Events for 02/29/2024 from all calendars

Departmental Colloquia

Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Alex Lubotzky, Weizmann Institute of Science

Title: Good locally testable codes

Abstract: Abstract: An error-correcting code is locally testable (LTC) if there is a random tester that reads only a small number of bits of a given word and decides whether the word is in the code, or at least close to it. A long-standing problem asks if there exists such a code that also satisfies the golden standards of coding theory: constant rate and constant distance.

Unlike the classical situation in coding theory, random codes are not LTC, so this problem is a challenge of a new kind. We construct such codes based on what we call (Ramanujan) Left/RightCayley square complexes. These objects seem to be of independent group-theoretic interest. The codes built on them are 2-dimensional versions of the expander codes constructed by Sipser and Spielman (1996).

The main result and lecture will be self-contained. But we hope also to explain how the seminal work of Howard Garland (1972) on the cohomology of quotients of the Bruhat-Tits buildings of p-adic Lie group has led to this construction (even though it is not used at the end). Based on joint work with I. Dinur, S. Evra, R. Livne, and S. Mozes.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Dr. Prabir Daripa, Texas A&M University

Title: Introduction to modeling of population dynamics

Abstract: We will introduce some models, continuous and discrete, for population dynamics. Then we will study these at a very elementary level and discuss pros and cons of these models. We will show why mathematical understanding of these models are important before their use for estimating future population. There will be several takeaways from this talk including the emergence of chaos lurking in very simple models. The hallmark of this is that when "present" determines the future but the approximate present does not approximately determine the future". This is in essence "Chaos" (In Wikipedia, you find this as one of the definitions of "Chaos" within "Chaos Theory") as opposed to classical stability theory in which when the present determines the future and the approximate present does determine the future but may be a drastically different one. The content of the talk will be kept very simple so that it is accessible to even first year undergraduate students.