Events for 01/25/2019 from all calendars

Working Seminar on Quantum Groups

Time: 10:30AM - 12:00PM

Location: BLOC 624

Speaker: John Weeks, TAMU

Title: Introduction to compact quantum groups

Abstract: We will work through the first few chapters of ``Compact Quantum Groups and Their Representation Categories'', by Sergey Neshveyev and Lars Tuset

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Aleksandra Sobieska, TAMU

Title: Minimal Free Resolutions over Rational Normal Scrolls

Abstract: Free resolutions of monomial ideals over the polynomial ring are well-studied and reasonably well-understood, though they are still an active area of research in commutative algebra. However, resolutions over quotients of the polynomial ring are much more mysterious, and even simple examples can violate the nicer properties that the polynomial ring provides. Starting in the 1990's, there is some work on resolutions over toric rings, a particular (and well-behaved) quotient of the polynomial ring. In this talk, we will present a minimal free resolution of the ground field over a specific toric ring that arises from rational normal scrolls. We also provide a computation of the Betti numbers for the resolution of the ground field for all rational normal $k$-scrolls.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Xiaoxian Tan, TAMU

Title: Applying Algebraic Methods in Mathematical Biology

Abstract: Many challenging problems in mathematical biology, for instance, in biochemical reaction networks and phylogenetics, are to solve non-linear polynomial systems. Therefore, methods and tools in algebraic geometry and combinatorics are more applicable and powerful. One typical example is the multistationarity problem: whether a given biochemical reaction network has two or more positive steady states? In this talk, we introduce a simple criterion to determine multistationarity for networks arising from biology and to identify the parameter values for which the given network exhibits multistationarity. For linearly binomial networks, we prove our method is much less expensive than standard real quantifier elimination method in computational algebraic geometry. The two key ideas for improving the efficiency are: 1. whether a given network is linearly binomial can be read off easily from graphs associated to the network. 2. linearly binomial networks have nice algebraic and geometric structures.