In the 1980's, Greene defined hypergeometric functions over finite fields using Jacobi sums. The framework of his theory establishes that these functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gauss and Kummer. These functions have played important roles in the study of Apéry-style supercongruences, the Eichler-Selberg trace formula, Galois representations, and zeta-functions of arithmetic varieties. We study the value distribution (over large finite fields) of natural families of these functions, which turn out to encode the arithmetical statistical properties of families of elliptic curves and K3 surfaces. We use these results to obtain Sato-Tate type distributions. For the \(2F1\) functions, the limiting distribution is semicircular (i.e. \(SU(2)\)), whereas the distribution for the \(3F2\) functions is the Batman distribution for the traces of the real orthogonal group \(O_3\).
This is joint work with Hasan Saad and Neelam Saikia.

Contact the organizer for the Zoom link.

The idea that math and music are related to each other goes back to the ancient Greeks, and the relations found since then can get quite sophisticated. This talk will describe how the tasks of tuning instruments, playing instruments, hearing music, and (digitally) recording music are connected with a broad range of mathematics, including infinite series, differential equations, linear algebra, and number theory.


Note: Free refreshments. The talk starts at 5:45.

The Jacobian variety, named after 19th century mathematician Carl Gustav Jacobi, constructs from every algebraic curve a so-called Abelian variety, roughly speaking a manifold that is also an Abelian group. These Abelian varieties can be used to attack elliptic curve cryptosystems (ECE) that are used in every day electronic communication. Therefore, efficient algorithms for performing the group law in the Jacobian varieties of other curves, in particular so-called hyperelliptic curves, are important as they can break ECE. In this talk, I will give a basic introduction to the group law on hyperelliptic Jacobians. I will start with the basic examples of conics and elliptic curves, and then I will show how these ideas are generalized to a geometric interpretation of the group law on hyperelliptic Jacobians.

Join us in the Logic Colloquium for a talk by

Damian Szmuc (Buenos Aires / IIF-SADAF, CONICET):

"On sequent calculi for Classical Logic where Cut is admissible"

The aim of this talk is to examine the class of Gentzen-style sequent calculi where Cut is admissible but not derivable that prove all the (finite) inferences that are usually taken to characterize Classical Logic—conceived with conjunctively-read multiple premises and disjunctively-read multiple conclusions. We’ll do this starting from two different calculi, both counting with Identity and the Weakening rules in unrestricted form. First, we’ll start with the usual introduction rules and consider what expansions thereof are appropriate. Second, we’ll start with the usual elimination or inverted rules and consider what expansions thereof are appropriate. Expansions, in each case, may or may not consist of additional standard or non-standard introduction or elimination rules, as well as of restricted forms of Cut.

Please contact logic@uconn.edu for log-in information.

https://logic.uconn.edu/calendar/

Abstract: In this talk, we give a concise introduction to stochastic approximation. We begin with motivations and discussions. Next, the basic procedures will be presented followed by more general algorithms. Then we give a brief account of some aspects of convergence, rates of convergence, and asymptotic efficiency. Several application examples will be mentioned.

Speaker's short bio: George Yin is a Full Professor in the Department of Mathematics at the University of Connecticut. Previously, he was a Distinguished Professor at Wayne State University. His main research interests include stochastic control, optimization and approximation, and their applications in finance, biology, signal processing, communication network and more. He is the current editor-in-chief of the SIAM Journal on Control and Optimization. Please visit his website for more information: https://gyin.math.uconn.edu/index.html

We are going to talk about Fourier transform: continuous and discrete, fun and amazing; to discover (or rediscover) its properties for ourselves; and to demonstrate some pretty cool applications.

Join us for the Linguistics Colloquium with Kathryn Davidson (Harvard University)!

Details t.b.a.

https://scholar.harvard.edu/kathryndavidson

https://linguistics.uconn.edu/events/colloquium/

Linkages, networks of nearly rigid bars meeting at freely rotating joints, serve as a simple mathematical model underpinning a variety of physical systems, from molecules to disordered spring networks to origami. Recent advances in fabrication has driven a resurgence of interest in designing mechanical systems based on linkages that can serve as “mechanical metamaterials”, materials whose properties can be controlled by cleverly designing their structure. I will discuss recent work in our group on understanding the mechanics of origami and other metamaterials from the point of view of designing and controlling “singularities,” places where the configuration space of the mechanism fail to be well-behaved. This allows us to understand the onset of rigidity in under-coordinated spring networks and, ultimately, develop mechanisms that can can perform simple — and robust — logical operations.

TBA

An important question about minimal surfaces is the
uniqueness of their tangent cones. Of particular difficulty are
tangent cones with non-isolated singular sets, such as cylindrical
tangent cones of the form C x R. I will talk about a uniqueness result
for the tangent cone C x R where C is the Simons cone over S^3 x S^3,
extending a result of Leon Simon on such cylindrical tangent cones.
The main new difficulty is that the cone we consider is not
integrable, and so we need a version of the Lojasiewicz-Simon
inequality that can be used in the setting of tangent cones with
non-isolated
singularities.

Join us for the Logic Colloquium for a talk by Salvatore Florio, Stewart Shapiro, and Eric Snyder on definitional equivalence and plural logic.

All welcome.

Many advanced concepts in analysis can be quickly understood in the graph case. It is an interpretation of linear algebra from a certain functional analytic viewpoint, rather than the usual vectors-in-real-space viewpoint. It is especially helpful to keep this example in mind while taking analysis and stochastic processes courses. In this talk we will go over:

* Random walks on graphs, and the connection between random walks and analysis.
* Harmonic functions on discrete spaces, and the graph Laplacian.
* Direct and numerical approaches to solving these problems, namely,
** The linear algebra direct approach
** The energy-minimization direct approach (which is equivalent, and I will show why)
** The Monte Carlo method
** The method of relaxations
* Discrete-space Fourier analysis and Poisson's equation.

The talk is intended for first and second year graduate students as well as advanced undergraduates. No prior knowledge of Fourier analysis, PDEs, or probability theory is assumed.

Abstract: This paper proposes a dynamic credibility model for claim frequency that combines the advantages of Hawkes processes and generalized linear models (GLMs). The cumulative claim frequency of a policy is modeled by a self-excited Hawkes process with exponential decay, which captures the insurance practice in ratemaking that a recent claim should have a bigger impact on the credibility premium than an outdated claim. The proposed model yields a closed-form expression of the posterior expectation, and its calibrations are simple. The empirical results show that the proposed dynamic credibility model outperforms the standard Poisson GLM in both in-sample goodness-of-fit and out-of-sample prediction.

Speaker's short bio: Himchan is an assistant professor in the Department of Statistics & Actuarial Science at Simon Fraser University (Canada). He obtained his Ph.D. in 2020 under the supervision of Emil Valdez at the University of Connecticut. His current research interest is predictive modeling for ratemaking and reserving of property and casualty insurance. Please see his website for more information: https://ssauljin.github.io/hjeong/