Thursday, November 9, 2017 - 15:00 , Location: Skiles 006 , Elliot Paquette , The Ohio State University , email@example.com , Organizer: Lutz Warnke
We study an online algorithm for making a well—equidistributed random set of points in an interval, in the spirit of "power of choice" methods. Suppose finitely many distinct points are placed on an interval in any arbitrary configuration. This configuration of points subdivides the circle into a finite number of intervals. At each time step, two points are sampled uniformly from the interval. Each of these points lands within some pair of intervals formed by the previous configuration. Add the point that falls in the larger interval to the existing configuration of points, discard the other, and then repeat this process. We then study this point configuration in the sense of its largest interval, and discuss other "power of choice" type modifications. Joint work with Pascal Maillard.
Series: Algebra Seminar
In this talk we will discuss the following question: When does there exist a curve of degree d and genus g passing through n general points in P^r? We will focus primarily on what is known in the case of space curves (r=3).
Series: Geometry Topology Seminar
Monday, November 6, 2017 - 13:55 , Location: TBA , Prof. Kevin Lin , University of Arizona , Organizer: Molei Tao
Friday, November 3, 2017 - 15:00 , Location: Skiles 005 , Joel Spencer , Courant Institute, New York University , Organizer: Lutz Warnke
The search for the asymptotics of the Ramsey function R(3,k) has a long and fascinating history. It begins in the hill country surrounding Budapest and winding over the decades through Europe, America, Korea and Rio de Janiero. We explore it through a CS lens, giving algorithms that provide the various upper and lower bounds. The arguments are various more or less sophisticated uses of Erdoes Magic and, indeed, many of the most important advances in the Probabilistic Method have come from these investigations.
Friday, November 3, 2017 - 15:00 , Location: Skiles 154 , Hassan Attarchi , Georgia Tech , Organizer:
This presentation is about the results of a paper by L. Bunimovich in 1974. One considers dynamical systems generated by billiards which are perturbations of dispersing billiards. It was shown that such dynamical systems are systems of A. N. Kolmogorov (K-systems), if the perturbation satisfies certain conditions which have an intuitive geometric interpretation.
Series: Stochastics Seminar
The Sherrington-Kirkpatirck (SK) model is a mean-field spin glass introduced by theoretical physicists in order to explain the strange behavior of certain alloys, such as CuMn. Despite of its seemingly simple formulation, it was conjectured to possess a number of profound properties. This talk will be focused on the energy landscapes of the SK model and the mixed p-spin model with both Ising and spherical configuration spaces. We will present Parisi formule for their maximal energies followed by descriptions of the energy landscapes near the maximum energy. Based on joint works with A. Auffinger, M. Handschy, G. Lerman, and A. Sen.