## Benjamin K. Breen

## Welcome!

I am mathematician working in number theory and arithmetic statistics. I am currently an Affiliated Scientist for the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. Prior to this, I was an RTG Postdoc at Clemson University with the RTG on Coding, Cryptography, and Number Theory.

## Interests

I am interested in number theory, arithmetic geometry, and arithmetic statistics.

My research program centers on studying objects that arise in cohomology from the perspective of arithmetic statistics. In particular, my work focuses on exploring connections between Selmer groups of elliptic curves and Selmer groups of number fields.

I am also interested in effective methods for computation with algebraic objects. A large portion of my research focuses on advancing explicit methods for Hilbert modular forms.

## News

Jan. 2023: New paper A database of basic numerical invariants of Hilbert modular surfaces (with Eran Assaf, Angelica Babei, Edgar Costa, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone, and John Voight).

Dec. 2022: Talk in the AMS special session on quadratic forms, modular forms and applications I.

Jul. 2022: TA for the IAS/PCMI Program on Number Theory Informed by Computation.

Apr. 2022: Talk in the AMS special session on explicit methods for modularity.

Apr. 2022: Talk at JMM in the AMS special session on quadratic forms, theta functions, and modularity.

Mar. 2022: Talk at the Algebra Seminar at University of Idaho.

Feb. 2022: Panelist in the Math for all Conference in Clemson.

Feb. 2022: Talk at the Algebra and Algebraic Geometry Seminar at McMaster University.

Jan. 2022 (Postponed): Talk at JMM in the AMS special session on quadratic forms, theta functions, and modularity.

Jan. 2022 (Postponed): Talk at JMM in the AMS special session on explicit methods for modularity.

Oct. 2021: New paper

*The 2-Selmer group of S_n number fields of even degree*.Sep. 2021: Organized the Palmetto joint arithmetic, modularity, and analysis series (PAJAMAS) III.

Aug. 2021:

*On unit signatures and narrow class groups of odd degree abelian number fields*(with Ila Varma and John Voight) accepted to Trans. Amer. Math Soc.June 2021: Talk at CMS special session on Algebraic number theory.