Seminars Sorted by Series

Analysis & Mathematical Physics

Dec
14
2022

Analysis & Mathematical Physics

Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal Uncertainty Principle
3:00pm|Simonyi 101 and Remote Access

We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions...

Analysis and Beyond: Celebrating Jean Bourgain’s Work and Its Impact

Analysis and Mathematical Physics

Dec
14
2022

Analysis and Mathematical Physics

Classical Turbulence as Quantum Geometry
Alexander Migdal
4:30pm|Simonyi 101 and Remote Access

The loop equation for circulation PDF as functional of the loop shape is derived from the Hopf equation. This equation is $\textbf{exactly}$ equivalent to the Schrödinger equation in loop space, with viscosity playing the role of Planck's constant...

Jan
18
2023

Analysis and Mathematical Physics

Regularity of Vortex and SQG Patches
3:00pm|Simonyi Hall 101 and Remote Access

I will review some recent progress on regularity properties of vortex and SQG patches. In particular, I will present an example of a vortex patch with continuous initial curvature that immediately becomes infinite but returns to $(C^2)$ class at all...

Feb
08
2023

Analysis and Mathematical Physics

On Co-dimension One Stability of the Soliton for the 1D Focusing Cubic Klein-Gordon Equation
3:00pm|Simonyi Hall 101 and Remote Access

Solitons are particle-like solutions to dispersive evolution equations whose shapes persist as time evolves. In some situations, these solitons appear due to the balance between nonlinear effects and dispersion, in other situations their existence...

Feb
15
2023

Analysis and Mathematical Physics

Degenerate Dispersion and Illposedness for Generalized SQG Equations
Dr. In-Jee Jeong
3:00pm|Simonyi Hall 101 and Remote Access

Given a linear equation whose principal term is given by a degenerate dispersive pseudo-differential operator, we provide a framework for the construction of degenerating wave packet solutions. As an application, we prove strong ill-posedness for...

Feb
22
2023

Analysis and Mathematical Physics

A tricritical point in the Blume-Capel model
Trishen Gunaratnam
3:00pm|Simonyi Hall 101 and Remote Access

This talk will be about a ferromagnetic spin system called the Blume-Capel model. It was introduced in the '60s to model an exotic multi-critical phase transition observed in the magnetisation of uranium oxide. Mathematically speaking, the model can...

Mar
08
2023

Analysis and Mathematical Physics

The adjoint Brascamp-Lieb inequality
3:00pm|Simonyi Hall 101 and Remote Access

The Brascamp-Lieb inequality is a fundamental inequality in analysis, generalizing more classical inequalities such as Holder's inequality, the Loomis-Whitney inequality, and Young's convolution inequality: it controls the size of a product of...

Mar
22
2023

Analysis and Mathematical Physics

Diffusion and Mixing for Two-dimensional Hamiltonian Flows
Michele Coti-Zelati
3:00pm|Simonyi Hall 101 and Remote Access

We consider general two-dimensional autonomous velocity fields and prove that their mixing and dissipation features are limited to algebraic rates. As an application, we consider a standard cellular flow on a periodic box, and explore potential...

Apr
05
2023

Analysis and Mathematical Physics

Scattering for nonlinear wave equations
3:00pm|Simonyi Hall 101 and Remote Access

We construct solutions with prescribed radiation fields for wave equations with polynomially decaying sources close to the lightcone. In this setting, which is motivated by semi-linear wave equations satisfying the weak null condition, solutions to...

Apr
12
2023

Analysis and Mathematical Physics

Generalized Entropy Methods and Stability in Sobolev and Related Inequalities
Jean Dolbeault
3:00pm|Simonyi Hall 101 and Remote Access

This lecture is devoted to a survey on explicit stability results in Gagliardo-Nirenberg-Sobolev and logarithmic Sobolev inequalities. Generalized entropy methods based on carré du champ computations and nonlinear diffusion flows can be used for...

Apr
26
2023

Analysis and Mathematical Physics

Global Stability of Kaluza-Klein Spacetimes
Zoe Wyatt
3:00pm|Simonyi Hall 101 and Remote Access

Spacetimes formed from the cartesian product of Minkowski space and a flat torus play an important role as toy models for theories of supergravity and string theory. In this talk, I will discuss an upcoming work, joint with Huneau and Stingo...

May
03
2023

Analysis and Mathematical Physics

The Alt-Phillips Functional for Negative Powers
Daniela De Silva
3:00pm|Simonyi Hall 101 and Remote Access

We discuss a one-phase degenerate free boundary problem which arises from the minimization of the so-called Alt-Phillips functional $$\int_\Omega (|\nabla u|^2 + u^\gamma \chi_{\{u>0\}}) dx$$ for $\gamma \in (-2,0).$ We establish partial regularity...

May
17
2023

Analysis and Mathematical Physics

Resonances as a Computational Tool
Katharina Schratz
3:00pm|Simonyi Hall 101 and Remote Access

A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full equation...

