Colloquium Series

Spring 2019

All talks are 3:45-4:45 p.m. in the Colloquium room (Chauvenet 110), unless otherwise specified.

Cookies will be served in the lecture room starting shortly before the talk.

• Apr

  17
• Optimal post-donation blood screening strategies under uncertainty

  Hadi El-Amine

  George Mason

  Time: 03:45 PM

  View Abstract

  Blood products are essential components of any healthcare system, and their safety, in terms of being free of transfusion-transmittable infections, is crucial. While the Food and Drug Administration (FDA) in the United States requires all blood donations to be tested for a set of infections, it does not dictate which particular tests should be used by Blood Collection Centers. Multiple FDA-licensed blood screening tests are available for each infection, but all screening tests are imperfectly reliable and have different costs. In addition, infection prevalence rates and other donor characteristics within the donor population are uncertain, while surveillance methods are highly resource- and time-intensive. Therefore, only limited information is available to Blood Collection Centers on infection prevalence rates and other donor characteristics. In this setting, the budget-constrained Blood Collection Center needs to devise a post-donation blood screening scheme so as to minimize the risk of an infectious donation being released into the blood supply. The focus is on “robust” screening schemes under limited information. Toward this goal, various objectives are considered, and structural properties of the optimal solutions under each objective are characterized. This allows to gain insight and to develop efficient, exact algorithms. My research shows that using the proposed optimization-based approaches provides robust solutions with significantly lower expected infection risk compared to other testing schemes that satisfy the FDA requirements. This has important public policy implications.

• Apr

  10
• Theta polynomials in geometry, Lie theory, and combinatorics

  Harry Tamvakis

  U. Maryland

  Time: 03:45 PM

  View Abstract

  The classical Schur polynomials form a natural basis for the ring of symmetric polynomials, and have geometric significance since Giambelli showed that they represent the Schubert classes in the cohomology ring of Grassmannians. Moreover, these polynomials enjoy rich combinatorial properties. In the last decade, an exact analogue of this picture has emerged in the symplectic and orthogonal Lie types, with the Schur polynomials replaced by the theta and eta polynomials of Buch, Kresch, and the speaker. I will discuss this correspondence in the case of the symplectic group and theta polynomials.

• Mar

  27
• Counting in flag manifolds

  Leonardo Mihalcea

  Virginia Tech

  Time: 03:45 PM

  View Abstract

  Consider the following enumerative questions: how many points are there in a projective space over a finite field; how many lines pass through 4 given lines in 3-space; how many lines are on a non-singular cubic surface; how many (rational) plane curves pass through a number of points ? All of these can be answered by analyzing classical and quantum intersection rings for appropriate parameter (or moduli) spaces. The intersection rings have a particularly rich structure in the case flag manifolds, with connections to many areas in mathematics. I will give a brief overview of these rings, and sketch some techniques useful for calculations such as those above.

• Mar

  20
• The Waring-Goldbach Problem

  Angel Kumchev

  Towson U.

  Time: 03:45 PM

  View Abstract

  The Waring-Goldbach problem is the central question in the additive theory of prime numbers. In simplest terms, this is the question which positive integers can be represented as sums of $s$ $k$-th powers of primes: Given fixed positive integers $s > k \ge 1$, under what conditions on $n$ does the Diophantine equation $$ p_1^k + p_2^k + \dots + p_s^k = n $$ have solutions in primes $p_1, p_2, \dots, p_s$? When $k=1$, this question turns into Goldbach’s problem; and when the variables are not restricted to the primes, it becomes Waring’s problem. I will review the history of the Waring-Goldbach problem, including some recent developments, and will provide a brief glimpse into the kind of mathematics that lies behind the proofs of the theorems.

• Jan

  25
• Growth and groups

  Moon Duchin

  Tufts

  Time: 12:00 PM

  View Abstract

  Mathematicians have long studied the question of volume growth in manifolds and combinatorial growth in groups. I want to explain some of how these are related and why they're interesting, and I'll use the Heisenberg group and its geometry as the main example.

• Jan

  14
• Population persistence under prolonged and reoccurring disturbances

  Amy Veprauskas

  U. Louisiana-Lafayette

  Time: 03:45 PM

  View Abstract

  An important focus for management and conservation is determining whether a species or a system of interacting species can sustain itself. This question becomes increasingly important as populations are exposed to various disturbances, both natural and anthropogenic, such as hurricanes, habitat fragmentation, toxicants, and invasive species. Here we examine how disturbances may impact species persistence from two perspectives. First, for short-lived species, prolonged exposure to a disturbance has the potential to result in rapid evolution of toxicant resistance. We apply evolutionary game theory to a Leslie matrix model for daphniids to obtain Darwinian equations that couple population and evolutionary dynamics. Using bifurcation analysis, we examine how evolutionary changes in response to a disturbance may allow a population to persist at higher levels of the disturbance than is possible without evolution. Next, we develop a non-autonomous matrix model to consider the effect of reoccurring disturbances on population persistence. This model uses a two-state Markov chain to describe the frequency and average length of effect of the disturbances. We derive an approximation for a population’s stochastic growth rate and apply sensitivity analysis to examine how best to mitigate the impact of disturbances.