Noticias en español
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 Hurder.
Read MoreTheorems 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 manifold, the conclusion fails. However if we allow...
Read MoreThe 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 into an almost periodic and a weak mixing...
Read MoreMultiple 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 positive answer to 2^n is somewhat surprising and...
Read MoreSeminarios Sistemas Dinámicos de Santiago y Seminario Kawin
TIME (Mon 27th May) 4:30 pm – 5:30 pm LOCATION Sala 1, PUC, Facultad de Matemáticas, Av. Vicuña Mackenna 4860, Macul, La Florida SPEAKER Ryo Moore (PUC) TITLE Properties of Birkhoff spectra for the generic continuous functions on a shift space ABSTRACT (Attached please find the abstract of the talk) TIME (Mon 27th May) 3:30 pm – 4:20 pm LOCATION Sala 1, PUC, Facultad de Matemáticas, Av. Vicuña Mackenna 4860, Macul, La Florida SPEAKER Sebastián Donoso (UOH – UCH) TITLE Expansiveness and dimension of minimal sets ABSTRACT A remarkable theorem by Mañé...
Read MoreAssouad dimension of planar self-affine sets
ABSTRACT: We consider planar self-affine sets X satisfying the strong separation condition and the projection condition. We show that any two points of X, which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets. We also calculate the Assouad dimension of X. Finally, we prove that if X is dominated, then it is minimal for the conformal Assouad dimension. The talk is based on joint work with Balázs Bárány and Eino Rossi.
Read More