# Announcement

The Graduate Student / Postdoc Seminar has moved!

The new page can be found here.

# Next Talk

Speaker: Paul Bourgade TBA December 1, 1:00 p.m. (pizza and drinks at 12:45 p.m.) 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 non-specialists in the audience.

# Schedule Fall 2017

## October 6

Speaker: Robert Kohn Energy driven pattern formation Abstract Energy-driven 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 higher-order 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 Covariate-corrected biclustering methods for gene-expression and GWAS data Abstract A common goal in data-analysis 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 data-matrix involving several genetic-measurements taken across many patients. In this context a ‘bicluster’ would correspond to a subset of genetic-measurents 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 low-rank submatrices from within a larger data-matrix. The basic method itself is very straightforward (c.f. Rangan 2012), and involves examining the 'loops' (i.e., 2-x-2 submatrices) within the data-set. 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 continuous-covariates, as well as sparsity within the data. I'll illustrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS). In addition to being quite practical, this loop-counting 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 phase-transitions 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 loop-counting method is 'close to optimal' within a certain subset of local algorithms. Finally, I'll demonstrate that the loop-counting method actually outperforms what are called 'spectral-methods' (based on the singular-value-decomposition) near the computational phase-transition, and explain why this is the case.

## October 27

Speaker: Robert Young 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 best-known 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 simply-connected 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 Untangling the annual cycle of the tropical tropopause layer with an idealized moist model Abstract What is the tropical tropopause layer? Why should I care if it has an annual cycle? These, and more climate science oriented questions, will be addressed in my seminar this Friday. But as not to leaving you in total suspense, the tropical tropopause layer plays a critical role in regulating the chemical composition of the stratosphere, with significant impacts on surface climate. It also provides a curious dynamical puzzle, exhibiting a distinct annual cycle despite the semi-annual solar forcing of the tropics. In this talk, I will introduce a new intermediate complexity atmospheric model that allows us to explore the key processes regulating the tropical tropopause.

## December 1

Speaker: Paul Bourgade TBA Abstract tba

# Contact Info

Marguerite Brownbrownml [at] cims [dot] nyu [dot] edu
Reza Gheissarireza [at] cims [dot] nyu [dot] edu
Benjamin McKennamckenna [at] cims [dot] nyu [dot] edu

## Previous semesters

### Spring 2011 schedule

Descriptions of earlier talks are here.

Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
251 Mercer St.
New York, NY 10012