Department of

Mathematics


Seminar Calendar
for events the day of Monday, January 27, 2020.

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Monday, January 27, 2020

2:00 pm in 241 Altgeld Hall,Monday, January 27, 2020

Two-Part D-Vine Copula Models for Longitudinal Insurance Claim Data

Lu Yang (University of Amsterdam)

Abstract: Insurance companies keep track of each policyholder's claims over time, resulting in longitudinal data. Efficient modeling of time dependence in longitudinal claim data can improve the prediction of future claims needed, for example, for ratemaking. Insurance claim data have their special complexity. They usually follow a two-part mixed distribution: a probability mass at zero corresponding to no claim and an otherwise positive claim from a skewed and long-tailed distribution. We propose a two-part D-vine copula model to study longitudinal mixed claim data. We build two stationary D-vine copulas. One is used to model the time dependence in binary outcomes resulting from whether or not a claim has occurred, and the other studies the dependence in the claim size given occurrence over time. The proposed model can predict the probability of making claims and the quantiles of severity given occurrence straightforwardly. We use our approach to investigate a dataset from the Local Government Property Insurance Fund in the state of Wisconsin.

3:00 pm in Altgeld Hall 441,Monday, January 27, 2020

Organizational meeting

William Balderrama (Illinois Math)

3:00 pm in 243 Altgeld Hall,Monday, January 27, 2020

Organizational meeting

Abstract: An organizational meeting to discuss plans for the Spring 2020 semester.

4:00 pm in 245 Altgeld Hall,Monday, January 27, 2020

A new approach to bounding L-functions

Jesse Thorner   [email] (University of Florida)

Abstract: Analytic number theory began with studying the distribution of prime numbers, but it has evolved and grown into a rich subject lying at the intersection of analysis, algebra, combinatorics, and representation theory. Part of its allure lies in its abundance of problems which are tantalizingly easy to state which quickly lead to deep mathematics, much of which revolves around the study of L-functions. These extensions of the elusive Riemann zeta function $\zeta(s)$ are generating functions with multiplicative structure arising from either arithmetic-geometric objects (like number fields or elliptic curves) or representation-theoretic objects (automorphic forms). Many equidistribution problems in number theory rely on one's ability to accurately bound the size of L-functions; optimal bounds arise from the (unproven!) Riemann Hypothesis for $\zeta(s)$ and its extensions to other L-functions. I will discuss some motivating problems along with recent work (joint with Kannan Soundararajan) which produces new bounds for L-functions by proving a suitable "statistical approximation" to the (extended) Riemann Hypothesis.

5:00 pm in 241 Altgeld Hall,Monday, January 27, 2020

To Be Announced

Abstract: We are going to read the new paper disproving Connes' embedding's conjecture. We start with an organization today.