Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, November 21, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 21, 2019

11:00 am in 241 Altgeld Hall,Thursday, November 21, 2019

#### Sums with the Mobius function twisted by characters with powerful moduli

###### William Banks (University of Missouri)

Abstract: In the talk, I will describe some recent joint work with Igor Shparlinski, in which we have combined classical ideas of Postnikov and Korobov to derive new bounds on short character sums for certain nonprincipal characters of powerful moduli. Our results are used to bound sums with the Mobius function twisted by such characters, and we obtain new results on the size and zero-free region of Dirichlet L-functions attached to the same class of moduli.

1:00 pm in 347 Altgeld Hall,Thursday, November 21, 2019

#### Robust Analysis of Metabolic Pathways

###### Al Holder (Rose-Hulman Institute of Technology)

Abstract: Flux balance analysis (FBA) is a widely adopted computational model in the study of whole-cell metabolisms, often used to identify drug targets, to study cancer, and to engineer cells for targeted purposes. The most common model is a linear program that maximizes cellular growth rate subject to achieving steady metabolic state and to satisfying environmental bounds. Quadratic and integer modifications are also common. Standard stoichiometry decides the preponderance of data in most instances, and hence, the majority of information defining an optimization model is certain. However, several key parts of a model rely on inferred science and are less certain; indeed, the method of deciding several of these values is opaque in the literature. This prompts the question of how the resulting science might depend on our lack of knowledge. We suggest a robust extension of FBA called Robust Analysis of Metabolic Pathways (RAMP) that accounts for uncertain information. We show that RAMP has several mathematical properties concomitant with our biological understanding, that RAMP performs like a relaxation of FBA in practice, and that RAMP requires special numerical awareness to solve.

3:00 pm in 347 Altgeld Hall,Thursday, November 21, 2019

#### Degree of Grothendieck polynomials and Castelnuovo-Mumford regularity

###### Colleen Robichaux   [email] (UIUC)

Abstract: Matrix Schubert varieties are sets of matrices satisfying certain rank conditions. We explore the connection between the degree of the Grothendieck polynomial and the Castelnuovo-Mumford regularity of coordinate rings of matrix Schubert varieties. Further we give an easily computable formula for this degree for the case of $w$ grassmannian. We end with a connection to a conjecture of Kummini-Lakshmibai-Sastry-Seshadri on regularity of standard open patches of Grassmannian Schubert varieties. This is joint work with Jenna Rajchgot, Yi Ren, Avery St. Dizier, and Anna Weigandt.

4:00 pm in 245 Altgeld Hall,Thursday, November 21, 2019

#### Metric embeddings of graphs into Banach spaces

###### Pavlos Motakis   [email] (University of Illinois at Urbana-Champaign)

Abstract: The embedding of a graph into a Banach space can be used to study either object by exploiting the properties of the other. The type of information that can be retrieved depends on the type of graph, the type of Banach space, and the type of metric embedding at hand. Various cases in which this approach has been useful will be explored. Particular weight will be given to finite lamplighter graphs and infinite Hamming graphs and their relation to local properties of Banach spaces and asymptotic properties of Banach spaces respectively.