Oct
20
2023

Analysis and Mathematical Physics

Lipschitz Graphs in Carnot Groups
2:30pm|Simonyi Hall 101 and Remote Access

Submanifolds with intrinsic Lipschitz regularity in Carnot groups (i.e.,
stratified groups endowed with a sub-Riemannian structure) can be
introduced using the theory of intrinsic Lipschitz graphs started years
ago by B. Franchi, R. Serapioni and F...

Oct
27
2023

Analysis and Mathematical Physics

Frobenius-type Results on Submanifolds and Currents
2:30pm|Simonyi Hall 101 and Remote Access

The question of producing a foliation of the n-dimensional Euclidean space with k-dimensional submanifolds which are tangent to a prescribed k-dimensional simple vectorfield is part of the celebrated Frobenius theorem: a decomposition in smooth...

Nov
03
2023

Analysis and Mathematical Physics

Optimization Problem Over the Space of Functions with Second Order Bounded Variation
Camillo Brena
2:30pm|Simonyi Hall 101 and Remote Access

This talk is a discussion about the extremal points of the unit ball with respect to the Hessian-Schatten variation seminorm, i.e. the total variation of the second distributional differential with respect to the Schatten matrix norm. The main...

Nov
10
2023

Analysis and Mathematical Physics

Probabilistic Scaling, Propagation of Randomness and Invariant Gibbs Measures
Andrea Nahmod
2:30pm|Simonyi Hall 101 and Remote Access

In this talk, we will start by describing how classical tools from probability offer a robust framework to understand the dynamics of waves via appropriate ensembles on phase space rather than particular microscopic dynamical trajectories. We will...

Dec
08
2023

Analysis and Mathematical Physics

The Influence of Edges in First-Passage Percolation on Z^d
2:30pm|Simonyi Hall 101 and Remote Access

We study the probability that a geodesic passes through a prescribed edge in first-passage percolation on Z^d. Benjamini, Kalai and Schramm conjectured that this probability tends to zero as the length of the geodesic tends to infinity, as long as...

Dec
15
2023

Analysis and Mathematical Physics

PDE and Discrete Models of 2D Quantum Materials
2:30pm|Simonyi Hall 101 and Remote Access

We consider 2D quantum materials (non-magnetic and constant magnetic field cases), modeled by a continuum Schroedinger operator, whose potential is a sum of translates of an atomic well, centered on the vertices of a discrete subset of the plane...

Jan
26
2024

Analysis and Mathematical Physics

Hawking Mass Monotonicity for Initial Data Sets
2:30pm|Simonyi Hall 101 and Remote Access

An interesting feature of General Relativity is the presence of singularities which can occur in even the simplest examples such as the Schwarzschild spacetime. However, in this case the singularity is cloaked behind the event horizon of the black...

Feb
02
2024

Analysis and Mathematical Physics

Robin Harmonic Measure in Rough Domains
2:30pm|Simonyi Hall 101 and Remote Access

I will describe the construction of a harmonic measure that reproduces a harmonic function from its Robin boundary data, which is a combination of the value of the function and its normal derivative. I shall discuss the surprising fact that this...

Feb
09
2024

Analysis and Mathematical Physics

Existence of Four Minimal Spheres in S^3 with a Bumpy Metric
2:30pm|Simonyi Hall 101 and Remote Access

In 1982, S. T. Yau conjectured that there exists at least four embedded minimal 2-spheres in the 3-sphere with an arbitrary metric. In this talk, we will show that this conjecture holds true for bumpy metrics and metrics with positive Ricci...

Feb
16
2024

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...

Feb
23
2024

Analysis and Mathematical Physics

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...

Mar
01
2024

Analysis and Mathematical Physics

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...

Mar
08
2024

Analysis and Mathematical Physics

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...

Apr
05
2024

Analysis and Mathematical Physics

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...

Analysis Seminar

Feb
27
2008

Analysis Seminar

Orbit of the Diagonal of a Power of a Nilmanifold
Alexander Leibman
2:00pm|S-101

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...

Mar
12
2008

Analysis Seminar

Constructing Wild Groups
Lior Siberman
2:00pm|West Bldg. Lecture Hall
Apr
02
2008

Analysis Seminar

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...

Apr
23
2008

Analysis Seminar

A Hardy Field Extension of Szemeredi's Theorem
2:00pm|S-101

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...

May
14
2008

Analysis Seminar

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...

Oct
21
2011

Analysis Seminar

On the Instability for 2D Fluids
3:00pm|S-101

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.

Oct
25
2011

Analysis Seminar

On the Rigidity of Black Holes
Sergiu Klainerman
2:30pm|S-101

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...

Nov
01
2011

Analysis Seminar

The Defocusing Cubic Nonlinear Wave Equation in the Energy-Supercritical Regime
3:15pm|S-101

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...

Nov
10
2011

Analysis Seminar

Around the Davenport-Heilbronn Function
3:00pm|S-101

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...

Nov
17
2011

Analysis Seminar

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...

Nov
29
2011

Analysis Seminar

The Energy-Critical Defocusing NLS in Periodic Settings
2:30pm|S-101

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.

Dec
06
2011

Analysis Seminar

On the Ergodic Properties of Square-Free Numbers
2:30pm|S-101

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...