Posted August 21, 2024
Last modified August 28, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Rahul Kumar, Pennsylvania State University
Period function from Ramanujan's Lost Notebook and Kronecker limit formulas
The Lost Notebook of Ramanujan contains a number of beautiful formulas, one of which can be found on page 220. It involves an interesting function, which we denote as $\mathcal{F}_1(x)$. In this talk, we show that $\mathcal{F}_1(x)$ belongs to the category of period functions as it satisfies the period relations of Maass forms in the sense of Lewis and Zagier. Hence, we refer to $\mathcal{F}_1(x)$ as the Ramanujan period function. The Kronecker limit formulas are concerned with the constant term in the Laurent series expansion of certain Dirichlet series at $s=1$. We will also discuss that $\mathcal{F}_1(x)$ naturally appears in a Kronecker limit-type formula of a certain zeta function.
Posted August 14, 2024
Last modified September 5, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Heidi Goodson, Brooklyn College, CUNY
An Exploration of Sato-Tate Groups of Curves
The focus of this talk is on families of curves and their associated Sato-Tate groups -- compact groups predicted to determine the limiting distributions of coefficients of the normalized L-polynomials of the curves. Complete classifications of Sato-Tate groups for abelian varieties in low dimension have been given in recent years, but there are obstacles to providing classifications in higher dimension. In this talk I will give an overview of the techniques we can use for some nice families of curves and discuss the ways in which these techniques fall apart when there are degeneracies in the algebraic structure of the associated Jacobian varieties. I will include examples throughout the talk in order to make the results more concrete to those new to this area of research.
Posted August 21, 2024
Last modified August 29, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Wanlin Li, Washington University in St. Louis
TBA
Posted August 14, 2024
Algebra and Number Theory Seminar Questions or comments?
Brian Grove, LSU
TBA
Posted August 21, 2024
Last modified August 29, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Brett Tangedal, University of North Carolina, Greensboro
TBA
Posted August 29, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Jiuya Wang, University of Georgia
TBA