Seminars and Colloquia by Series

Algebraic Systems Biology, Model Selection and Parameter Estimation

Series
Algebra Seminar
Time
Tuesday, May 31, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Elizabeth GrossSan Jose State University
Systems biology focuses on modeling complex biological systems, such as metabolic and cell signaling networks. These biological networks are modeled with polynomial dynamical systems. Analyzing these systems at steady-state results in algebraic varieties that live in high-dimensional spaces. By understanding these varieties, we can provide insight into the behavior of the models. Furthermore, this algebro-geometric framework yields techniques for model selection and parameter estimation that can circumvent challenges such as limited or noisy data. In this talk, we will introduce biochemical reaction networks and their resulting steady-state varieties. In addition, we will discuss the questions asked by modelers and their corresponding geometric interpretation, particularly in regards to model selection and parameter estimation.

Tropical Varieties for Exponential Sums

Series
Algebra Seminar
Time
Monday, April 4, 2016 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alperen ErgurTexas A&M
We define a variant of tropical varieties for exponential sums. These polyhedral complexes can be used to approximate, within an explicit distance bound, the real parts of complex zeroes of exponential sums. We also discuss the algorithmic efficiency of tropical varieties in relation to the computational hardness of algebraic sets. This is joint work with Maurice Rojas and Grigoris Paouris.

On the average height of abelian varieties with complex multiplication

Series
Algebra Seminar
Time
Monday, March 28, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Keerthi Madapusi PeraUniversity of Chicago
In the 90s, generalizing the classical Chowla-Selberg formula, P. Colmez formulated a conjectural formula for the Faltings heights of abelian varieties with multiplication by the ring of integers in a CM field, which expresses them in terms of logarithmic derivatives at 1 of certain Artin L-functions. Using ideas of Gross, he also proved his conjecture for abelian CM extensions. In this talk, I will explain a proof of Colmez's conjecture in the average for an arbitrary CM field. This is joint work with F. Andreatta, E. Goren and B. Howard.

Hurwitz correspondences on compactifications of M0,N

Series
Algebra Seminar
Time
Monday, March 14, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rohini RamadasUniversity of Michigan
Hurwitz correspondences are certain multivalued self-maps of the moduli space M0,N parametrizing marked genus zero curves. We study the dynamics of these correspondences via numerical invariants called dynamical degrees. We compare a given Hurwitz correspondence H on various compactifications of M0,N to show that, for k ≥ ( dim M0,N )/2, the k-th dynamical degree of H is the largest eigenvalue of the pushforward map induced by H on a comparatively small quotient of H2k(M0,N). We also show that this is the optimal result of this form.

Toric compactifications of semi-algebraic sets

Series
Algebra Seminar
Time
Monday, February 22, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel PlaumannUniversität Konstanz
We study compactifications of real semi-algebraic sets that arise from embeddings into complete toric varieties. This makes it possible to describe the asymptotic growth of polynomial functions on such sets in terms of combinatorial data. We discuss the phenomena that arise in examples along with some applications to positive polynomials. (Joint work with Claus Scheiderer)

A Grassmann algebra for matroids

Series
Algebra Seminar
Time
Monday, February 15, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Noah GiansiracusaUniversity of Georgia
I'll discuss joint work with my brother Jeff Giansiracusa in which we introduce an exterior algebra and wedge product in the idempotent setting that play for tropical linear spaces (i.e., valuated matroids) a very similar role as the usual ones do for vector spaces. In particular, by working over the Boolean semifield this gives a new perspective on matroids.

Constancy regions for mixed test ideals

Series
Algebra Seminar
Time
Monday, February 8, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Felipe PérezGeorgia State University
For the last four decades, mathematicians have used the Frobenius map to investigate phenomena in several fields of mathematics including Algebraic Geometry. The goal of this talk is twofold, first to give a brief introduction to the study of singularities in positive characteristic (aided by the Frobenius map). Second to define an explain the constancy regions for mixed test ideals in the case of a regular ambient; an invariant associated to a family of functions that shows a Fractal behavior.

Dual complexes of unirational varieties

Series
Algebra Seminar
Time
Monday, February 1, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dustin CartwrightUT Knoxville
The dual complex of a semistable degeneration records the combinatorics of the intersections in the special fiber. More generally, one can associate a polyhedral dual complex to any toroidal degeneration. It is natural to ask for connections between the geometry of an algebraic variety and the combinatorial properties of its dual complex. In this talk, I will explain one such result: The dual complex of an n-dimensional uniruled variety has the homotopy type of an (n-1)-dimensional simplicial complex. The key technical tool is a specialization map to dual complexes and a balancing condition for these specialization.

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