Jeff Breeding-Allison

I am a Data Scientist. I am interested in time-series, neural networks, clustering, and other machine learning algorithms.

I am also a mathematician. I received my Ph.D. in Mathematics at the University of Oklahoma in 2011 under the supervision of Ralf Schmidt. I wrote my thesis on the irreducible non-cuspidal characters of GSp(4, k), where k is a finite field of odd order.

My main research interests are in number theory and the Langlands program. In particular, I am interested in representations of p-adic reductive groups, automorphic forms, and modularity. Much of my recent work has focused on topics related to A. Brumer and K. Kramer's Paramodular Conjecture. This conjecture is a degree two analogue of the Shimura Conjecture (Modularity Theorem) that all rational elliptic curves are modular.

Education

• Doctor of Philosophy (Ph.D.) University of Oklahoma (2006 — 2011)
• Master of Arts - MA University of Oklahoma (2006 — 2008)
• Bachelor of Science (B.S.) with Special Distinction University of Oklahoma (2002 — 2005)

Publications and Preprints:

The Gelfand-Graev representation of GSp(4, Fq) (with Julianne Rainbolt), Comm. Algebra 47 (2019), no. 2, pp. 560-584.

Computations of spaces of paramodular forms of general level (with Cris Poor and David S. Yuen), J. Korean Math. Soc. 53 (2016), no. 3, pp. 645-689.

Irreducible characters of GSp(4,q) and dimensions of spaces of fixed vectors, Ramanujan J. 36 (2015), no. 3, pp. 305-354.

Irreducible non-cuspidal characters of GSp(4,Fq), Ph.D. Thesis, University of Oklahoma, 2011. 145 pp.