Jacob H. Swenberg
Dartmouth '21, UCLA Math Ph.D. Student
Email: jaswenberg [AT] math [DOT] ucla [DOT] edu
Office: MS 2951
Teaching
 Fall 2021: Math 31A (Differential and Integral Calculus) Disc
2E/2F
 Winter 2022: Math 33A (Linear Algebra and Applications) Disc
1A/1B
 Spring 2022: Math 33A (Linear Algebra and Applications) Disc
2G/2H
 Summer 2022 (Session C): Math 32B (Multivariable Calculus II) Disc
1A/1B
 Fall 2022: Math 110AH (Honors Algebra) Disc 1A
 Winter 2023: Math 110BH (Honors Algebra) Disc 1A
 Spring 2023: Math 33A (Linear Algebra and Applications) Disc
3E/3F
Publications and Preprints

Do Link Polynomials Detect Causality in Globally Hyperbolic
Spacetimes?
Joint with Samantha Allen. J. Math. Phys. 62 (2021), no. 3, 032503.
doi:10.1063/5.0040956. https://arxiv.org/abs/2011.09415
Ongoing Projects
 A HeegnerShimura Approach to Class Number One. (Based on
work in my undergraduate
thesis).
Joint with
John Voight.
Motivated by
the class number 1 problem of Gauss, we provide a complete description
of the Galois action on the set of principally polarized abelian
surfaces with QM by a maximal quaternion order O and CM by an imaginary
quadratic order S. The set A of such abelian surfaces is in bijection
with a set of classes of optimal embeddings of S into O. We describe an
action of the absolute Galois group on these optimal embeddings and show
that the action agrees with the action on abelian surfaces. By
completely describing the action on optimal embeddings, we describe the
action on abelian surfaces. As a consequence, we determine various
fields of moduli of abelian surfaces. Using recent progress on finding
rational points on curves using the technique of quadratic Chabauty, we
apply the results to give a new solution to the Gauss class number 1
problem.