Self-genericity axioms II

Speaker: 

Andres Forero

Institution: 

UCI

Time: 

Monday, March 31, 2014 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 440R

We continue the exposition on self-genericity axioms for ideals on P(Z) (Club Catch, Projective Catch and Stationary Catch). We establish some relations with forcing axioms and with the existence of certain regular forcing embeddings, and also point out connections with Precipitousness. In particular we observe that if Projective Catch holds for an ideal, then that ideal is precipitous, and the converse holds for ideals that concentrate on countable sets. Finally we give an overview of the method used for proving the existence of models with Woodin cardinals coming from these axioms, using the Core Model Theory.

On Multi-Dimensional Compressible Navier-Stokes Systems with Large Oscillations (joint with Applied and Computational Math seminar)

Speaker: 

Zhouping Xin

Speaker Link: 

http://www.math.cuhk.edu.hk/en/people/teaching_staff/teaching.php?id=zpxin

Institution: 

The Chinese University of Hongkong

Time: 

Wednesday, April 30, 2014 - 3:00pm to 4:00pm

Host: 

Yifeng Yu (he/him/his)

Location: 

RH306

 In this talk, I will discuss recent results on the
 large time well-posedness of classical solutions to the
 multi-dimensional compressible Navier-Stokes system with possible
 large oscillations and vacuum.
 The focus will be on finite-time blow-up of classical solutions for
 the 3-D full compressible Navier-Stokes system, and the global
 existence of classical solutions to the isentropic compressible
 Navier-Stokes system in both 2-D and 3-D in the presence of vacuum
 and possible large oscillations.  New estimates on the fast decay
 of the pressure in the presence of vacuum will be presented,  which
 are crucial for the well-posedness theory in 2-dimensional case.

On Multi-Dimensional Compressible Navier-Stokes Systems with Large Oscillations (joint with Nonlinear PDEs seminar)

Speaker: 

Zhouping Xin

Speaker Link: 

http://www.math.cuhk.edu.hk/en/people/teaching_staff/teaching.php?id=zpxin

Institution: 

The Chinese University of Hongkong

Time: 

Wednesday, April 30, 2014 - 3:00pm to 4:00pm

Host: 

Jack Xin (he/him/his)

Location: 

RH 306

 In this talk, I will discuss recent results on the
 large time well-posedness of classical solutions to the
 multi-dimensional compressible Navier-Stokes system with possible
 large oscillations and vacuum.
 The focus will be on finite-time blow-up of classical solutions for
 the 3-D full compressible Navier-Stokes system, and the global
 existence of classical solutions to the isentropic compressible
 Navier-Stokes system in both 2-D and 3-D in the presence of vacuum
 and possible large oscillations. New estimates on the fast decay
 of the pressure in the presence of vacuum will be presented,  which
 are crucial for the well-posedness theory in 2-dimensional case.

Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation

Speaker: 

Jianliang Qian

Institution: 

Michigan State University

Time: 

Monday, June 9, 2014 - 4:00pm to 5:00pm

Host: 

Hongkai Zhao

Location: 

RH306

We introduce a new multiscale Gaussian beam method for the
 numerical solution of the wave equation with smooth variable
 coefficients. The first computational question addressed in this
 paper is how to generate a Gaussian beam representation from general
 initial conditions for the wave equation. We propose fast multiscale
 Gaussian wavepacket transforms and introduce a highly efficient
 algorithm for generating the multiscale beam representation for a
 general initial condition. Starting from this multiscale
 decomposition of initial data, we propose the multiscale Gaussian
 beam method for solving the wave equation. The second question is
 how to perform long time propagation. Based on this new
 initialization algorithm, we utilize a simple reinitialization
 procedure that regenerates the beam representation when the beams
 become too wide. Numerical results in one, two, and three dimensions
 illustrate the properties of the proposed algorithm. The methodology
 can be readily generalized to treat other wave propagation problems.

Units in function rings

Speaker: 

Daniel Bertrand

Institution: 

Université Pierre et Marie Curie and MSRI

Time: 

Thursday, April 24, 2014 - 2:00pm

Host: 

Alice Silverberg

Location: 

RH 440R

Contrary to their classical namesakes over the ring of integers, Pell equations over function rings in characteristic zero need not have infinitely many solutions. How often this occurs has been the theme of recent work of D. Masser and U. Zannier. The case of smooth curves is governed by the relative Manin-Mumford conjecture on abelian schemes. We pursue this study by considering singular curves and the associated generalized jacobians.

 

Chancellor's Professor John Lowengrub named the SIAM Julian Cole Lecturer for 2014

Congratulations to Chancellor's Professor John Lowengrub on being named the SIAM Julian Cole Lecturer for 2014! John was recognized for "seminal contributions to fluid dynamics, materials science, and computational biology through the development of mathematical models, computation methods, and numerical simulations of free-boundary problems and tumor growth." This award is given every four years for an outstanding contribution to the mathematical characterization and solution of a challenging problem in the physical or biological sciences, or in engineering.

Isoperimetric inequality and Q-curvature

Speaker: 

Yi Wang

Institution: 

Stanford University

Time: 

Tuesday, April 29, 2014 - 4:00pm

Location: 

RH 306

A well-known question in differential geometry is to prove the
isoperimetric inequality under intrinsic curvature conditions. In
dimension 2, the isoperimetric inequality is controlled by the integral of
the positive part of the Gaussian curvature. In my recent work, I prove
that on simply connected conformally flat manifolds of higher dimensions,
the role of the Gaussian curvature can be replaced by the Branson's
Q-curvature. The isoperimetric inequality is valid if the integral of the
Q-curvature is below a sharp threshold. Moreover, the isoperimetric
constant depends only on the integrals of the Q-curvature. The proof
relies on the theory of A_p weights in harmonic analysis.

Dynamics and emergent structures in active fluids

Speaker: 

Aparna Baskaran

Speaker Link: 

http://www.brandeis.edu/departments/physics/people/faculty/aparna.html

Institution: 

Brandeis University

Time: 

Friday, March 14, 2014 - 1:00pm

Host: 

John Lowengrub

Location: 

Rowland Hall 340N

Abstract:

Active fluids are inherently out of equilibrium fluid systems that are
driven at the scale of the individual units. Examples include bacterial
colonies, the cytoskeleton of a cell, tissues and synthetic systems such as
diffusophoretic janus colloids. In this talk I will discuss simple
theoretical models for active fluids and illustrate mechanisms at play that
lead to emergent structures in active fluids such as athermal phase
separation, accumulation at boundaries and propagating density waves.

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