Events for 03/31/2017 from all calendars

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Elizabeth Gross , San Jose State University

Title: Combinatorial and algebraic problems in systems biology

Abstract: Systems biology focuses on modeling complex biological systems, such as metabolic and cell signaling networks. These biological networks are modeled with polynomial dynamical systems that can be described with directed graphs. Analyzing these systems at steady-state results in polynomial ideals with significant combinatorial structure. Using the Wnt shuttle model as an example, we will discuss some of the combinatorial and algebraic techniques available for parameter estimation and model selection. We will then look at the algebraic problems that arise when constructing new network models from smaller models through gluing operations on the corresponding directed graphs. This talk draws on joint work with Heather Harrington, Zvi Rosen, and Bernd Sturmfels, as well as joint work with Heather Harrington, Nicolette Meshkat, and Anne Shiu.

Seminar on Banach and Metric Space Geometry

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Andrew Swift, Texas A&M Univeristy

Title: Coarse embeddings into superstable spaces

Abstract: If a Banach space coarsely embeds into a superstable Banach space, then it must contain a basic sequence with an ℓp spreading model for some p∈[1,∞). This is a coarse analogue to a result of Y. Raynaud, which says that if a Banach space uniformly embeds into a superstable Banach space, then it must contain a subspace isomorphic to ℓp for some p∈[1,∞). The result obtained implies that not every reflexive Banach space is coarsely embeddable into a superstable Banach space. A sketch of the proof will be given, and comparisons to Raynaud's proof in the uniform case will be made. This is joint work with B. M. Braga.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Ata Firat Pir, TAMU

Title: Irrational Toric Varieties

Abstract: Classical toric varieties come in two flavors: Normal toric varieties are given by rational fans in R^n. A (not necessarily normal) affine toric variety is given by finite subset A of Z^n. Toric varieties are well understood and they can be approached in a combinatorial way, making it possible to compute examples of abstract concepts. Applications of mathematics have long studied the positive real part of a toric variety as the main object, where the points in A may be arbitrary points in R^n. In 1963, Birch showed the such an irrational toric variety is homeomorphic to the convex hull of the set A. Recent work showing that all Hausdorff limits of translates of irrational toric varieties are toric degenerations suggested the need for a theory of irrational toric varieties associated to arbitrary fans in R^n. These are R^n_>-equivariant cell complexes dual to the fan. Among the pleasing parallels with the classical theory is that the space of Hausdorff limits of the irrational projective toric variety of a finite set A in R^n is homeomorphic to the secondary polytope of A. This talk will sketch this story of irrational toric varieties. It represents work in progress with Sottile.