Talks

A famous question of Greenberg (which was also formulated independently by Coleman) asks the following:
Suppose p is a prime and f is a p-ordinary modular eigenform of weight at least 2. If the restriction of the p-adic Galois representation attached to f to the local Galois group at p splits into a direct sum of two characters, then does f have complex multiplication?
In this talk, we will explore an analogue of this question in the setting of Siegel modular forms of genus 2.
This talk is based on a joint work in progress with Bharathwaj Palvannan.

We discuss new applications of some "zeta elements" which form Kolyvagin systems. A portion of this talk originated from discussions with Minhyong Kim, and another portion is joint work in progress with Gyujin Oh.

I will introduce via examples, and then state and prove generalizations of Chen's cross ratios theorem on the special values of Rankin-Selberg L-functions for GL(n) x GL(m). I will then discuss applications of this theorem to Deligne's conjecture on the special values of various automorphic L-functions. This talk is a report of an ongoing collaboration with Harald Grobner, Michael Harris, and Jie Lin.

The original spinfoam amplitude, Ponzano-Regge, has two properties in seeming contradiction: (1.) It can be written as an integral of a product of Dirac delta functions imposing that holonomies be exactly flat, and (2.) In its original sum-over-spins form, its leading order large spin asymptotics consist in Regge calculus, modified to include an additional local discrete orientation variable for each tetrahedron, which, when fixed inhomogeneously, leads to critical point equations for the edge lengths which do not necessarily imply flatness, but allow spikes. Of course, this apparent contradiction between flatness and spikes appears only for triangulations with bubbles, for which both of these formulations of the model are divergent and ill-defined anyway, and this may be the resolution of the paradox. However, we explore the possibility of another resolution of this paradox which may also have relevance for the semiclassical regime of 4D spinfoams, in which a similar sum over local orientations appears.

As part of a visit to Perimeter of a delegation from the ELI Beamlines laser facility in the Czech Republic, Dr. Bulanov will speak about potential topics for collaboration between Perimeter Institute and 
ELI theorists on topics related to high energy laser physics. To highlight the interplay between theory and experiment, Dr. Bulanov will briefly mention two experiments where this was realized and is currently planned at the ELI Beamlines facility.

Let p \geq 5 be a prime. We construct a lattice in a self-dual modular Galois representation for which the p-torsion of the corresponding Bloch-Kato Selmer group is arbitrarily large. This extends the work of Matsuno for elliptic curves and small primes. Our representation is constructed by appropriately modifying an argument of Hamblen and Ramakrishna which allows one to lift reducible mod p Galois representations to characteristic zero with local conditions at a prescribed set of primes. This talk is based on recent joint work with Anwesh Ray (https://arxiv.org/pdf/2504.16287).

Let E/F be an elliptic curve with CM by an imaginary quadratic field K, and assume that the extension of F generated by the torsion points of E is abelian over K. In this talk I will outline the proof of the p-part of the Birch-Swinnerton-Dyer formula for E in analytic rank 1 for primes p>3 of ordinary reduction. For F=Q, this was originally proved by Rubin in 1991 as a consequence of his proof of the Iwasawa main conjecture for K. In contrast, our approach to the problem is based on the study of an auxiliary Rankin-Selberg convolution, and extends to CM abelian varieties A/K and higher weight CM modular forms.

I will explain the theory of Kolyvagin systems of Gauss sum type (or of rank 0) for certain self-dual representations over a number field. I especially discuss a remarkable, decisive property of the systems for the structure of Selmer groups, based on joint work with R. Sakamoto.

Title: The correlation coefficient in representation theory Abstract: Given a group G and two Gelfand subgroups H and K of G, associated to an irreducible representation \pi of G, there is a notion of H and K being correlated with respect to \pi in G. We discuss this theme in the context of toric periods for GL(2) over a finite field.