Analysis Seminar

Date:
Mar
06
2012

Analysis Seminar

Various Approaches to Semiclassical Quantum Dynamics
George A. Hagedorn
2:00pm|S-101

I shall describe several techniques for finding approximate solutions to the time-dependent Schr\"odinger equation in the semiclassical limit. The first of these involves expansions in "semiclassical wave packets" that are also sometimes called...

Feb
28
2012

Analysis Seminar

A Centre-Stable Manifold for the Energy-Critical Wave Equation in $R^3$ in the Symmetric Setting
2:00pm|S-101

Consider the focusing semilinear wave equation in $R^3$ with energy-critical non-linearity \[ \partial_t^2 \psi - \Delta \psi - \psi^5 = 0,\ \psi(0) = \psi_0,\ \partial_t \psi(0) = \psi_1. \]

This equation admits stationary solutions of the form \[...

Feb
21
2012

Analysis Seminar

Reducibility for the Quasi-Periodic Liner Schrodinger and Wave Equations
Lars Hakan Eliasson
2:30pm|S-101

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...

Feb
14
2012

Analysis Seminar

On Zaremba's Conjecture on Continued Fractions
2:30pm|S-101

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.

Dec
13
2011

Analysis Seminar

Two-Point Problem for the Ideal Incompressible Fluid
2:30pm|S-101

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...

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...

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.

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
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...