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, November 11 at noon in Jepson Hall 120
Honors Thesis Presentation: Chen Peng, W '26, Bachelor of Science in Mathematics
Title: Assessing the Roles of Joint Prior Choice and Population Generation Algorithms in Virtual Clinical Trials
Abstract: Virtual clinical trials use mathematical models to study treatment outcomes across heterogeneous populations, but their results may depend on how those populations are generated. This thesis applies an existing mathematical model of oncolytic virotherapy to construct and compare plausible populations for VCTs. The tumor growth rate and viral infection rate were estimated from control and treated data, and individual fits were used to define parameter ranges for plausible population generation. Four population generation conditions were compared: accept-or-reject and accept-or-perturb, each under Normal and Uniform priors. The resulting populations all satisfied the same feasibility criterion, but their parameter distributions differed. Prior choice had a stronger effect under accept-or-reject, while accept-or-perturb reduced, but did not eliminate, this dependence. These populations were then used in VCTs with virus administered on Days 0, 2, and 4 while the dose per injection was varied. Across all four conditions, increasing dose shifted outcomes from tumor growth toward tumor shrinkage. Overall, the results show that the choice of prior distribution and population generation method can influence quantitative VCT outcomes, although the overall dose response pattern remained consistent across the four conditions.
Wednesday, March 17 at noon, location TBD, and partnering with our colleagues in the Department of Physics
Speaker: Solomon Quinn, R '17 (MATH & PHYS); Ph.D. in computational and applied mathematics, University of Chicago; Flatiron Research Fellow, Center for Computational Mathematics, Simons Foundation, New York.
Title: TBA
Abstract: TBA
Past Events for 2026-2027:
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.
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.