Finkelshtein (Almeira)
Phase transitions and equilibrium measures in random matrix
models
Abstract:
We are interested in the so-called phase transitions in the
Hermitian random matrix models with a polynomial potential. Or, in
a language more familiar to approximators, we study families of
equilibrium measures on the real line in a polynomial external
field. The total mass of the measure is considered as the main
parameter, which may be interpreted also either as temperature or
time. By phase transitions we understand the loss of analyticity
of the equilibrium energy.
Our main tools are differentiation formulas with respect to the
parameters of the problem, and a representation of the equilibrium
potential in terms of a hyperelliptic integral. This allows to find
a dynamical system that describes the evolution of families of
equilibrium measures. On this basis we are able to systematically
derive results on phase transitions, such as the local behavior of
the system at all kinds of phase transitions. We discuss in depth
the case of the quartic external field.
Monday, November 10, 14:30-15:30, Burnside 306
Raphaël Ponge (Seoul National University and Berkeley)
Noncommutative geometry and Vafa-Witten inequality
Abstract:
The inequality of Vafa-Witten produces an uniform bound for the first
eigenvalue of a Dirac operator with coefficients in a Hermitian vector
bundles. It's a remarkable fact that bound does not depend on the vector
bundle. In this talk, we will explain how to use the framework of
noncommutative geometry to reformulate Vafa-Witten inequality in various
new geometric settings such as conformal geometry, noncommutative
tori, and some symmetric spaces.
Friday, November 14, 14:30-15:30, Burnside 920
Monica Ludwig (TU Wien)
On the geometric classification of functions
Abstract:
A fundamental theorem of Hadwiger classifies all rigid-motion-invariant
and continuous functionals on convex bodies that satisfy the
inclusion-exclusion principle. Moreover, Hadwiger's theorem characterizes
the n+1 intrinsic volumes (volume, surface area, etc.) in Euclidean n-space.
Recently, important functions in analysis and probability theory have been
characterized by geometric properties and the inclusion-exclusion property,
for example, the Fisher information matrix and the operator that associates
with a function its optimal Sobolev norm. An overview of these results
will be given.
Monday, November 24, 13:30-14:30, Concordia, LB 921-04
Boaz Slomka (Concordia, CRM)
Functional covering numbers
Abstract:
Covering and separation (packing) numbers are useful tools in
various areas of mathematics. In particular, they play an important role
in the theory of convex bodies. In this talk we will introduce natural
extensions of these geometric concepts to the realms of functions, and
discuss their properties as well as related inequalities. We will mainly
consider log-concave functions, as our original motivation is the study of
their geometry and interplay with convex bodies.
Joint work with Shiri Artstein-Avidan.
Friday, November 28, Burnside 920, 14:30-15:30
Todd Oliynik (Monash University)
Dynamical compact bodies in General Relativity
Abstract:
The visible universe contains many different types of dynamical compact
bodies including asteroids, comets, planets, stars and even more exotic
objects such as neutron stars. In spite of their fundamental importance to
astrophysics and cosmology, there are currently very few analytical results
available that apply to these dynamical bodies. In particular, even the most
basic problem of establishing the (local) existence and uniqueness of
solutions that represent gravitating compact bodies was, until very recently,
a long standing open problem in General Relativity (GR). In this talk, I
will discuss this problem and pay particular attend to the case of elastic
matter. After presenting some general background on the dynamics of
compact bodies in GR, I will describe, in detail, the initial value
formulation for the particular case of elastic matter and outline the
analytic difficulties that have hindered progress in understand the initial
value problem for this system. I will then summarize recent results obtained
in collaboration with Lars Anderson and Bernd Schmidt in which we establish
the existence and uniqueness of solutions that represent gravitating
dynamical elastic bodies. Time permitting, I will describe some open
problems and promising directions for future work.
Tuesday, December 2, Burnside 1205, 13:00-14:00 (time changed!)
