Webex Meeting link:
https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m2597628acb83c077e45f759cf86c6489

Meeting number: 120 743 4364

Password: UConn

Host key:935694

Abstract: We study bilateral risk sharing under no aggregate uncertainty, where one agent has Expected-Utility (EU) preferences and the other agent has Rank-Dependent Utility (RDU) preferences with a general probability distortion function. We impose exogenous constraints on the risk exposure for both agents, and we allow for any type or level of belief heterogeneity. We show that Pareto-optimal risk-sharing contracts can be obtained via a constrained utility maximization of one agent, under a participation constraint of the other agent. This allows us to give an explicit characterization of optimal risk-sharing contracts. In particular, we show that an optimal contract is a monotone function of the likelihood ratio, where the latter is obtained from Lebesgue’s Decomposition Theorem. Moreover, unlike in the case where both agents have EU preferences, common beliefs might still lead to a risk-sharing situation in which betting is Pareto-improving; and betting might not always be Pareto-improving when beliefs are divergent. We also show that if agents disagree about likelihoods but not about zero-probability events, then Pareto-optimal allocations are deterministic (no-betting allocations), as long as the counterparty’s level of probabilistic risk-aversion exceeds the level of belief heterogeneity between the agents. Finally, we examine the case in which both agents are RDU-maximizers, and we characterize Pareto-optima. (This is joint work with Tim J. Boonen).

Speaker's bio: Dr. Ghossoub is currently an Assistant Professor at the Department of Statistics and Actuarial Science, University of Waterloo (Canada).

We describe the crystal structure on generic minuscule modules for the preprojective algebra of a simply-laced quiver in terms of the so-called glass bead game. This description is a consequence of joint work in progress with B. Elek, T. Libman, J. Kamnitzer, C. Morton-Ferguson. Time permitting, we discuss a geometric interpretation in type A.

Please contact the organizer for the WebEx link.

This talk will give a brief history of some classical encryption techniques, and how to defeat them.




Note: Join the meeting at https://uconnvtc.webex.com/meet/mathclub

Speaker: James Norris
(University of Cambridge)

Title: The master field on the sphere

Abstract: The Yang-Mills measure is a natural probabiity distribution on G-connections over
a given surface S, where G is a given Lie group. When S is the 2-sphere, this is
strongly related to the Brownian bridge in the group G. In this talk I will describe
the high-dimensional (large N) limit of the Yang-Mills measure over the 2-sphere when the group
is that of NxN unitary matrices. This makes rigorous some earlier work in the physics literature
where the limit object is called the master field on the sphere.

The talk will assume no knowledge of connections or the Yang-Mills measure.

This is joint work with Antoine Dahlqvist.

The heat equation and the wave equation are
two classical and important evolution equations,
which have been widely studied in various settings.
In this talk, I will consider them on non-compact symmetric spaces,
which include in particular hyperbolic spaces.
I will try to give the state of the art in this subject
and I will emphasize some features showing that
the large scale behavior in negative curvature may be different
and actually better compared to the Euclidean case.

The standard way to write down real numbers explicitly is with decimal expansions. Continued fractions are a different way of describing real numbers. They are far better than decimals at revealing the "best" rational approximations to a number. Areas of math where continued fractions appear include coding theory, cluster algebras, dynamical systems, knot theory, hyperbolic geometry, and number theory.

In this talk we will see what continued fractions are as well as some of their properties and applications.


https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m86369e51cc4cbf4727aa0462e6ae7280

Speaker: Xin Dong (UConn)

Title: Rigidity theorems by the Bergman kernel and logarithmic capacity

Abstract:
In light of the Suita conjecture, we explore various rigidity phenomena concerning the Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance and volume. This is a joint work with Yuan Zhang.

Meeting link:

https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=ma3888f4704b6dba433bdc49ce6879030

Meeting number: 120 375 7805

Password: 1109

The bicharacter twisted tensor product of graded algebras is an interesting source of algebras, often producing especially computable examples, such as the quantum complete intersections, and certain skew group rings.

I will spend some time introducing Hochschild Cohomology, then I will explain how to compute the Hochschild cohomology of a twisted tensor product in terms of the Hochschild cohomology of the two component algebras.

This description generalises a result of Bergh and Oppermann. I'll try to give lots of examples, showing how this can be used to give simple calculations of Hochschild cohomology in cases where the computations were previous quite complicated. In particular this gives a short, intuitive calculation for Buchweitz-Green-Madsen-Solberg's example of an algebra with infinite global dimension but bounded Hochschild cohomology.

