Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, September 6, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, September 6, 2017

3:00 pm in 345 Altgeld Hall,Wednesday, September 6, 2017

Modeling Dependent Insurance Risks: Customer Loyalty and Risk in Personal Insurance

Edward W. Frees (University of Wisconsin-Madison, Risk and Insurance)

Abstract: In the first portion of the talk I discuss the importance of modeling dependencies among insurance risks. I set the stage for this by describing various risk control mechanisms that the insurer has at its disposal and use this platform for describing the types of associations that are of concern to insurers. To model dependencies, I focus on the use of a copula, a probabilistic tool widely used in insurance and other disciplines. The second portion of the talk, on "Customer Loyalty and Risk in Personal Insurance," is joint work with Catalina Bolancé, Montserrat Guillén, and Emiliano Valdez. This work connects two strands of research on modeling personal (automobile and homeowners) insurance. One strand involves understanding the joint outcomes of separate personal insurance contracts, e.g., do higher automobile claims suggest more severe homeowner claims? A second strand of the literature involves understanding determinants of customer loyalty. For example, we now know that when a customer cancels one insurance contract, he or she is likely to cancel all other contracts soon after. We use copula regression to model the joint outcomes of auto and home claims as well as customer loyalty. Including customer loyalty, or duration with the company, is complicated because of the censoring of this time variable as well as the discreteness. Although customers may cancel the contract at any time, cancellation typically occurs at contract renewal, making this variable essentially a discrete outcome. Composite likelihood and generalized method of moments techniques allow us to address the special features of this data structure.

4:00 pm in 245 Altgeld Hall,Wednesday, September 6, 2017

Truncation in Generalized Series Fields

Santiago Camacho (Illinois Math)

Abstract: Taylor polynomials are very useful for approximating analytic functions, nevertheless there is increasing interest in understanding so-called analyzable functions that are not necessarily analytic. For this reason fields of generalized series (Hahn fields) that extend Laurent series have been studied. A natural analogue of Taylor or Laurent polynomials in these series fields are truncated series. We explore some of the stability properties of truncation closed subsets of Hahn Fields.

4:00 pm in 245 Altgeld Hall,Wednesday, September 6, 2017

Truncation in Generalized Series Fields

Santiago Camacho (UIUC Math)

Abstract: Taylor polynomials are very useful for approximating analytic functions, nevertheless there is increasing interest in understanding so-called analyzable functions that are not necessarily analytic. For this reason fields of generalized series (Hahn fields) that extend Laurent series have been studied. A natural analogue of Taylor or Laurent polynomials in these series fields are truncated series. We explore some of the stability properties of truncation closed subsets of Hahn Fields.

4:00 pm in 141 Altgeld Hall,Wednesday, September 6, 2017

Some fun with Hilbert schemes of points on surfaces

Joshua Wen (Illinois Math)

Abstract: The Hilbert scheme of points of $X$, parametrizes zero-dimensional subschemes of $X$. These spaces can be messy in general, but in the case that $X$ is a smooth surface, the Hilbert scheme is smooth as well. Rather than being some esoteric moduli space, the Hilbert scheme in this case is something one can get to know. I’ll introduce the Nakajima-Grojnowski construction of a Heisenberg algebra action that can be used to compute its Borel-Moore homology in a somewhat surprising way. Focusing on the case where $X$ is the plane, I’ll highlight connections with symmetric function theory. The goal is to give an overview of the surprising and useful structures the Hilbert scheme has, and perhaps this semester we can either study those structures in more detail or study larger-picture explanations for why those structures exist in the first place (moduli of sheaves on surfaces, 4d-gauge theory, etc.).

5:00 pm in 314 Altgeld Hall,Wednesday, September 6, 2017

Math Contests Open House

Abstract: An informational session about our extensive program of math contests, training sessions, and related activities.