Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Theorems of Borsuk-Ulam Type
Abstract: The Borsuk-Ulam Theorem states that for any continuous function f from S^n to R^n there is some x in S^n such that f(x) = f(-x). Replace S^n by the boundary of some open set A of E=R^{n+1} and replace R^n by some n dimensional manifold B. The conclusion of the theorem remains, with the pair x, -x replaced by some x,y on the boundary whose convex combinations contain some fixed point z in the interior of that open set. Indeed there is a topological structure to all such solutions when the z is considered a variable. If B is not a...
Super-logarithmic cliques in dense inhomogeneous random graphs
Abstract: In the theory of dense graph limits, a graphon is a symmetric measurable function W from [0,1]^2 to [0,1]. Each graphon gives rise naturally to a random graph distribution, denoted G(n,W), that can be viewed as a generalization of the Erdos-Renyi random graph. Recently, Dolezal, Hladky, and Mathe gave an asymptotic formula of order log(n) for the size of the largest clique in G(n,W) when W is bounded away from 0 and 1. We show that if W is allowed to approach 1 at a finite number of points, and displays a moderate rate of growth...
El conjunto minimal de los flujos de Kuperberg
ABSTRACT : En 1994, K. Kuperberg construyó ejemplos de flujos suaves sin órbitas periódicas en cualquier variedad cerrada y sin frontera de dimensión 3, demostrando así que la conjetura de Seifert es falsa. En la plática presentaré una descripción topológica del conjunto minimal de estos ejemplos, que es un conjunto minimal excepcional de dimensión topológica 2. Explicaré además algunos resultados relacionados con la forma (shape theory) y la entropía de dichos ejemplos. Los resultados fueron obtenidos en colaboración con Steve...
Hidden Convexity in the l0 Pseudonorm and Lower Bound Convex Programs for Exact Sparse Optimization
Abstract: In sparse optimization problems, one looks for solution that have few nonzero components. We consider problems where sparsity is exactly measured by the l0 pseudonorm. We display a suitable conjugacy for which we show that the l0 pseudonorm is equal to its biconjugate. As a corollary, we obtain that the (nonconvex) l0 pseudonorm coincides, on the sphere, with a convex lsc function that we characterize. With this conjugacy, we display a lower bound for the original exact sparse optimization problem, which is a...
Balancing Vectors in any Norm
Abstract: In the vector balancing problem, we are given symmetric convex bodies C and K in R^n, and our goal is to determine the minimum number β ≥ 0, known as the vector balancing constant from C to K, such that for any sequence of vectors in C there always exists a signed combination of them lying inside βK. Many fundamental results in discrepancy theory, such as the Beck-Fiala theorem (Discrete Appl. Math ‘81), Spencer’s “six standard deviations suffice” theorem (Trans. Amer. Math. Soc ‘85) and Banaszczyk’s vector balancing theorem (Random...
Multiple correlations and nilsequences
ABSTRACT Multiple correlation sequences first appeared implicitly in Furstenberg’s proof of Szemeredi’s theorem. Bergelson, Host and Kra later proved they can be decomposed into the sum of a nilsequence and a sequence tending to zero in density. Motivated by this, Frantzikinakis asks whether we have a similar decomposition along the sequence of primes p_n, or Hardy sequence [n^c], or 2^n. In this talk, I’ll answer this question affirmatively. Even though the positive answers to the prime and Hardy sequences are expected, the...
The Erdos sumset conjecture
ABSTRACT The Erdos sumset conjecture predicts that any set of natural numbers with positive density must contain the arithmetic sum A+B of two infinite sets A and B. I will present a recent solution to this conjecture, obtained jointly with F. Richter and D. Robertson. The proof involves a modified version of the correspondence principle devised by Furstenberg in 1977 to convert certain problems from combinatorics into the realm of ergodic theory, and two variations of the decomposition of an arbitrary function on a measure preserving system...
Efficient Implementation of a Practical Leakage-Resilient ID Scheme
Abstract: Instead of viewing cryptographic algorithms as simple black-boxes, leakage-resilient cryptography accepts that certain traditionally secret parts of the algorithm will be available to the attacker through side channel attacks and aims to ensure the security of these algorithms in the presence of such leakage. We present a leakage resilient identification scheme based on the continuous memory leakage model, which assumes that the leakage of information is unrestricted in time and space. We design a three message sigma protocol,...
Funciones p-armónicas con condiciones de Neumann en el borde que involucran medidas
Abstract: En esta presentación discutiré el problema de encontrar funciones p-armónicas en el semi-espacio superior con condiciones de Neumann en el borde de tipo no lineal y con medidas. Para ello introduciré el concepto de soluciones renormalizadas en dominios acotados y explicaré como usar esta teoría para obtener soluciones de nuestro problema. La idea principal es usar estabilidad local y la simetría del dominio. Las técnicas a utilizar también nos permitirán establecer algunos resultados de no existencia y de eliminación de...
