Analysis Seminar

Date:
May
18
2020

Analysis Seminar

Square function estimate for the cone in R^3
11:00am|Remote Access via Zoom videoconferencing (link below)

We prove a sharp square function estimate for the cone in R^3 and consequently the local smoothing conjecture for the wave equation in 2+1 dimensions. The proof uses induction on scales and an incidence estimate for points and tubes. This is joint...

May
12
2020

Analysis Seminar

Quantitative decompositions of Lipschitz mappings
Guy C. David
11:00am|https://theias.zoom.us/j/562592856

Given a Lipschitz map, it is often useful to chop the domain into pieces on which the map has simple behavior. For example, depending on the dimensions of source and target, one may ask for pieces on which the map behaves like a bi-Lipschitz...

May
04
2020

Analysis Seminar

Exponential mixing of 3D Anosov flows
11:00am|https://theias.zoom.us/j/562592856

We show that a topologically mixing C^\infty Anosov flow on a 3 dimensional compact manifold is exponential mixing with respect to any equilibrium measure with Holder potential. This is a joint work with Masato Tsujii.

Apr
28
2020

Analysis Seminar

Ellipses of small eccentricity are determined by their Dirichlet (or, Neumann) spectra
Steven Morris Zelditch
11:00am|https://theias.zoom.us/j/562592856

In 1965, M. Kac proved that discs were uniquely determined by their Dirichlet (or, Neumann) spectra. Until recently, disks were the only smooth plane domains known to be determined by their eigenvalues. Recently, H. Hezari and I proved that ellipses...

Apr
20
2020

Analysis Seminar

A variational approach to the regularity theory for the Monge-Ampère equation
Felix Otto
11:00am|https://theias.zoom.us/j/562592856

We present a purely variational approach to the regularity theory for the Monge-Ampère equation, or rather optimal transportation, introduced with M. Goldman. Following De Giorgi’s philosophy for the regularity theory of minimal surfaces, it is...

Apr
13
2020

Analysis Seminar

Flows of vector fields: classical and modern
Camillo DeLellis
11:00am|https://theias.zoom.us/j/373002666

Consider a (possibly time-dependent) vector field $v$ on the Euclidean space. The classical Cauchy-Lipschitz (also named Picard-Lindel\"of) Theorem states that, if the vector field $v$ is Lipschitz in space, for every initial datum $x$ there is a...

Mar
09
2020

Analysis Seminar

Higher order rectifiability and Reifenberg parametrizations
5:00pm|Simonyi Hall 101

We provide geometric sufficient conditions for Reifenberg flat sets of any integer dimension in Euclidean space to be parametrized by a Lipschitz map with Hölder derivatives. The conditions use a Jones type square function and all statements are...

Feb
24
2020

Analysis Seminar

"Observable events" and "typical trajectories" in finite and infinite dimensional dynamical systems
5:00pm|Simonyi Hall 101

Some words in the title are between quotation marks because it is a matter of interpretation. For dynamical systems on finite dimensional spaces, one often equates observable events with positive Lebesgue measure sets, and invariant distributions...