Yaiza Canzani (Harvard and IAS)
Pointwise Weyl Law and Universal scaling asymptotics
Abstract:
In this talk I will present new off-diagonal remainder estimates for the
kernel of the spectral projector of the Laplacian onto frequencies up to
$\lambda$. One of the consequences is that the kernel of the spectral
projector onto frequencies $(\lambda,\lambda+1]$ has a universal scaling
limit as $\lambda \to \infty$ near any non self-focal point. These results
have applications to immersions by eigenfunctions, gradient estimates, and
to the study of zero sets of random waves. This is joint work with Boris
Hanin.
ANALYSIS-RELATED TALKS ELSEWHERE,
FALL 2014
UdeM-McGill Spectral Theory seminar
Thursday, September 11, Universite de Montreal, pav. Andre-Aisenstadt,
room 5448, 14:00-15:00
Guillaume Roy-Fortin (UdeM)
Nodal sets and growth exponents of Laplace eigenfunctions on surfaces
Seminar
website
UdeM-McGill Spectral Theory seminar
Thursday, September 25, McGill, Burnside 1120, 14:00-15:00
John Toth (McGill)
L^2-restriction lower bounds for Schrodinger eigenfunctions in
classically forbidden regions.
Seminar
website
UdeM-McGill Spectral Theory seminar
Thursday, October 2, Universite de Montreal, pav. Andre-Aisenstadt,
room 5448, 14:00-15:00
Frederic Naud (Avignon)
Sharp Resonances on hyperbolic manifolds
Seminar
website
McGill Mathematical Physics mini-course
Jakob Yngvanson (Vienna)
A crash course on thermodynamics and entropy
Montreal Probability seminar and Analysis seminar
Tuesday, October 14, 16:30, McGill, Burnside 1214
Mark Freidlin (University of Maryland)
Long time effects of small perturbations
Mathematical Physics Week
October 27-31, Burnside Hall
More details
here.
UdeM-McGill Spectral Theory seminar
Thursday, November 6, McGill, Burnside 1120, 14:00-15:00
Annalisa Panati (CRM/McGill)
Spectral and scattering theory for abstract QFT Hamiltonians (joint
work with Christian Gerard)
Abstract.
UdeM-McGill Spectral Theory seminar
Thursday, November 13, Universite de Montreal,
pav. Andre-Aisenstadt, room 5448, 14:00-15:00
Frederic Rochon (UQAM)
Title TBA
UdeM-McGill Spectral Theory seminar
Thursday, November 20, Universite de Montreal,
pav. Andre-Aisenstadt, room 5448, 14:00-15:00
Iosif Polterovich (UMontreal)
Spectral geometry of the Steklov problem
Abstract:
The Steklov problem is an elliptic eigenvalue problem with the
spectral parameter in the boundary conditions. While this problem shares
some common properties with its more well known Dirichlet and Neumann cousins,
the Steklov eigenvalues and eigenfunctions have a number of distinctive
geometric features. We will discuss some recent advances in the subject,
particularly in the study of spectral asymptotics, spectral invariants,
eigenvalue estimates, and nodal geometry. The talk is based on a joint survey
article with A. Girouard.
Concordia Dynamical Systems seminar
Friday, November 21, 11:45-12:45, LB-921-4 (Library Building)
Maciej P. Wojtkowski (University of Warmia i Mazury, Olsztyn,
Poland)
Bi-partitions of the 2-d torus, 1-dimensional tilings,
hyperbolic automorphisms and their Markov partitions
Abstract:
Bi-partitions are partitions of the 2-dim torus by two parallelograms.
They give rise to 2-periodic tilings of the plane, and further to
1-dim tilings which have a host of well known combinatorial properties,
e.g. these are Sturmian sequences. When a bi-partition is a Markov
partition
for a hyperbolic toral automorphism (= Berg partition),
the tilings are substitution tilings. Substitutions preserving Sturmian
sequences have the remarkable ``3-palindrome property''. The number
of different substitutions was determined by Seebold '98, and the number
of nonequivalent Berg partitions by Siemaszko and Wojtkowski '11.
