MenuEvents for 04/24/2017 from all calendars
Analysis/PDE Reading Seminar
Time: 1:00PM - 2:00PM
Location: Bloc628
Speaker: Vitaly Moroz, Swansea University
Title: Variational methods in nonlinear elliptic problems
Abstract: We discuss variational approach to nonlinear elliptic equations on bounded and unbounded domains. In particular, we prove existence, positivity and in some cases radial symmetry of the ground-state solutions. Topics include: Sobolev and Poincare inequalities, Rellich-Kondrachov theorem, Pohozaev identity, constrained minimization.
Probability Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 628
Speaker: Alexandros Eskenazis, Princeton
Title: Gaussian mixtures and geometric inequalities
Abstract: A random variable $X$ is called a (centered) Gaussian mixture if there exist a positive random variable $Y$ and a standard Gaussian random variable $Z$, independent of $Y$, such that $X$ has the same distribution as the product $YZ$. We will explain how Gaussian mixtures appear in various extremization problems originating in probability and convex geometry. Examples include finding sharp constants in Khintchine-type inequalities and identifying extremal sections and projections of the unit ball of $\ell_p^n$ with respect to different geometric parameters, such as volume and mean width. Time permitting, we'll also discuss a correlation inequality on the Euclidean sphere. The talk is based on joint work with P. Nayar and T. Tkocz.
Geometry Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 220
Speaker: Corey Harris, Florida State
Title: Chern-Mather class of the multiview variety
Abstract: The multiview variety associated to a collection of N cameras records which sequences of image points in P^2N can be obtained by taking pictures of a given world point x∈P3 with the cameras. In order to reconstruct a scene from its picture under the different cameras it is important to be able to find the critical points of the function which measures the distance between a general point u∈P^2N and the multiview variety. We calculate a specific degree 3 polynomial that computes the number of critical points as a function of N. In order to do this, we construct a resolution of the multiview variety, and use it to compute its Chern-Mather class.
Industrial and Applied Math
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Kim Laine, Microsoft
Title: Overview of Homomorphic Encryption and Applications
Abstract: The rise of homomorphic encryption is undoubtedly one of the most exciting developments in the history of modern cryptography. Essentially, it allows computations to be applied to encrypted data, without the evaluating party learning any information about either the input or the output of the computation. In this talk I will give a high-level overview of homomorphic encryption, and show some of the core definitions and constructions using ideal lattices from power-of-2 cyclotomic number fields. In particular, I will show how the homomorphic property is achieved in the Fan-Vercauteren scheme, which is implemented by several open-source libraries. While theoretically powerful, all known constructions of homomorphic encryption introduce a significant performance overhead. I will discuss our attempts at overcoming this overhead in the cases of specific example applications. Time permitting, I will mention some exciting directions for future research.
