# MSCS Seminar Calendar

Monday April 21, 2014

**Applied Mathematics Seminar**

$L^2$ asymptotic stability of mild solutions to the Navier-Stokes system

Maria Schonbek (University of California, Santa Cruz)

4:00 PM in SEO 636

We consider the initial value problem for the Navier-Stokes equations modeling an incompressible fluid in three dimensions:
$$
u_t + u\cdot \nabla u +\nabla p = \Delta u +F,\;\;\; (x,t) \in \mathbb{R}^3\times (0,\infty),
$$
$$
\mbox{div}\; u=0\,,
$$
$$
u(x,0) =u_0(x)\,.
$$
It is well-known that this problem has a unique global-in-time mild solution for a sufficiently
small initial condition $u_0$ and for a small external force $F$ in suitable scaling
invariant spaces. We show that these global-in-time mild solutions are asymptotically
stable under every (arbitrary large) $L^2$-perturbation of their initial conditions.

Tuesday April 22, 2014

**Graduate Statistics Seminar**

Integrative network analysis of TCGA data for ovarian cancer

Qingyang Zhang (Northwestern)

3:30 PM in SEO 636

Traditional cancer studies have been mainly focusing on single
gene or single type of data including mRNA expression, DNA methylation, copy number variation, and etc.
However, such analyses lack power to reveal the molecular mechanisms from the view of system
biology. In this talk, I will present an integrative framework to identify important genetic and epigenetic
features and to quantify the causal relations among these features. I will first talk about what is a Bayesian
Network and what the TCGA data looks like. Then I will introduce the proposed feature selector and Bayesian
Network model. Simulated and real data sets will be used for illustration.

Wednesday April 23, 2014

**Geometry, Topology and Dynamics Seminar**

Regular CAT(0) Cube Complexes

Nir Lazarovich (Techion)

3:00 PM in SEO 612

Over the past years CAT(0) cube complexes have played a major role in geometric group theory and have provided many examples of interesting group actions on CAT(0) spaces. In the search for highly symmetric CAT(0) cube complexes -- just as for their 1-dimensional analogues, trees -- it is natural to consider the sub-class of “regular” CAT(0) cube complexes, i.e., cube complexes with the same link at each vertex. However, unlike regular trees, general regular CAT(0) cube complexes are not necessarily uniquely determined by their links.
In this talk, we will discuss a necessary and sufficient condition for uniqueness. We will then explore some examples of unique regular cube complexes and the properties of their automorphism groups.

**Algebraic Geometry Seminar**

A simplicial approach to effective divisors in $\bar{M}_{0,n}$

Noah Giansiracusa (UC Berkeley)

4:00 PM in SEO 427

The moduli space $\bar{M}_{0,n}$, a compactification of the space of n distinct points on the Riemann sphere, has served as a fertile testing ground to explore many phenomena of moduli spaces in algebraic geometry. One tantalizing question is to describe the convex cone of effective divisor classes and Cox ring of these spaces. I'll discuss joint work with B. Doran and D. Jensen in which we provide a new perspective on this question in terms of simplicial complexes and show how this relates to recent exciting work of Castravet, Tevelev, and Opie.

Thursday April 24, 2014

**Graduate Number Theory Seminar**

Height Functions

Dylon Chow (UIC)

3:00 PM in SEO 512

Fundamental to the proofs of several important results in arithmetic geometry (e.g. the Mordell-Weil Theorem and Faltings' Theorem) is a way of assigning a size to points on a variety. Weil's height machine turns geometric properties of the variety into arithmetic information about the points on the variety. If time permits, we will discuss the conjectures of Batyrev and Manin on the distribution of rational points.

Friday April 25, 2014

**Departmental Colloquium**

Combinatorics and topology of toric maps

Mircea Mustata (University of Michigan)

3:00 PM in SEO 636

Toric varieties are algebraic varieties endowed with a "nice"
action of an algebraic torus. A remarkable feature is that their geometry
can be fully described in terms of combinatorics of fans and polytopes.
After explaining what these objects are and some classical facts about
their cohomology, I will discuss some results concerning the topology of
the fibers of toric maps and a combinatorial invariant that comes out of
these considerations. This is based on joint work in progress with Marc de
Cataldo and Luca Migliorini.

Monday April 28, 2014

Wednesday April 30, 2014

Thursday May 1, 2014

Friday May 2, 2014