The Department of Mathematics is committed to producing world-class research, providing high quality undergraduate, graduate and professional programs of study that attract the best students, and to attending to the mathematical needs of the University and the community.

Henry R. Monteith Building, home of the Department of Mathematics.

- Srinivasa Varadhan (NYU Courant) Delivers Distinguished Lecture on “The The Polaron Measure”
- Liang Xiao awarded NSF CAREER grant
- “Complex Math Visuals are This Researcher’s Handiwork” — work of David Nichols, graduate student in mathematics, profiled by UConn Today
- Students present at 2018 Spring Frontiers Exhibition
- Actuarial program named Center for Actuarial Excellence for eighth consecutive year
- Graduate student receives CETL Outstanding Teaching Award
- Damir Dzhafarov spotlighted by the Connecticut Institute for the Brain and Cognitive Science
- Lan-Hsuan Huang Huang and Damin Wu receive appointments at IAS; Prof. Huang awarded Simons and von Neumann Fellowships
- “Very Special Snowflakes” — the work of Vyron Vellis (Assistant Research Professor in Math) featured in UConn Today
- Talitha M. Washington, first African American to receive math PhD from UConn, writes about journey from student to math professor, in the AMS Notices

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Actuarial Science Seminar

Title: Ratemaking application of Bayesian LASSO with conjugate hyperprior

Speaker: Emiliano Valdez (University of Connecticut)

Time: Monday, October 22, 2018 at 11:00 am

Place: MONT 214Abstract: The generalized linear model (GLM) is a well developed statistical model widely used in actuarial practice for insurance ratemaking, risk classification, and even reserving. Recently, there has been an explosion of data mining techniques to refine statistical models for better variable selection procedure and for improved prediction accuracy. Such techniques include the increased interest in regularization techniques, or penalized likelihood, to achieve these goals. In this paper, we explore the idea of Least Absolute Selection and Shrinkage Operator (LASSO) in a Bayesian framework within a dependent frequency-severity model as a refinement to the dependent GLM developed by Garrido et al. (2016). The LASSO technique is a penalized least squares procedure developed by Tibshirani (1996) and is extended to a Bayesian interpretation framework by Park and Casella (2008). We show that a new penalty function emerges if we further theoretically extend the Bayesian LASSO using conjugate hyperprior distributional assumptions. While this result has the ease of implementation for variable selection and prediction, we recognize that the use of least squares has been poorly viewed in insurance ratemaking. Instead however, we modify the setting to a penalized dependent GLM within this extended Bayesian LASSO framework. Within such framework, the regression estimates are derived by optimizing a penalized likelihood assuming a hyperprior distribution for the $L_1$ penalty parameter $\lambda$. This has the advantage of avoiding the use of ex-post cross-validation to determine the optimal $\lambda$. We calibrated our proposed model using an auto insurance dataset from a Singapore insurance company where we have observed claim counts and amounts from a portfolio of policyholders. This is joint work with Himchan Jeong of the University of Connecticut.

Title: The Ricci flow under almost non-negative curvature conditions 2

Speaker: Gunhee Cho

Time: Monday, October 22, 2018 at 5:00 pm

Place: MONT313 Abstract: This talk is aimed to understand the Theorem 2 in the paper https://arxiv.org/pdf/1707.03002.pdf. Theorem 2 is about five different types of curvature operator conditions including the non-negative curvature operator condition of the Theorem 1. Two main ingredients would be considered, the first one is how to control the non-linear term of the evolution equation of the curvature operator nicely for each curvature conditions, and the other is to establish the Gaussian upper bound of the heat kernel associated with the heat equation coupled with the Ricci flow.

Title: Converse theorems and the grand simplicity hypothesis

Speaker: Thomas Oliver (Oxford University)

Faculty Sponsor: Kyu-Hwan Lee

Time: Wednesday, October 24, 2018 at 11:15 am

Place: MONT 313Abstract: In this talk, we will be interested in two manifestations of the so-called grand simplicity hypothesis for the zeros of automorphic L-functions. Specifically, we will see how the simplicity and independence of zeros can be related to the characterisation of automorphic L-functions in terms of analytic data. We will state two converse theorems in low degree and outline their proof in terms of the asymptotics of hypergeometric functions.

Title: Chebyshev Polynomials

Speaker: Maxim Derevyagin (University of Connecticut)

Time: Wednesday, October 24, 2018 at 5:45 pm

Place: MONT 226Abstract: Chebyshev polynomials were introduced by the Russian mathematician P. L. Chebyshev in 1854 and they play a prominent role in various branches of mathematics, such as differential equations and numerical analysis. In this talk we will discuss the underlying fundamental problem in approximation theory and define Chebyshev polynomials the way it was done by Chebyshev himself. Then we will obtain an equation satisfied by Chebyshev polynomials that is a polynomial analogue of Pell's equation in number theory. Finally, we will derive a couple of explicit formulas for Chebyshev polynomials. Comments: Free pizza and drinks!

Title: A new approach to prove tightness based on Malliavin calculus

Speaker: David Nualart

Time: Thursday, October 25, 2018 at 4:00 pm

Place: MONT 214Abstract: In this talk we will first present the basic elements of the stochastic calculus of variations in the Wiener space. As an application we will establish a functional version of the central limit theorem for Gaussian stationary sequences, established by Breuer and Major. The corresponding tightness property will be derived using the continuity of the divergence operator proved by Meyer.

Title: TBA

Speaker: Jungang Li

Time: Friday, October 26, 2018 at 12:20 pm

Place: MONT 214

Title: Use of genomic recursions in single-step genomic best linear unbiased predictor (BLUP) with a large number of genotypes

Seminar Framework : SIAM Event

Speaker: Breno Fragomeni (Department of Animal Science)

Time: Friday, October 26, 2018 at 2:30 pm

Place: MONT 225Abstract: In order to run genetic evaluations, it is necessary to solve the mixed model system of equations, which is dependent on the inverse of the genetic relationship matrix. The matrix is sparse, and a simple recursive algorithm can be used to build the inverse directly. For inclusion of genomic information on those evaluations, the main difference is on the relationship matrix, which now is dense and has to be explicitly inverted. With the increasing number of genotyped animals it became infeasible to inverted that matrix. A new algorithm called `algorithm for proven and young animals' (APY) was developed to avoid direct inversion of the genomic relationship matrix. This algorithm implements genomic recursions on a subset of `proven' animals. Only a subset matrix for animals treated as `proven' needs to be inverted, and the extra costs of adding animals treated as `young' are linear.

Title: A geometric realization of representations of posets of width 2 as diagonals of polygons

Speaker: Robinson Julian Serna Vanegas (Universidad Nacional de Colombia)

Time: Friday, October 26, 2018 at 3:00 pm

Place: MONT 313

Title: Non-commutative disintegration

Speaker: Arthur Parzygnat (University of Connecticut)

Time: Friday, October 26, 2018 at 3:30 pm

Place: MONT 414Abstract: The notion of a disintegration of positive measures can be formulated diagrammatically in a category of measure spaces and transition kernels. Combining this with the functor relating transition kernels to positive operators on C*-algebras, a notion of non-commutative disintegration can be made for states on C*-algebras. While a certain degree of uniqueness holds as in the classical measure-theoretic case, existence of such disintegrations is not guaranteed even on finite-dimensional matrix algebras. Such disintegrations are closely related to reversible quantum channels in quantum information theory and non-commutative conditional probabilities. This is joint work with Benjamin P. Russo (Farmingdale State College SUNY).