College of Liberal Arts and Sciences

# Department of Mathematics

## All Seminars

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Actuarial Science Seminar

Title: Upper Bounds for Strictly Concave Distortion Risk Measures on Moment Spaces
Speaker: Steven Vanduffel (Vrije Universiteit Brussel)
Time: Monday, November 12, 2018 at 11:00 am
Place: MONT 214Abstract: The study of worst-case scenarios for risk measures (e.g., Value-at-Risk) when the underlying risk (or portfolio of risks) is not completely specified is a central topic in the literature on robust risk measurement. In this paper, we tackle the open problem of deriving upper bounds for strictly concave distortion risk measures on moment spaces. Building on early results of Rustagi (1957,1976), we show that in general this problem can be reduced to a parametric optimization problem. We completely specify the sharp upper bound (and corresponding maximizing distribution function) when the first moment and any other higher moment are fixed. Specifically, in the case of a fixed mean and variance, we generalize the Cantelli bound for (Tail) Value-at-Risk in that we express the sharp upper bound for a strictly concave distorted expectation as a weighted sum of the mean and standard deviation. This is a joint work with Dries Cornilly (VUB) and Luger Ruschendorf (University of Freiburg).

PDE and Differential Geometry Seminar

Title: A Sharp Divergence Theorem with Non-Tangential Pointwise Traces
Speaker: Irina Mitrea (Temple University)
Time: Monday, November 12, 2018 at 2:30 pm
Place: MONT 214Abstract: The Integration by Parts Formula, which is equivalent with the Divergence Theorem, is one of the most basic tools in Analysis. Originating in the works of Gauss, Ostrogradsky, and Stokes, the search for an optimal version of this fundamental result continues through this day and these efforts have been the driving force in shaping up entire subbranches of mathematics, like Geometric Measure Theory. In this talk I will review some of these developments (starting from elementary considerations to more sophisticated versions) and I will discuss recents result regarding a sharp divergence theorem with non-tangential traces.

Connecticut Logic Seminar

Title: A transdisciplinary aspect of infinite time Turing machines
Speaker: Sabrina Ouazzani (Ecole Polytechnique)
Time: Monday, November 12, 2018 at 4:45 pm
Place: MONT 214Abstract: After recalling the main concepts involved in infinitary computations, we will present some results about extending ITTMs to other fiels of Computer Science and Mathematics. We will explain some properties of the gaps in the ordinal computation times as well as some applications of the model such like its interaction with differential equations.

Geometric Flows

Title: Gaussian bounds on the heat kernel in Ricci flow with bounded scalar curvature
Speaker: Hyun Chul Jang (University of Connecticut)
Time: Monday, November 12, 2018 at 5:00 pm
Place: MONT 245 Abstract: This talk will continue the results about Ricci flow with bounded scalar curvature. I will present about the Gaussian bounds on the heat kernel: Assuming a global bound on the scalar curvature, it is obtained that the heat kernel K(x,t;y,s) is bounded from above and below by an expression consisting of the Gaussian function. It will cover some part of Section 4 and Section 5 of the same paper from the previous talk.

Algebra Seminar

Title: Equations for point configurations to lie on a rational normal curve
Speaker: Luca Schaffler (Univeriversity of Massachusetts Amherst )
Time: Wednesday, November 14, 2018 at 11:15 am
Place: MONT 313Abstract: Let $V_{d,n}\subseteq(\mathbb{P}^d)^n$ be the Zariski closure of the set of $n$-tuples of points lying on a rational normal curve. The variety $V_{d,n}$ was introduced because it provides interesting birational models of $\overline{M}_{0,n}$: namely, the GIT quotients $V_{d,n}/ /SL_{d+1}$. In this talk our goal is to find the defining equations of $V_{d,n}$. In the case $d=2$ we have a complete answer. For twisted cubics, we use the Gale transform to find equations defining $V_{3,n}$ union the locus of degenerate point configurations. We prove a similar result for $d\geq 4$ and $n=d+4$. This is joint work with Alessio Caminata, Noah Giansiracusa, and Han-Bom Moon.

Mathematical Physics Seminar

Title: Direct Integrals V
Speaker: Arthur Parzygnat (University of Connecticut)
Time: Wednesday, November 14, 2018 at 2:30 pm
Place: MONT 214Abstract: In the previous talk, we described (a) constructions on families and direct integrals and (b) decomposable linear operators between direct integrals. In this talk, we will provide many explicit examples. Most of this talk should be accessible to a wider audience.Comments: If anyone is interested in giving a talk at this seminar, please contact Arthur at arthur.parzygnat@uconn.edu. Graduate students are particularly encouraged to give talks.

UConn Math Club

Title: Morse Theory: Describing Space Using Critical Points
Speaker: Gianmarco Molino (University of Connecticut)
Time: Wednesday, November 14, 2018 at 5:45 pm
Place: MONT 226Abstract: Second derivatives are useful in single-variable calculus and multivariable calculus, since they help us determine where functions have local maxima and minima. This talk will explain a more subtle application of second derivatives, called Morse theory, that is used to understand the topology of surfaces and higher-dimensional spaces.Comments: Free pizza and drinks!

Colloquium

Title: Mean Field Games with finite states in the weak formulation, and application to contract theory.
Speaker: Rene Carmona
Time: Thursday, November 15, 2018 at 4:00 pm
Place: MONT 214Abstract: Models for Mean Field Games (MFGs) with finite state spaces are typically introduced using controlled Markov chains and studied through the solutions of Hamilton-Jacobi-Belman and Fokker-Planck equations. We introduce the weak formulation based on change of measure techniques for stochastic integral equations and prove existence and uniqueness in this setting. We then apply these results to a contract theory problem in which a principal faces a field of agents interacting in a mean field manner. We reduce the problem to the optimal control of dynamics of the McKean-Vlasov type, and we solve this problem explicitly in a special case reminiscent of the linear - quadratic mean field game models. We conclude with a numerical example of epidemic containment.

S.I.G.M.A. Seminar

Title: An Introduction to Heisenberg Type Groups
Speaker: Joshua Flynn (University of Connecticut)
Time: Friday, November 16, 2018 at 12:20 pm
Place: MONT 214

Analysis and Probability Seminar

Title: Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
Speaker: David Herzog (Iowa State University)
Time: Friday, November 16, 2018 at 1:30 pm
Place: MONT 313Abstract: We discuss Langevin dynamics of N particles on R^d interacting through a singular repulsive potential, e.g. the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the result turns on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions.