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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Algebra Seminar

Title: Polynomials of high strength

Speaker: Steven Sam (UCSD)

Faculty Sponsor: Jerzy Weyman

Time: Wednesday, September 19, 2018 at 11:15 am

Place: MONT 313Abstract: A polynomial has high strength if it cannot be decomposed into a small sum of a product of lower degree polynomials. Inspired by a conjecture of Stillman, Ananyan and Hochster recently proved that polynomials of a fixed degree and sufficiently high strength acquire very good properties mimicking algebraically independent variables. I will make this precise and outline one way this can be proven. This is based on joint work with Daniel Erman and Andrew Snowden.

Title: The eigenvalue problem of the Dirichlet to Neumann operator 3

Speaker: Gunhee Cho (University of Connecticut)

Time: Wednesday, September 19, 2018 at 2:30 pm

Place: MONT 214Abstract: We will see how the Dirichlet to Neumann operator becomes the self-adjoint operator. If time allows, we will see the essential part of the proof of the gap estimate of the Dirichlet-Laplacian to investigate the unknown direction of D-N map.

Title: Using Linear Algebra in Data Science

Speaker: Matt Lamoureux (Travelers)

Time: Wednesday, September 19, 2018 at 5:45 pm

Place: MONT 226Abstract: When building statistical models, we are often interested in dimension reduction: the idea of boiling down many, often correlated, predictors into a few uncorrelated ones. We will discuss one method of doing this, called principal component analysis, which is an application of eigenvalues and matrix decompositions. Some previous exposure to what eigenvalues are would be helpful, although the talk will include a review of the concept.Comments: Free pizza and drinks!

Title: Nonlinear PDEs, random walk, Gaussian processes, random matrices and heat kernels

Speaker: Ofer Zeitouni (NYU Courant)

Time: Thursday, September 20, 2018 at 4:00 pm

Place: SCHN 151Abstract: The solution to the one dimensional Fisher-KPP equation (1937) $u_t=\frac{1}{2} u_{xx} u(1-u)$ starting from a step initial condition, converges after centering by $2t-\frac32 \log t$ to a traveling wave. The logarithmic correction term, and in particular the coefficient $3/2$, was computed by Bramson (1978), through a connection with the maximum of branching Brownian motion. Recently, this computation proved crucial in the solution of a variety of problems: the law of the maximum of the critical Gaussian free field, the cover time of the 2-sphere by Brownian sausage, the maxima of the characteristic polynomials of random matrices, and even the values of the Riemann zeta function on the critical line. These problems all share a hidden logarithmic (i.e., multiscale) correlation. In the talk I will describe these development and will emphasize the common philosophy in studying these very different models. If time permits, I will discuss recent results concerning heat kernel estimates for the so-called Liouville quantum gravity.

Title: The Gaussian Limit for High Dimensional Spherical Means

Speaker: Amy Peterson

Time: Friday, September 21, 2018 at 12:20 pm

Place: MONT 214Abstract: We will discuss the Gaussian measure and spherical surface area measure. Then we will discuss how the limit of integrals along circular slices of a high dimensional sphere is a Gaussian integral on a corresponding affine subspace in infinite dimensions.

Title: The Traveling Salesman Theorem in Carnot groups

Speaker: Scott Zimmerman (University of Connecticut)

Time: Friday, September 21, 2018 at 1:30 pm

Place: MONT 313Abstract: Peter Jones proved his famous Traveling Salesman Theorem in the plane in 1990. His result classified those sets in the plane which are contained in a rectifiable curve via the boundedness of a certain Carleson integral. The methods introduced by Jones have seen applications in harmonic analysis and geometric measure theory, and his theorem has since been generalized to the setting of Hilbert spaces, the Heisenberg group, and the graph inverse limits of Cheeger and Kleiner. I will present recent work with V. Chousionis and S. Li in which we proved one direction of the Traveling Salesman Theorem for rectifiable curves in any Carnot group. A Carnot group is a type of nilpotent Lie group whose abelian members are precisely Euclidean spaces, and these groups have been the focus of much recent study in geometric measure theory. As an application, I will show that this theorem may be used to prove uniform boundedness of the singular integral operator associated with a certain non-negative kernel on any set contained in a rectifiable curve.

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Speaker: Jerzy Weyman

Time: Friday, September 21, 2018 at 3:00 pm

Place: MONT 313

Title: Strichartz estimates on compact symmetric spaces I

Speaker: Yunfeng Zhang (University of Connecticut)

Time: Friday, September 21, 2018 at 3:30 pm

Place: MONT 414Abstract: In the first talk, I will introduce the problems of Fourier restriction and Strichartz estimates. In the second talk, I will review the fundamental tools of harmonic analysis on compact symmetric spaces. In the final talk, I will sketch a proof of some Strichartz estimates on compact Lie groups.