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Found 4 Results
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Local data for elliptic curves with non-trivial torsion

Given a rational elliptic curve, one can use Tate's algorithm to determine local data of the elliptic curve at each prime. This includes the Néron type, conductor, and Tamagawa number. It is well known that the isogenous elliptic curves have the same conductor. For an elliptic curve with non-trivial torsion, we investigate how the Néron type and Tamagawa [Read More...]

Presenter: Bella Tobin, Oklahoma State University
Authors: Alexander J. Barrios, Manami Roy, Nandita Sahajpal, Bella Tobin, Hanneke Wiersema, Darwin Xavier Tallana Chimarro}
Symposium Year: 2022
Session: Rethinking Number Theory
Presentation Time: June 18, 2022; 3:20 pm

A Dedekind-Rademacher homomorphism for Bianchi groups*

We construct a generalization of the Dedekind-Rademacher homomorphism to congruence subgroups of $\mathrm{SL}_2(\mathbb C)$, and derive some of its basic properties. These results have applications of this work including special values of L-functions and Sharifi's Conjectures. Time permitting, we may also discuss an extension of this work to the [Read More...]

Presenter: Kim Klinger-Logan, Kansas State University
Authors: Kim klinger-Logan, Kalani Thalagoda, Tung Nguyen, Tian An Wong
Symposium Year: 2022
Session: Rethinking Number Theory
Presentation Time: June 18, 2022; 3:45 pm

Computing the endomorphism ring of a supersingular elliptic curve*

In recent years, isogeny-based cryptosystems have captured the attention of the math/crypto community for their potential resistance to quantum attacks. In this context, the most promising protocols have as central objects supersingular elliptic curves defined over a finite field, and their security is therefore based on the mathematical problem of [Read More...]

Presenter: Annamaria Iezzi, Università degli Studi di Napoli Federico II
Authors: Jenny G. Fuselier, Annamaria Iezzi, Mark Kozek, Travis Morrison, Changningphaabi Namoijam.
Symposium Year: 2022
Session: Rethinking Number Theory
Presentation Time: June 18, 2022; 4:10 pm

Towards a converse theorem for mod $\ell$ gamma factors. (prerecorded)

How can one describe all irreducible representations of a finite group? One usually first learns about the character of a representation, which attaches a number to each conjugacy class. Can we tell apart representations using even fewer invariants? For the groups $GL_n$ over a finite field, the local converse theorem of Piatetski-Shapiro says that $\Gamma$ [Read More...]

Presenter: Mathilde Gerbelli-Gauthier, IAS
Authors: Jacksyn Bakeberg, Mathilde Gerbelli-Gauthier, Heidi Goodson, Ashwin Iyengar, Gil Moss, Robin Zhang
Symposium Year: 2022
Session: Rethinking Number Theory
Presentation Time: June 18, 2022; 4:35 pm
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