Seminars Sorted by Series
Analysis and Mathematical Physics
Quantitative Regularity Theory for the Axisymmetric Navier-Stokes Equations
2:30pm|Simonyi Hall 101 and Remote Access
In the search for possible blow-up of the incompressible
Navier-Stokes equations, there has been much recent attention on
the class of axisymmetric solutions with swirl. Several interesting
structures of this system have led to regularity criteria...
Chaos in Lattice Spin Glasses and Some Questions for Analysts
2:30pm|Simonyi Hall 101 and Remote Access
In spite of tremendous progress in the mean-field theory of spin
glasses in the last forty years, culminating in Giorgio Parisi’s
Nobel Prize in 2021, the more “realistic” short-range spin glass
models have remained almost completely intractable. In...
Arithmetic Study Behind Spectra of Quantum Interactions
Masato Wakayama
4:00pm|Simonyi Hall 101 and Remote Access
Interaction models discussed here are the (asymmetric) quantum
Rabi model (QRM), which describes the interaction between a photon
and two-level atoms, and the non-commutative harmonic oscillator
(NCHO). The latter can be considered as a covering...
Variations on Fefferman's Ball Multiplier Theorem
2:30pm|Simonyi Hall 101 and Remote Access
What happens to an Lp function when one truncates its Fourier
transform to a domain? This question is now rather well understood,
thanks to famous results by Marcel Riesz and Charles Fefferman, and
the answer depends on the domain: if it is a...
Generic Properties of Laplace Eigenfunctions in the Presence of Symmetry
2:30pm|Simonyi Hall 101 and Remote Access
Let $G$ be a compact Lie group acting on a closed manifold $M$.
Partially motivated by work of Uhlenbeck (1976), we explore the
generic properties of Laplace eigenfunctions associated to
$G$-invariant metrics on $M$. We find that, in the case
where...
Some Analytic Applications of the Polynomial Method
2:30pm|Simonyi Hall 101 and Remote Access
This talk will be about the polynomial method and its
applications to questions that have traditionally been tackled by
Fourier analysis, with emphasis on the Kakeya conjecture, the cap
set problem, arithmetic progressions in dense sets, and the...
Supersymmetric Approach to the Analysis of Random Band Matrices
2:30pm|Simonyi Hall 101 and Remote Access
We discuss an application of the SUSY approach to the analysis
of spectral characteristics of hermitian and non hermitian random
band matrices. In 1D case the obtained integral representations for
correlation functions of characteristic polynomials...
Continuous Symmetry Breaking: A Rigorous Approach
Sara Daneri
2:30pm|Simonyi Hall 101 and Remote Access
At the base of spontaneous pattern formation is universally
believed to be the competition between short range attractive and
long range repulsive forces. Though such a phenomenon is observed
in experiments and simulations, a rigorous understanding...
Global Well-Posedness of Stochastic Abelian-Higgs in Two Dimensions
Sky Cao
2:30pm|Simonyi Hall 101 and Remote Access
There has been much recent progress on the local solution theory
for geometric singular SPDEs. However, the global theory is still
largely open. In my talk, I will discuss the global well-posedness
of the stochastic Abelian-Higgs model in two...
Inertial Manifolds for the Hyperbolic Cahn-Hilliard Equation
Ahmed Bonfoh
2:30pm|Simonyi Hall 101 and Remote Access
An inertial manifold is a positively invariant smooth
finite-dimensional manifold which contains the global attractor and
which attracts the trajectories at a uniform exponential rate. It
follows that the infinite-dimensional dynamical system is...
Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties
Pavel Kurasov
2:30pm|Simonyi Hall 101 and Remote Access
Fourier Quasicrystals (FQ) are defined as crystalline measures
$$ \mu = \sum_{\lambda \in \Lambda} a_\lambda \delta_\lambda, \quad
\hat{\mu} = \sum_{s \in S} b_s \delta_s, $$ so that not only $ \mu
$ (and hence $ \hat{\mu} $) are tempered...
