# Seminars & Events for 2013-2014

##### Modal Analysis with Compressive Measurements

Structural Health Monitoring (SHM) systems are critical for monitoring aging infrastructure (such as buildings or bridges) in a cost-effective manner. Such systems typically involve collections of battery-operated wireless sensors that sample vibration data over time. After the data is transmitted to a central node, modal analysis can be used to detect damage in the structure.

##### Strictly pseudo-effective classes

The pseudo-effective cone is the closure of the convex cone of effective cycle classes of arbitrary fixed (co)dimension in the numerical group of a projective variety. Of particular interest are the boundary classes that were added upon closing.

##### THIS SEMINAR HAS BEEN MOVED TO OCTOBER 15. PLEASE SEE NEW POSTING.The quantum Shannon-McMillan theorem and rank of spectral projections of macroscopic observables

The classical Shannon-McMillan theorem states that an ergodic system has typical sets satisfying the asymptotic equipartition property. This theorem demonstrates the significance of entropy which gives the size of the typical sets. There has recently been great progress in the quantum version of the Shannon-McMillan theorem .In particular, Bjelakovic et al.

##### Ricci flow on quasiprojective manifolds

PLEASE NOTE SPECIAL DAY (WEDNESDAY). The talk is about Ricci flow on noncompact Kaehler manifolds. I'll discuss four types of spatial asymptotics: cuspidal, cylindrical, bulging and conical. The results are about the preservation of the asymptotics, long-time existence, parabolic blowdown limits and the role of the Kaehler-Ricci flow on the divisor. This is joint work with Zhou Zhang

##### Sphere Packing

We discuss a beautiful method of Cohn and Elkies which gives bounds on how densely spheres can be packed in Euclidean space of any dimension. Their method has been elaborated by Cohn and Kumar to show that the Leech lattice is the unique densest lattice packing in 24-dimensional space and that the E8 lattice is the unique densest lattice packing in 8-dimensional space.

##### Turan's theorem for random graphs

PLEASE NOTE DIFFERENT TIME. CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT. Write t_r(G) (resp. b_r(G)) for the maximum size of a K_r-free (resp. (r-1)-partite) subgraph of a graph G. Of course t_r(G) is at least b_r(G) for any G, while Turan's Theorem (or Mantel's Theorem if r = 3) says that equality holds if G = K_n.

##### The space of metrics of positive scalar curvature

Given a closed smooth manifold admitting a Riemannian metric of positive scalar curvature, we are interested in the space of all such metrics. We will give a survey on recent results concerning the homotopy type of this space and of the associated moduli space of positive scalar curvature metrics.

##### Nearby cycles and local convolution

**PLEASE NOTE SPECIAL TIME AND LOCATION. ** I will explain how to use Deligne's theory of nearby cycles over general bases to prove Thom-Sebastiani type theorems.

##### Minerva Lecture I: An introduction to the Ribe program

A classical theorem of Martin Ribe asserts that finite dimensional linear properties of normed spaces are preserved under uniformly continuous homeomorphisms. Thus, normed spaces exhibit a strong rigidity property: their structure as metric spaces determines the linear properties of their finite dimensional subspaces. This clearly says a lot about the geometry of normed spaces, but it turns out that one can also use it to understand the structure of metric spaces that have nothing to do with linear spaces, such as graphs, manifolds or groups. PLEASE CLICK ON LECTURE TITLE FOR COMPLETE ABSTRACT.

##### Finite Energy Foliations and Connect Sums

I will present some recent joint work with Richard Siefring on the behavior of finite energy foliations under the action of a 0-surgery (i.e. a connect sum) and a 2-surgery. We will then discuss applications to the restricted three body problem.

##### Minerva Lecture II: Dichotomies and universality in metric embeddings.

It is a basic fact that the space of continuous functions on the interval [0,1] contains an isometric copy of every separable metric space, and in particular of every finite metric space. However, it is a subtle question to

decide whether or not a given metric space is universal in the sense that it contains a copy of every finite metric space with O(1) bi-Lipschitz distortion. PLEASE CLICK ON LECTURE TITLE FOR COMPLETE ABSTRACT.

##### Stability of the neutral state for the 2 fluid Euler-Maxwell system

This is a joint work with Y. Guo and A. Ionescu. We consider the 2 fluid Euler-Maxwell problem in the whole 3d space. We show that small and smooth irrotational initial perturbations lead to solutions which remain globally smooth and scatter back to equilibrium.

##### Dissolution driven convection for carbon dioxide sequestration: The stability problem

The dissolution-driven convection in porous media is potentially a rate limiting process for sequestering carbon dioxide in underground aquifers. Super critical carbon dioxide introduced in the aquifer is lighter than the water that fills the surrounding porous rock, and hence quickly rises to the top. However, the solution of carbon dioxide in water is heavier than water.

##### Minerva Lecture III: Super-expanders and nonlinear spectral calculus

While the topic of this talk initially arose in the context of the Ribe program, it will take us further afield. A bounded degree n-vertex graph $G = (V, E)$ is an expander if and only if for every choice of $n$ vectors ${x_v}_{v\in V}$ in $R^k$ the average of the Euclidean distance between $x_u$ and $x_v$ is within a constant factor of the average of the same terms over those pairs ${u, v}$ that form an edge in $E$. PLEASE CLICK ON LECTURE TITLE FOR COMPLETE ABSTRACT.

##### The quantum Shannon-McMillan theorem and rank of spectral projections of macroscopic observables

The classical Shannon-McMillan theorem states that an ergodic system has typical sets satisfying the asymptotic equipartition property. This theorem demonstrates the significance of entropy which gives the size of the typical sets. There has recently been great progress in the quantum version of the Shannon-McMillan theorem .In particular, Bjelakovic et al.

##### Deformations of Fano 3-folds with terminal singularities

Fano 3-folds with terminal singularities are important in the classification of 3-folds. Fano 3-folds with terminal Gorenstein singularities are roughly classified. However, in the non-Gorenstein case, things get complicated and the classification is not done. In order to make the classification easier, it is useful to consider the deformations.

##### Ricci Curvature and Infinite Dimensional Analysis on Path Space

In this talk we discuss recent connections between the Ricci curvature of a Riemannian manifold and the analysis on the path space of the manifold. We will see that bounded Ricci curvature controls the analysis on the path space P(M) of a manifold in much the same way that lower Ricci curvature controls the analysis on M itself. PLEASE CLICK ON COLLOQUIUM TITLE FOR COMPLETE ABSTRACT.

##### The Eguchi-Hanson metric

In 1978 the physicists Eguchi and Hanson discovered a "gravitational pseudoparticle." It was quickly stolen by mathematicians. I will discuss some topological, analytic, differential-geometric and algebro-geometric properties of the Eguchi-Hanson construction.

##### Double commutants of multiplication operators on $C(K)$

We consider the following topological property of a compact Hausdorff space $K$: for every operator $M$ of multiplication by a real-valued function from $C(K)$, its double commutant coincides with the norm-closed algebra generated by $M$ and the identity operator $I$. If it is the case, we say that $K \in DC$.

##### G-valued flat deformations and local models

I will begin with a brief introduction to the deformation theory of Galois representations and its role in modularity lifting. This will motivate the study of local deformation rings and more specifically flat deformation rings.