Next Talk
 Speaker: 
LaiSang Young 
 Title: 
Dynamics of the brain: mathematics meets neuroscience

 Date and time: 
May 6, 1:00 p.m. (light refreshments at 12:45 p.m.) 
 Venue: 
WWH 1302

Abstract
Dynamical systems is the study of time evolutions of processes, natural
and engineered, and one of the most fascinating dynamical systems is
the brain. This talk is about the visual cortex. From pointtopoint
representation of visual images, the visual cortex extracts edges, shapes,
color, motion etc. — features that enable us to make sense of visual scenes.
This complex task is accomplished through the interaction of very large
numbers of neurons, which we model individually as relatively simple
dynamical systems coupled together to form a large network. In this talk
I would like to (1) give you a flavor of the dynamics describing the
interaction between local excitatory and inhibitory populations, and
(2) discuss a little piece of modeling work in which my collaborators and I
tried to reconcile experimental evidence with some prevailing ideas in
theoretical neuroscience, namely the feedforward picture of orientation
selectivity in the monkey (or human) visual cortex.
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 Spring 2016
February 12
 Speaker: 
David Kelly 
 Title:  Data assimilation in high dimensions 

 
Abstract
This will be an introduction to data assimilation and in particular to methods that are useful for high dimensional forecasting problems. Data assimilation describes any method of using observational data in order to guide model predictions in the right direction. The most prominent application is numerical weather prediction, where forecasts are obtained by blending oceanatmosphere models with partial observed data in order to reduce prediction uncertainty. We will discuss the basic mathematical ideas (Bayes’ theorem, Kalman filters), the problem of high dimensionality and how methods can be successful in high dimensions. 

March 25
 Speaker: 
Zineb Hassainia 
 Title:  Existence of rotating vortex patches for inviscid flows 

 
Abstract
We shall discuss in this talk some aspects of the vortex motion for
different nonlinear transport models arising in fluid dynamics such as
Euler equations and the inviscid generalized surface quasigeostrophic
equations. Specifically we will study the existence of rotating
vortex patches (also called Vstates) for different topological
structures: simply connected and doubly connected patches. The proof
relies on the bifurcation theory combined with special functions.The
existence of the Vstates in a disc and their interaction with the
boundary will also be analyzed. 

April 8
 Speaker: 
Zsolt PajorGyulai 
 Title:  On the averaging principle of Freidlin and Wentzell and its refinement along trajectories containing saddle points.


 
Abstract
Hamiltonian systems arise in many areas of classical mechanics. The FreidlinWentzell averaging principle describes the long time behavior of such in the prescence of a small Brownian noise. In this talk we give an exposition of this classical result and then discuss a recent refining result on the local behavior of the averaged process along level sets of the Hamiltonian that contain saddle points obtained by the speaker and his collaborators.


April 15
 Speaker: 
Boyce Griffith 
 Title:  Special AMS Seminar for Charlie Peskin's 70th birthday : History of the immersed boundary method 

 
Abstract
Refer AMS: http://cims.nyu.edu/ams/ 

April 22
 Speaker: 
Oded Regev 
 Title:  Lattices and a Reverse Minkowski Conjecture 

 
Abstract
I will start with some background on lattices and why we care about them so much. I will then talk about some work with Daniel Dadush on a conjectured reverse form of Minkowski's classical theorem, and its various applications.


April 29
 Speaker: 
EinYa Gura 
 Title:  Insights into Game Theory: An Alternative Mathematical Experience 

 
Abstract
Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for social scientists studying strategic behavior of competing individuals, firms, and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only a basic understanding of mathematics. Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. We use four very different topics (college admissions, social justice and majority of voting, coalitions and cooperative games, and a bankruptcy problem from the Talmud) to investigate four areas of game theory.
The book was written with the late Michael Maschler and was published by Cambridge University Press in 2008. 

May 6
 Speaker: 
LaiSang Young 
 Title:  Dynamics of the brain: mathematics meets neuroscience


 
Abstract
Dynamical systems is the study of time evolutions of processes, natural
and engineered, and one of the most fascinating dynamical systems is
the brain. This talk is about the visual cortex. From pointtopoint
representation of visual images, the visual cortex extracts edges, shapes,
color, motion etc. — features that enable us to make sense of visual scenes.
This complex task is accomplished through the interaction of very large
numbers of neurons, which we model individually as relatively simple
dynamical systems coupled together to form a large network. In this talk
I would like to (1) give you a flavor of the dynamics describing the
interaction between local excitatory and inhibitory populations, and
(2) discuss a little piece of modeling work in which my collaborators and I
tried to reconcile experimental evidence with some prevailing ideas in
theoretical neuroscience, namely the feedforward picture of orientation
selectivity in the monkey (or human) visual cortex. 

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 
Guillaume Dubach   dubach [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