Please contact the organizer for the WebEx link.

The math club will host a panel discussion on undergraduate mathematics research opportunities. This panelists will include both faculty and students. They will discuss what the research process is like and how to become involved in mathematics research as an undergraduate.


Note: Join the meeting at https://uconnvtc.webex.com/meet/mathclub

The characters of the general linear group are symmetric functions. In fact, the irreducible characters are found by evaluating Schur polynomials at eigenvalues of matrices. In this talk I will discuss bases of ring of symmetric functions that evaluate to characters of the symmetric group when evaluated at roots of unity. I will discuss how these basis relate to two major outstanding open problems in algebraic combinatorics: the restriction problem and the Kronecker problem. The main combinatorial objects in this talk are tableaux filled with multisets.

This is joint work with Mike Zabrocki.

Functional integrals form the basis of quantum field theory, and lead to physical predictions that have been confirmed to remarkable precision. Attempts to make them better defined mathematically have also led to novel insights, conjectures and results in mathematics. I will discuss some examples, and also some open problems, coming from the physics side.

Join us in the online Logic Colloquium for a talk by Sandra Villata (UConn Departments of Linguistics and Psychological Science) on

"Intermediate grammaticality"

Formal theories of grammar and traditional sentence processing models start from the assumption that the grammar is a system of rules. In such a system, only binary outcomes are generated: a sentence is well-formed if it follows the rules of the grammar and ill-formed otherwise. This dichotomous grammatical system faces a critical challenge, namely accounting for the intermediate/gradient modulations observable in experimental measures (e.g., sentences receive gradient acceptability judgments, speakers report a gradient ability to comprehend sentences that deviate from idealized grammatical forms, and various online sentence processing measures yield gradient effects). This challenge is traditionally met by accounting for gradient effects in terms of extra-grammatical factors (e.g., working memory limitations, reanalysis, semantics), which intervene after the syntactic module generates its output. As a test case, in this talk I will focus on a specific kind of violation that is at the core of the linguistic investigation: islands, a family of encapsulated syntactic domains that seem to prohibit the establishment of syntactic dependencies inside of them (Ross 1967). Islands are interesting because, although most linguistic theories treat them as fully ungrammatical and uninterpretable, I will present experimental evidence revealing gradient patterns of acceptability and evidence that some island violations are interpretable. To account for these gradient data, in this talk I explore the consequences of assuming a more flexible rule-based system, where sentential elements can be coerced, under specific circumstances, to play a role that does not fully fit them. In this system, unlike traditional ones, structure formation is forced even under sub-optimal circumstances, which generates semi-grammatical structures in a continuous grammar.

Please contact Marcus Rossberg for log-in information.

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

This talk, which is a continuation of last week's, will show connections between continued fractions and other topics such as hyperbolic geometry and orthogonal polynomials.


https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m86369e51cc4cbf4727aa0462e6ae7280

Meeting link:
https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=mdca7b0967a30f3521f7df43b6c5b9891

Meeting number: 120 126 2604
Password: Uconn

Abstract: Recently, an increasing number of researchers and practitioners from different disciplines have analyzed cyber risk and different approaches to understanding and quantifying this new type of risk have been proposed. Still, an agreed-upon framework and a unified quantitative understanding of cyber risk and its underlying drivers is still at its infancy. Due to the particular properties of cyber risk such as lack of historical data, interdependence of risk and IT security and difficult impact determination (e.g. intangible losses due to data loss, business interruption or reputational damages), classical actuarial approaches face numerous challenges.

The present work scrutinizes technical, legal, financial, and actuarial aspects of cyber risk as a basis to propose a new approach for modelling cyber risk using marked point processes.

The resulting model is able to include the influence of key covariables, required to model frequency and severity of cyber claims, and the dynamic nature of cyber risk, while also capturing accumulation risk in a realistic way. It takes into account different types of cyber attacks (classified according to their compromise of defined information security goals) and their causes, namely malicious untargeted and targeted attacks as well as human and technical failure.

The model is studied with respect to its statistical properties and applied to the pricing of cyber insurance and risk measurement. The results are illustrated in a simulation study, with particular focus on the importance of considering accumulation risk and prudent policy design in the cyber context.

The presentation concludes with an outlook of opportunities for future research in the cyber risk and insurance domain, such as the design of cyber insurance products transcending mere risk transfer.

Speaker's bio: Gabriela is a Ph.D. student at the ERGO Center of Excellence in Insurance, the group of Mathematical Finance, Technical University of Munich. Her supervisor is Prof. Matthias Scherer.