Serrin’s Overtermined Problem In Rough Domains
2:30pm|Simonyi Hall 101 and Remote Access
The classical Serrin’s overdetermined theorem states that a C^2
bounded domain, which admits a function with constant Laplacian
that satisfies both constant Dirichlet and Neumann boundary
conditions, must necessarily be a ball. While extensions of...
Evolution of Coherent Structures in Incompressible Flows
2:30pm|Simonyi Hall 101 and Remote Access
In this talk, we will explore recent developments in the study
of coherent structures evolving by incompressible flows. Our focus
will be on the behavior of fluid interfaces and vortex filaments.
We include the dynamics of gravity Stokes interfaces...
Duality of Fluid Mechanics and Solution of Decaying Turbulence
2:30pm|Simonyi Hall 101 and Remote Access
I will describe the duality of incompressible Navier-Stokes
fluid dynamics in three dimensions, leading to its reformulation in
terms of a one-dimensional momentum loop equation.
The decaying turbulence is a solution of this equation equivalent
to a...
Absolute Continuity of the Robin Harmonic Measure On Rough Domains
Guy David
2:30pm|Simonyi Hall 101 and Remote Access
The question of asbolute continuity, with respect to the
reference measure, of the harmonic measure on a domain with rough
boundary has been the object of many important results. Here we ask
about the similar question, but where the Dirichlet...
2:30pm|Simonyi Hall 101 and Remote Access
New Estimates for Navier–Stokes and the Inviscid Limit Problem
2:30pm|Simonyi Hall 101 and Remote Access
In this talk, I will present several a priori interior and
boundary trace estimates for the 3D incompressible Navier–Stokes
equation, which recover and extend the current picture of higher
derivative estimates in the mixed norm. Then we discuss the...
2:30pm|Simonyi Hall 101 and Remote Access
Spectral Minimal Partitions: Local vs Global Minimality
2:30pm|Simonyi Hall 101 and Remote Access
In this overview talk we will explore a variational approach
to the problem of Spectral Minimal Partitions (SMPs).
The problem is to partition a domain or a manifold into k
subdomains so that the first Dirichlet eigenvalue on each subdomain
is as...
The 3D Kinetic Couette Flow Via The Boltzmann Equation In The Diffusive Limit
Robert Strain
2:30pm|Simonyi Hall 101 and Remote Access
This talk is about the study of the Boltzmann equation in the
diffusive limit in a channel domain $\mathbb{T}^2\times (-1,1)$
nearby the 3D kinetic Couette flow. We will begin the talk
with a substantial introduction for non-experts. Our
result...
Restriction Estimates Using Decoupling Theorem and Incidence Estimates For Tubes
Hong Wang
2:30pm|Simonyi Hall 101 and Remote Access
Suppose f is a function with Fourier transform supported on the
unit sphere in $R^d$. Elias Stein conjectured in the 1960s that the
$L^p$ norm of f is bounded by the $L^p$ norm of its Fourier
transform, for any $p> 2d/(d-1)$. We propose to
study...
2:30pm|Simonyi Hall 101 and Remote Access
On Minkowski's Monotonicity Problem
Ramon van Handel
2:30pm|Simonyi Hall 101 and Remote Access
More than 120 years ago, Minkowski published a seminal paper
that laid the foundation for the field of convex geometry (as well
as several other areas of mathematics). Despite numerous advances
in the intervening years, there are fundamental...
Geometry and Topology of Spectral Minimal Partitions
Graham Cox
2:30pm|Simonyi Hall 101 and Remote Access
A minimal partition is a decomposition of a manifold into
disjoint sets that minimizes a spectral energy functional. In the
bipartite case minimal partitions are closely related to
eigenfunctions of the Laplacian, but in the non-bipartite case
they...
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
2:30pm|Simonyi Hall 101 and Remote Access
Analysis Seminar
Orbit of the Diagonal of a Power of a Nilmanifold
Alexander Leibman
Let p_1,...,p_k be integer polynomials of one or several
variables. There is a relation between the density of polynomial
configurations a+p_1(n),...,a+p_k(n) in sets of integers and the
form of the closure of the diagonal of X^k under the...
