# Seminars & Events for 2013-2014

##### Tales of Our Forefathers

This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse.

##### I got 3 open problems but an application ain't one

I will describe and talk about 3 open math problems related to my work. They involve number theory, algebraic geometry, and random matrices. Would love to hear your thoughts on any of them.

##### Introduction to the quantum theory of experiments

##### Stable homology for moduli spaces of manifolds

THIS IS A JOINT ALGEBRAIC TOPOLOGY / TOPOLOGY SEMINAR. There will be two separate talks: 3:00-4:00 pm (Fine 214) and 4:30-5:30 pm (Fine 314). For a compact manifold $W$, possibly with boundary, we shall let $\mathrm{Diff}(W)$ denote the topological group of diffeomorphisms of $W$ fixing a neighborhood of $\partial W$. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Fragile matroids and excluded minors

Matroids abstract the notions of linear/geometric/algebraic dependence. More specifically, a matroid consists of a finite collection of points, and a distinguished family of dependent subsets. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Potentially Singular Solutions of the 3D Incompressible Euler Equations

Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in axisymmetric geometries. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Independence of l and local terms

Let $k$ be an algebraically closed field and let $c:C\rightarrow X\times X$ be a correspondence. Let $\ell $ be a prime invertible in $k$ and let $K\in D^b_c(X, \overline {\mathbb{Q}}_\ell )$ be a complex. An action of $c$ on $K$ is by definition a map $u:c_1^*K\rightarrow c_2^!K$.

##### Homological stability for moduli spaces of manifolds

THIS IS A JOINT TOPOLOGY / ALGEBRAIC TOPOLOGY SEMINAR. There will be two separate talks: 3:00-4:00 pm (Fine 214) and 4:30-5:30 pm (Fine 314). For a compact manifold $W$, possibly with boundary, we shall let $\mathrm{Diff}(W)$ denote the topological group of diffeomorphisms of $W$ fixing a neighborhood of $\partial W$. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Calabi-Yau mirror symmetry: from categories to curve-counts

I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds.

##### Singularities of the L^2 curvature flow

The L2 norm of the Riemannian curvature tensor is a natural energy to associate to a Riemannian manifold, especially in dimension 4. A natural path for understanding the structure of this functional and its

##### Higher-order analogues of the exterior derivative complex

I will begin by presenting earlier joint work with E. M. Stein concerning div-curl type inequalities for the exterior derivative complex and its adjoint in Euclidean space R^n.

##### The evolution of social traits in network structured populations

Over many decades theoretical biologists have grappled with the question of how to measure the relative selective advantage of different behavioral strategies. The various approaches to this question have fallen into one of the following categories: fixation probability of a mutant allele in a wild type population, some measures of gene frequency and gene frequency change, and a formulation of a different type of fitness called the inclusive fitness.

PLEASE CLICK ON COLLOQUIUM TITLE FOR COMPLETE ABSTRACT.

##### Rational curves in the log category

In birational geometry, log pairs are introduced for studying open varieties and for reducing problems to lower dimensional case. In this talk, I will explain that this framework can be used to study rational curves on varieties. I will introduce A^1-connectedness for log smooth pairs, i.e., the interior admits lots of rational curves which meet the boundary once.

##### TBA - Kiselev

**PLEASE NOTE SPECIAL DAY (WEDNESDAY) AND LOCATION.**

##### Computations in Algebraic Geometry

This will be a fairly expository talk on the role of computation in algebraic geometry. I will discuss basics of Groebner bases and the geometry associated to them. These give an easy way to construct algorithms to solve many computational problems about projective varieties.

##### Renormalization group and stochastic PDEs

I will discuss some recent works on applying rigorous renormalization group methods to the study of stochastic PDEs. I will mainly focus on a model of turbulent transport by the shear flow.

##### Scale invariant solutions to Navier Stokes equation and implications to Leray-Hopf weak solutions

In this talk, I will first discuss the existence of scale invariant solutions to Navier Stokes equation with arbitrary $-1$ homogeneous initial data. Since these solutions may not be small, linearized analysis seem to suggest nontrivial bifurcations.

##### Genus of abstract modular curves with level l structure

To any bounded family of \F_l-linear representations of the etale fundamental of a curve X one can associate families of abstract modular curves which, in this setting, generalize the `usual' modular curves with level l structure (Y_0(l), Y__1(l), Y(l) etc.). Under mild hypotheses, it is expected that the genus (and even the geometric gonality) of these curves goes to infty with l.

##### Topological Actions of Connected Compact Lie Groups on Manifolds

THIS IS A JOINT ALGEBRAIC TOPOLOGY / TOPOLOGY SEMINAR. PLEASE NOTE DIFFERENT TIME AND LOCATION. We survey some new methods and results on existence and on topological classification

of actions of connected, compact Lie groups on manifolds. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Topological Actions of Connected Compact Lie Groups on Manifolds

THIS IS A JOINT TOPOLOGY / ALGEBRAIC TOPOLOGY SEMINAR. We survey some new methods and results on existence and on topological classification of actions of connected, compact Lie groups on manifolds. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.