Announcement
The Graduate Student / Postdoc Seminar has moved!
The new page can be found here.
Next Talk
 Speaker: 
Robert Young 
 Title: 
Quantifying simple connectivity: an introduction to the Dehn function 
 Date and time: 
October 27, 1:00 p.m. (pizza and drinks at 12:45 p.m.) 
 Venue: 
WWH 1302

Abstract
Many theorems start by taking an existence theorem and asking ``How many?'' or ``How big?'' or ``How fast''. The bestknown example may be the prime number theorem. Euclid proved that infinitely many primes exist, and the prime number theorem describes how quickly they grow. I'll discuss what happens when you apply the same idea to simple connectivity. In a simplyconnected space, any closed curve is the boundary of some disc, but how big is that disc? And what can that tell you about the geometry of the space?
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 2017
October 6
 Speaker: 
Robert Kohn 
 Title:  Energy driven pattern formation 

 
Abstract
Energydriven pattern formation examines how energy minimization
leads to the formation of defects and microstructure in a variety of physical systems. Examples include the wrinkling of elastic membranes,
the formation of domains in a magnetic material, and the twinning produced
by martensitic phase transformation. These systems can be described
by ``Landau theories''  essentially, nonconvex variational problems
regularized by higherorder singular perturbations. I will show in various
examples  some old, some new  how one can identify the scaling law
of the minimum energy, and how this sheds light on the underlying
patterns. 

October 13
 Speaker: 
Aaditya Rangan 
 Title:  Covariatecorrected biclustering methods for geneexpression and GWAS data 

 
Abstract
A common goal in dataanalysis is to sift through a large matrix and detect any significant submatrices (i.e., biclusters) that have a low numerical rank. To give an example from genomics, one might imagine a datamatrix involving several geneticmeasurements taken across many patients. In this context a ‘bicluster’ would correspond to a subset of geneticmeasurents that are correlated across a subset of the patients. While some biclusters might extend across most (or all) of the patients, it is also possible for biclusters to involve only a small subset of patients. Detecting biclusters such as these provides a first step towards unraveling the physiological mechanisms underlying the heterogeneity within a patient population.
In this talk I'll describe a simple algorithm for tackling this biclustering problem – i.e., for detecting lowrank submatrices from within a larger datamatrix. The basic method itself is very straightforward (c.f. Rangan 2012), and involves examining the 'loops' (i.e., 2x2 submatrices) within the dataset. Importantly, this method can easily be modified to account for many considerations which commonly arise in practice. For example, by counting loops slightly differently, we can correct for controls: finding biclusters that manifest only within a ‘case’population without manifesting within a ‘control’population. Moreover, this methodology can also correct for categorical and continuouscovariates, as well as sparsity within the data. I'll illustrate these practical features with two examples; the first drawn from geneexpression analysis and the second drawn from a much larger genomewideassociationstudy (GWAS).
In addition to being quite practical, this loopcounting method exhibits a few interesting mathematical features, which I'll mention towards the second half of the talk.
To begin with, I'll point out some of the well known phasetransitions for the biclustering problem (i.e., parameters which determine whether or not the problem is 'easy' or 'hard').
I'll also briefly explain why the loopcounting method is 'close to optimal' within a certain subset of local algorithms.
Finally, I'll demonstrate that the loopcounting method actually outperforms what are called 'spectralmethods' (based on the singularvaluedecomposition) near the computational phasetransition, and explain why this is the case. 

October 27
 Speaker: 
Robert Young 
 Title:  Quantifying simple connectivity: an introduction to the Dehn function 

 
Abstract
Many theorems start by taking an existence theorem and asking ``How many?'' or ``How big?'' or ``How fast''. The bestknown example may be the prime number theorem. Euclid proved that infinitely many primes exist, and the prime number theorem describes how quickly they grow. I'll discuss what happens when you apply the same idea to simple connectivity. In a simplyconnected space, any closed curve is the boundary of some disc, but how big is that disc? And what can that tell you about the geometry of the space? 

November 10
 Speaker: 
Edwin Gerber 
 Title:  TBA 

 
Abstract
tba 

December 1
 Speaker: 
Paul Bourgade 
 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:
Marguerite Brown   brownml [at] cims [dot] nyu [dot] edu 
Reza Gheissari   reza [at] cims [dot] nyu [dot] edu 
Benjamin McKenna   mckenna [at] cims [dot] nyu [dot] edu 
David Padilla Garza   padilla [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