The 3D quasi-geostrophic equation is a model used in climatology to model the evolution of the atmosphere for small Rossby numbers. The surface quasi-geostrophic equation (SQG) is a special case where the atmosphere above the earth is at rest. The evolution then depends only on the boundary condition, and can be reduced to a 2D model. In this talk, we consider the full 3D QG and describe recent progress on the questions of both non-uniqueness of weak solutions and existence of strong and weak solutions on cylindrical domains, including a resolution of the appropriately formulated Onsager conjecture for 3D QG. In each setting, the boundary conditions will play a crucial role.

Dynamical algebraic combinatorics explores (often cyclic) group actions on sets of combinatorial objects. In many cases these actions can be extended to the piecewise-linear realm of polytopes, then further lifted to the
birational realm via detropicalization. Unexpectedly, many nice properties of the combinatorial actions such as
low-order periodicity or homomesy (statistics with constant average over each orbit) can also be lifted to these settings. Some even persist to the realm of "birational functions" in noncommutating variables.

Please contact the organizer for the WebEx link.

In this talk, we will consider whether a machine can be trained to recognize patterns in mathematics. As examples, some basic concepts in number theory will be tested through machine-learning tools. At the beginning of the talk, I will briefly mention what kind of mathematics is needed for machine-learning and this talk may serve as a preview of Math 3094, which will be offered in Spring 2021.

Note: Join the meeting at https://uconnvtc.webex.com/meet/mathclub

Weekly colloquium with invited external speakers

Creating math classrooms and communities where PEER students thrive

Thursday, November 19, 3:30-4:30 pm

Presenters: Dr. Carrie Diaz Eaton, Digital and Computational Studies, Bates College
Chair, MAA Committee for Minority Participation in Mathematics
&
Dr. Adriana Salerno Domínguez, Chair, Mathematics, Bates College

Abstract: PEER, a term coined by HHMI Senior Director of Education, David Asai, refers to “Persons Excluded because of Ethnicity or Race.” The profession of mathematics, and STEM more broadly, has historically excluded certain persons from access and/or success, and most of those barriers remain today. In this workshop, we will establish some common language and definitions around equity and inclusion, examine the axomatic neutrality and/or bias of mathematics, and then explore specific examples for classroom and department practice. The goal of this conversation is to provide a launching platform for future departmental conversations, to suggest ideas of easy-to-implement actions that better support PEER students, and to stimulate ideas for future professional development and reflection.

https://math.uconn.edu/wp-content/uploads/sites/2511/2019/09/Equity-Nov-2020-abstract.pdf

NOTE: If you are not in the Math Department and would like to attend, please send a quick email to erin.rizzie@uconn.edu so that we can let you in from the waiting room.

We consider quantum chains whose Hamiltonians are perturbations, by interactions of short range, of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. For interactions that are form-bounded w.r.t. the on-site Hamiltonian
terms, we prove that the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain, for small values of a coupling constant. Under the same hypothesis, we prove that the ground state energy is analytic for values of the coupling constant in a fixed interval, uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain, that can be also applied to complex Hamiltonians obtained by considering complex values of the coupling constant. We can treat fermions and bosons on the same footing, and our technique does not face a large field problem, even though bosons are involved, in contrast to most approaches.

Abstract: We show that the Fourier transform of the Patterson-Sullivan measure of a Kleinian Schottky subgroup of $\operatorname{PSL}_2(\mathbb{C})$ enjoys polynomial decay. This generalizes a result of Bourgain-Dyatalov for convex-cocompact Fuchsian groups and uses the decay of exponential sums based on Bourgain-Gamburd sum-product estimate on $\mathbb{C}$. These bounds on exponential sums require a delicate non-concentration hypothesis, which is proved using some representation theory and regularity estimates for stationary measures of certain random walks on linear groups. This is joint work with Jialun Li and Frédéric Naud.

Join Zoom Meeting
https://zoom.us/j/93189118174?pwd=SW1USXVqOHpyaDFlZ3VRdHBPMmJNUT09

Meeting ID: 931 8911 8174

Passcode: AP

Abstract: We prove a classical result in geometry. Consider a curve Q of equation f(x,y)=0, where f is a polynomial of degree 4 in x and y. For example x^4+x^4-1=0. We prove that at least when working over complex numbers, there are exactly 28 lines that are tangent to Q simultaneously at 2 distinct points.

https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m86369e51cc4cbf4727aa0462e6ae7280

Weekly colloquium with invited external speakers