Most talks will be preceded by a "pretalk" meant for graduate students and postdocs, starting at 3:00pm and lasting about 30 minutes (inperson only, in the same room as the seminar). In any case there will be tea and cookies in the department common room (adjacent to the seminar room) at 3:30pm.
Don't forget to register for Math 209 if you are a UCSD graduate student. Continued department financial support for this seminar is contingent on maintaining sufficient enrollment.
The organizers strive to ensure that all participants in this seminar enjoy a welcoming environment, conducive to the free expression and exchange of ideas. In particular, the pretalks are meant to provide a safe space for junior researchers to ask questions of the speaker. All participants are expected to cooperate with this effort and encouraged to contact the organizers with any concerns.
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For previous quarters' schedules, click here.
October 2 
Organizational meeting 
October 16 
Jon Aycock (UC San Diego)
The Jacobian (or sandpile group) is an algebraic invariant of a graph that plays a similar role to the class group in classical number theory. There are multiple recent results controlling the sizes of these groups in Galois towers of graphs that mimic the classical results in Iwasawa theory, though the connection to the values of the Ihara zeta function often requires some adjustment. In this talk we will give a new way to view the Jacobian of a graph that more directly centers the edges of the graph, construct a module over the relevant Iwasawa algebra that nearly corresponds to the interpolated zeta function, and discuss where the discrepancy comes from. 
October 23 
Jennifer JohnsonLeung (University of Idaho)
The Euler product expression of the Dirichlet series of Fourier coefficients of an elliptic modular eigenform follows from a formal identity in the Hecke algebra for GL(2) with full level. In the case of Siegel modular forms of degree two with paramodular level, the situation is more delicate. In this talk, I will present two rationality results. The first concerns the Dirichlet series of radial Fourier coefficients for an eigenform of paramodular level divisible by the square of a prime. This result is an application of the theory of stable Klingen vectors (joint work with Brooks Roberts and Ralf Schmidt). While we are able to calculate the action of certain Hecke operators on eigenforms, the structure of the Hecke algebra of deep level is not known in general. However, in the case of prime level, there is a robust description of the local Hecke algebra which yields a rationality result for a formal power series of Hecke operators (joint work with Joshua Parker and Brooks Roberts). In both cases, we obtain the expected local Lfactor as the denominator of the rational function. 
October 30 
Chengyang Bao (UCLA)
Crystalline deformation rings play an important role in Kisin's proof of the FontaineMazur conjecture for GL2 in most cases. One crucial step in the proof is to prove the BreuilMezard conjecture on the HilbertSamuel multiplicity of the special fiber of the crystalline deformation ring. In pursuit of formulating a horizontal version of the BreuilMezard conjecture, we develop an algorithm to compute arbitrarily close approximations of crystalline deformation rings. Our approach, based on reverseengineering the TaylorWilesKisin patching method, aims to provide detailed insights into these rings and their structural properties, at least conjecturally. 
November 6 
Brandon Alberts (Eastern Michigan)
We will discuss an inductive approach to determining the asymptotic number of Gextensions of a number field with bounded discriminant, and outline the proof of Malle's conjecture in numerous new cases. This talk will include discussions of several examples demonstrating the method. 
November 13 
Chris Xu (UC San Diego)

November 20 
Linli Shi (Connecticut)
The Birch and SwinnertonDyer conjecture relates the leading coefficient of the Lfunction of an elliptic curve at its central critical point to global arithmetic invariants of the elliptic curve. Beilinsonâ€™s conjectures generalize the BSD conjecture to formulas for values of motivic Lfunctions at noncritical points. In this talk, I will relate motivic cohomology classes, with nontrivial coefficients, of Picard modular surfaces to a noncritical value of the motivic Lfunction of certain automorphic representations of the group GU(2,1). 
December 4 
Yu Fu (Caltech)
