Welcome to the home page of the Mathematics Graduate Student Organization (MGSO) at Texas A&M University in College Station. The purpose of this organization is to encourage communication among students, faculty, and staff, and contribute to a rich social life in the department through cultural and scientific dialogue. We would also like to provide an environment where students in the mathematics department can practice their presentation skills as well as view the techniques of others. It is our goal to be a source of support and information for all graduate students.

The main activity of the MGSO is the Graduate Student Seminar. This seminar is for grad students, (largely) by grad students: Volunteer to give a talk!

Seminar: Fall 2018, Thursdays, Blocker 506A, 4:00-4:50 PM

Next Talk

Speaker:   Nida Obatake and Alexander Ruys de Perez

Title:   "Oscillations in the ERK Network" and "Max Intersection Completeness in the Neural Ideal"

Time / Date:   4:00 - 5:00 , March 7

Abstract

"Chemical Reaction Network theory is an area of mathematics that analyzes the behaviors of chemical processes. A major problem in this area is the stability of steady states of these networks. Rubinstein et al. (2016) showed that the ERK network exhibits multiple steady states, bistability, and undergoes periodic oscillations for some choice of rate constants and total species concentrations. The ERK network reduces to the processive dual-site phosphorylation network when certain reactions are omitted, and this network is known to have a unique, stable steady state (Conradi and Shiu, 2015). To investigate how multiple steady states and oscillations are lost as reactions are removed from the ERK network, we analyze subnetworks of the ERK network. In particular, we prove that oscillations persist even after we greatly simplify the model by making all reactions irreversible and removing intermediates. We prove this using an algebraic criterion for Hopf bifurcations that relies on analyzing polynomials (Yang, 2002). We introduce the Newton Polytope Method: an algorithmic procedure that uses techniques from polyhedral geometry to construct a positive point where a pair of polynomials achieve certain desired sign conditions. Joint work with Anne Shiu, Xiaoxian Tang, and Angelica Torres." and\\ "Max intersection completeness is a property of neural codes that guarantees convexity, but naively checking such a property takes exponential time. We answer a question posed by Curto et al. by providing an algebraic signature for max intersection completeness in the neural ideal. We do so by introducing a new simplicial complex called the factor complex, and describing its correspondence with the neural ideal."