Colloquium Series 2026-2027

This colloquium is sponsored by the Department of Mathematics & Statistics
For more information, contact the colloquium chair, Dr. Michael Kerckhove.

Upcoming: 

Wednesday, September 23 at 12:00 pm in Jepson Hall 120

Speaker: Nicola Tarasca, Ph.D., Associate Professor, Department of Mathematics & Statistics, Virginia Commonwealth University

Title: Symmetries, Quotients, and Moduli Spaces

Abstract: Given a vector space with a group, or a Lie algebra, acting on it, linear algebra suggests a natural construction: the quotient of the space by the span of everything the action moves. This quotient is called the space of coinvariants. When the vector space is infinite-dimensional, and the symmetries come from geometry, the construction turns out to be surprisingly rich. Traditionally, the geometry feeding the symmetries has come from algebraic curves, that is, from compact Riemann surfaces. In this talk, I will describe a new setting in which curves are replaced by abelian varieties: higher-dimensional tori carrying some extra algebraic structure. I will explain how infinite-dimensional Lie algebras encode the ways a curve or an abelian variety can be deformed, and how the resulting spaces of coinvariants fit together into natural geometric objects over the moduli spaces, the spaces whose points parametrize the curves or abelian varieties themselves. The talk will be largely expository. No prior exposure to algebraic curves, abelian varieties, or Lie algebras will be assumed.

 

Past Events for 2026-2027: 

Monday, August 31 at 5:00 p.m.
Jepson Hall 120
Student Research Presentations in Mathematics

Pepe Sánchez-Menchén
National Research Experiences for Undergraduates (REU)
 
Title: On Coefficients of the Quantum sl3 Invariant
Abstract: The sl3 link polynomial is a higher rank relative of the Jonespolynomial which can be studied entirely diagrammatically using Kuperberg’s web calculus. The invariant is known to detect whether a link is fibered and provides an obstruction to present positive links as positive braids. Building on the work of Harper and Kalfagianni, we construct formulae for the fourth and fifth coefficients of the quantum sl3 link invariant on positive alternating links in terms of data read from the associated Seifert graph. Then, we give a characterization of the invariant on positive alternating fibered links in terms of elementary symmetric polynomials. We also formulate the Garside element (∆3 ∈ B3) in terms of elementary webs, and give a closed formula for the polynomial on positive 3-braids. We outline additional results and work in progress towards a characterization of the sl3 polynomial on all 3-braids.
 
Nicolai Benz, Olga Brzecka, Leah Buckley, Dav Guo, Beckett Rebele-Henry, Xiaogeng Tan, Zihan Wu, and Bianca Yu
UR Summer Fellowships 
Mentor: Dr. Jim Davis
 
Title: Search for Denniston Partial Difference Sets in Groups of Order 512
Abstract: Partial difference sets are equivalent to projective 2 weight codes and hence are useful in digital communication systems. We investigated questions for the Denniston family, and particularly in groups of order 512. We will give a gentle introduction for those unfamiliar with the topic and describe the progress we have made.