Lior Siberman
2:00pm|West Bldg. Lecture Hall
Stationary Measures and Equidistribution on the Torus
10:30am|West Bldg. Lecture Hall
In this talk I will consider actions of non-abelian groups on
n-dimensional tori, explain the notions of stiffness and stationary
measures, and show how under fairly general assumptions stationary
measures can be classified. A key ingredient is a...
Expanders and Random Walks in SL(d,q)
A Hardy Field Extension of Szemeredi's Theorem
In 1975 Szemeredi proved that every subset of the integers with
positive density contains arbitrarily long arithmetic progressions.
Bergelson and Leibman showed in 1996 that the common difference of
the arithmetic progression can be a square, a cube...
On the Two dimensional Bilinear Hilbert Transform and Z^2 Actions
2:00pm|West Bldg. Lecture Hall
We investigate the Bilinear Hilbert Transform in the plane and
the pointwise convergence of bilinear averages in Ergodic theory,
arising from Z^2 actions. Our techniques combine novel one and a
half dimensional phase-space analysis with more...
On the Instability for 2D Fluids
For 2D Euler equation, we prove a double exponential lower bound
on the vorticity gradient. We will also discus some further results
on the singularity formation for other models.
On the Rigidity of Black Holes
Sergiu Klainerman
The classical result on the uniqueness of black holes in GR, due
to Hawking, which asserts that regular, stationary solutions of the
Einstein vacuum equations must be isometric to an admissible black
hole Kerr solution, has at its core a a highly...
The Defocusing Cubic Nonlinear Wave Equation in the Energy-Supercritical Regime
In this talk, we will present some recent results in the study
of the nonlinear wave equation with cubic defocusing nonlinearity,
describing the completion of a program to establish global
well-posedness and scattering in the energy-supercritical...
Around the Davenport-Heilbronn Function
The Davenport-Heilbronn function (introduced by Titchmarsh) is a
linear combination of the two L-functions with a complex character
mod 5, with a functional equation of L-function type but for which
the analogue of the Riemann hypothesis fails. In...
Tangent Cones to Calibrated Currents
Constante Bellettini
2:00pm|West Bldg. Lecture Hall
Calibrated currents are a particular class of volume-minimizers
and as such provide interesting explicit examples of solutions to
Plateau's problem. Their role goes however much beyond that: they
naturally appear when dealing with several geometric...
The Energy-Critical Defocusing NLS in Periodic Settings
I will discuss some recent work, joint with B. Pausader, on
constructing global solutions of defocusing energy-critical
nonlinear Schrodinger equations in periodic and semiperiodic
settings.
On the Ergodic Properties of Square-Free Numbers
I shall explain the structure of correlation functions for
square-free numbers and describe a 'natural' dynamical system
associated to them. Spectral analysis allows us to show that this
system is metrically isomorphic to a translation on a
compact...
Two-Point Problem for the Ideal Incompressible Fluid
Consider the flow of ideal incompressible fluid in a bounded 2-d
domain $M$ (say, $M= 3DT^2$, the 2-d torus). In the Lagrange
formulation, the flow is a geodesic $f_t$ on the group $SDif f(M)$
of volume-preserving diffeomorphisms of $M$ with respect...
On Zaremba's Conjecture on Continued Fractions
Zaremba's 1971 conjecture predicts that every integer appears as
the denominator of a finite continued fraction whose partial
quotients are bounded by an absolute constant. We confirm this
conjecture for a set of density one.
Reducibility for the Quasi-Periodic Liner Schrodinger and Wave Equations
Lars Hakan Eliasson
We shall discuss reducibility of these equations on the torus
with a small potential that depends quasi-periodically on time.
Reducibility amounts to "reduce” the equation to a time-independent
linear equation with pure point spectrum in which case...