The two formulas coincide. Using tilings we explain the formula
by the 3 palindrome property. The coincidence then shows that
every combinatorial substitution preserving a Sturmian sequence
is realized geometrically as a Berg partition.
UdeM-McGill Spectral Theory seminar
Thursday, November 27, McGill, Burnside Hall, room 1120,
14:00-15:00
Mikhail Karpukhin (McGill)
Regularity theorems for maximal metrics
Abstract:
Given a smooth surface M the first eigenvalue of the Laplace operator can
be seen as a functional on the space of Riemannian metrics on M of unit
volume. One of the important problems of spectral geometry is to find the
supremum of this functional. However it is not even clear that the supremum
is attained on a smooth metric. In this talk I will present a recent result
on the regularity theory of these maximal metrics, which states that under
fairly weak condition the maximal metric is a smooth metric with isolated
conical singularities. The talk is based on the results of R. Petrides
Mathematical Physics Seminar
Tuesday, December 2, CRM, UdeM, Pavillon Andre-Aisenstadt, 2920,
ch. de la Tour, salle 4336, 15:30-16:30
David Ruelle (IHES)
Introduction to hydrodynamic turbulence and non-equilibrium statistical
mechanics
Abstract:
We present here basic facts about hydrodynamic turbulence and
statistical mechanics (equilibrium and non-equilibrium). This introduction
should allow to understand the main talk without too much previous
knowledge of the relevant areas of physics and mathematics.
Analysis/Mathematical Physics seminar
Wednesday, December 3, McGill, Burnside 708, 16:30-17:30
David Ruelle (IHES)
The Lee-Yang Circle Theorem and some applications
UdeM-McGill Spectral Theory seminar
Thursday, December 4, Universite de Montreal,
pav. Andre-Aisenstadt, room 5448, 14:00-15:00
Daniel Valtorta (Polytechnique Lausanne)
Minkowski estimates on critical and nodal sets of solutions to elliptic
PDEs
Abstract:
Given a nonconstant harmonic function, we obtain Minkowski bounds on
its critical and almost critical set. The proof relies on a refined
blow-up analysis for harmonic functions based on the properties of
Almgren's frequency. With minor modifications, these estimates are valid
also for solutions to a very general class of elliptic PDEs. Given the
link between harmonic functions and eigenfunctions of the Laplacians,
with the necessary modifications these results apply also to nodal and
singular sets of eigenfunctions. This is joint work with Aaron Naber.
Analysis/Mathematical Physics seminar
Friday, December 5, McGill, 14:00-15:00, Burnside 920
David Ruelle (IHES)
Non-equilibrium Statistical Mechanics of Turbulence
Abstract:
The macroscopic study of hydrodynamic turbulence is equivalent, at an
abstract level, to the microscopic study of a heat flow for a suitable
mechanical system. Turbulent fluctuations (intermittency) then correspond
to thermal fluctuations, and this allows to estimate the exponents $\tau_p$
associated with moments of velocity fluctuations. In particular we derive
probability distributions at finite Reynolds number for the velocity
fluctuations which permit an interpretation of numerical experiments.
Specifically, if $p(z)dz$ is the probability distribution of the radial
velocity gradient we can explain why, when the Reynolds number ${\cal R}$
increases, $\ln p(z)$ passes from a concave to a linear then to a convex
profile for large $z$ as observed in Navier-Stokes studies. We show that
the central limit theorem applies to the velocity distribution functions,
so that a logical relation with the lognormal theory of Kolmogorov and
Obukhov is established. We find however that the lognormal behavior of the
distribution functions fails at large value of the argument, so that a
lognormal theory cannot correctly predict the exponents $\tau_p$ and
$\zeta_p$.
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