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Washington State University

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics

Neill Hall 5W

April 20, Monday, 4:10 - 5:00 PM

Jennifer Johnson-Leung

Department of Mathematics

University of Idaho

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics

Neill Hall 5W

April 20, Monday, 4:10 - 5:00 PM

Jennifer Johnson-Leung

Department of Mathematics

University of Idaho

Title: Modularity of Abelian Surfaces

Abstract: In 2013, Freitas, Bao V. Le Hung, and Samir Siksek released a paper proving that elliptic curves over real quadratic fields are modular. This result generalizes the celebrated theorem of Wiles, et. al., proving that elliptic curves over Q are modular. I will recall the statement of these theorems and explain how we expect them to generalize to abelian surfaces in the Paramodular Conjecture of Brumer and Kramer. The Paramodular Conjecture is known for surfaces that arise as Weil restrictions of elliptic curves over real quadratic fields by a result of Brooks Roberts and myself.

Abstract: In 2013, Freitas, Bao V. Le Hung, and Samir Siksek released a paper proving that elliptic curves over real quadratic fields are modular. This result generalizes the celebrated theorem of Wiles, et. al., proving that elliptic curves over Q are modular. I will recall the statement of these theorems and explain how we expect them to generalize to abelian surfaces in the Paramodular Conjecture of Brumer and Kramer. The Paramodular Conjecture is known for surfaces that arise as Weil restrictions of elliptic curves over real quadratic fields by a result of Brooks Roberts and myself.