Next Talk
 Speaker: 
David Kelly 
 Title: 
TBA 
 Date and time: 
December 4, 1:00 p.m. (light refreshments at 12:45 p.m.) 
 Venue: 
WWH 1302

Abstract
TBA
This seminar is meant to benefit young mathematicians, particularly graduate students and postdocs.
It aims to accomplish the following:
 provide a venue for talks that young mathematicians will understand
 expose students to areas of research at the Courant Institute
The research talks should be fairly introductory and accessible to students and nonspecialists in the audience.
Schedule Fall 2015
October 9
 Speaker: 
Charles S. Peskin 
 Title:  FluidStructure Interaction by the Immersed Boundary Method 

 
Abstract
An example of an immersed boundary is a heart valve leaflet. These
thin membranes are immersed in blood and move at the local fluid
velocity while they simultaneously apply forces to the surrounding
fluid that prevent backflow when the valve is closed, and shear the
forward flow when the valve is open to create vortices that
subsequently promote efficient valve closure. The immersed boundary
(IB) method was created to deal with this problem, and has since grown
into a generally useful tool for the computer simulation of
fluidstructure interaction, especially in biology.
In this talk I'll introduce the IB method in the context of the
heart, and then show movies that illustrate various ways in which
the IB method has been generalized and applied. 

October 23
 Speaker: 
Ofer Zeitouni 
 Title:  Extremal processes for some Gaussian random fields 

 
Abstract
Consider a (locally finite) random configuration ${\bf X}=\{X_i\}$ with values in $R$ (such a collection is called a \textit{point process}). Let $Z_i$ be i.i.d. random variables, independent of ${\bf X}$. Assume that the distribution of ${\bf X}$ is invariant under the transformation $X_i\mapsto X_i+Z_i$.
Liggett has identified all possible such distributions, as mixtures of Poisson processes with
(constant or exponential) intensities. Recently, this identification has played an important role in
identifying the point process of extremes of certain Gaussian random fields. I will describe Liggett's results and explain how it is applied to the study of such extremes, as well as applications to the
study of the Gaussian free field and to certain spinglass systems. All terms will be defined in the talk. 

October 30
 Speaker: 
Jonathan Goodman 
 Title:  Monte Carlo sampling for Bayesian statistics with complex models: theory, algorithms, applications. 

 
Abstract
A basic problem in statistics is to make inferences about physical parameters from experimental data.
Because of measurement and modeling errors, data do not determine parameter values exactly. Bayesian
statistics represents the remaining parameter uncertainty as a “posterior” probability distribution of the
parameters conditional on the measurements and prior information. For high dimensional problems, it
is hard to represent this posterior except as a collection of random samples from it. This talk discusses
the problem of producing such samples.
We describe MCMC ( Markov chain Monte Carlo) samplers, which are guaranteed to “work” in principle
but may be too slow in practical applications. There are several theoretical approaches to understanding
the convergence of MCMC samplers, including Sobolev and log Sovolev inequalities, the beautiful methods
of the Lovasz school (which are based on “Cheeger’s inequality”), and work of Hairer and Stuart. Each of
these has led to better samplers for specific problems.
Some of my work is motivated by an analogy between MCMC samplers and optimization algorithms.
One idea from optimization is that a good method for generic problems should be invariant under affine
transformations. This allows the method to work well for poorly conditioned problems. I present two
affine invariant sampling algorithms, one of which is the basis of a popular software package that will
be described later this afternoon by David Hogg. Line search is another method from optimization that
we have imported to MCMC samplers. I will list several open problems and opportunities. 

November 6
 Speaker: 
Benjamin HarropGriffiths 
 Title:  Modified scattering for the modified Kortewegde Vries equation (mKdV) 

 
Abstract
The Kortewegde Vries (KdV) equation arises as an asymptotic limit of numerous dispersive systems and together with its generalizations has a wide range of physical applications including fluid mechanics, plasma physics and nonlinear optics. In this talk we will provide a brief introduction to the generalized KdV family of equations with particular emphasis on their asymptotic behavior. In particular we will discuss why solutions to the modified KdV (mKdV) do not scatter to linear waves, even for small initial data and will sketch a proof of modified scattering using the method of testing by wave packets. This robust approach does not rely on the inverse scattering transform and hence may be applied to short range perturbations of the mKdV as well as numerous other nonintegrable equations. 

November 13
 Speaker: 
Tom Trogdon 
 Title:  Corner singularities, Gibbs phenomenon and the Unified Transform Method 

 
Abstract
Abstract: Consider solving a linear, constantcoefficient evolution PDE in one spatial dimension where the initial data vanishes on the negative half line (x < 0). One can interpret this solution, restricted to x > 0, t > 0, as the solution of an initialboundary value problem where the boundary data is not compatible with the initial data. This solution exhibits a corner singularity. Furthermore, in a dispersive and nondissipative setting such a solution typically exhibits Gibbslike highoscillation and nonvanishing overshoot as t tends to zero. In this talk, I will discuss the explicit solution of general (1+1)dimensional initialboundary value problems using the socalled Unified Transform Method, the behavior of corner singularities and their relation to the classical Gibbs phenomenon. I will also discuss the computation of these singular solutions. 

November 20
 Speaker: 
Alena Pirutka 
 Title:  Rationality: reasonable or not 

 
Abstract
An algebraic variety is rational if it has an open subset isomorphic
to an open of an affine space. However, these varieties are still
quite difficult to understand. For instance, it could be very tricky
to determine whether a given variety is rational or not. In this talk
we will discuss various properties related to the rationality, provide
examples where these properties hold and give some ideas on methods
used for these questions.


December 4
 Speaker: 
David Kelly 
 Title:  TBA 

 
Abstract
TBA 

If you would like to give a talk or ask a question about the seminar,
please contact one of the seminar organizers:
Monty Essid   essid [at] cims [dot] nyu [dot] edu 
Alex Kaiser   kaiser [at] cims [dot] nyu [dot] edu 
Reza Gheissari   reza [at] cims [dot] nyu [dot] edu 
Previous semesters
Descriptions of earlier talks are
here.
Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
251 Mercer St.
New York, NY 10012