Department of

Mathematics


Seminar Calendar
for events the day of Thursday, September 3, 2020.

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Thursday, September 3, 2020

3:00 pm in Zoom meeting (see https://c3dti.ai/events/colloquium/),Thursday, September 3, 2020

Metapopulation and Age-Structured Epidemic Models for the COVID-19 Pandemic

Zoi Rapti (University of Illinois at Urbana-Champaign)

Abstract: Zoi Rapti will first address the issue of parameter identifiability from reported data, such as confirmed cases and deaths. Parameter identifiability analysis is used to determine whether unknown parameters in ordinary differential equation models can be determined from the available data. She will then introduce age-structured and spatial (metapopulation) models for the spread of COVID-19, demonstrating that in some multi-group models that are structured by age, the basic reproductive number of each group is smaller than the basic reproductive number of the entire community. Hence, in most cases, it is not informative to consider separately groups that are known to interact, as this may underestimate the overall severity of the outbreak. In metapopulation models, she will show how traffic data is used in mobility models of epidemic spread. Raptiís talk represents joint work of a research team that includes Eleftheria Kontou (Civil and Environmental Engineering, University of Illinois, Urbana-Champaign), Yannis Kevrekidis (Chemical and Biomolecular Engineering & Applied Mathematics and Statistics, Johns Hopkins University), and P. G. Kevrekidis (Mathematics and Statistics, University of Massachusetts at Amherst).

3:00 pm in Zoom,Thursday, September 3, 2020

Coloring K-Theoretic Schubert Calculus

Travis Scrimshaw   [email] (The University of Queensland)

Abstract: Double Grothendieck polynomials were introduced as polynomial representatives of Schubert varieties in the equivariant K-theory ring of the full flag variety. Recently, a combinatorial formula using bumpless pipe dreams of Lam-Lee-Shimozono was proven by Weigandt using a formula due to Lascoux that describes double Grothendieck polynomials using alternating sign matrices. In this talk, we will give another proof of this formula by translating bumpless pipe dreams into the language of colored integrable vertex models. We then show the generating function (aka the partition function) of our colored lattice model satisfies the same functional relations as double Grothendiecks up to a known factor by using the Yang-Baxter equation. By exploiting a natural duality, we use our vertex model to give a new proof that double Grothendieck polynomials for vexillary permutations are flagged Grothenieck polynomials and that the stable limit is a factorial Grothendieck polynomial. This is joint work with Valentin Buciumas. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

4:00 pm in 245 Altgeld Hall,Thursday, September 3, 2020

To Be Announced

Marius Junge   [email] (University of Illinois at Urbana-Champaign)

Abstract: To come.