College of Arts and Sciences
|Office Hours:||Tue 11:30-12:30, Thu/Fri 9:00-10:00|
Curriculum Vitae [pdf]
Department of Mathematics
Ph.D., Mathematics, University of Wisconsin, 2008
B.A., Mathematics, Rice University, 1999
Assistant/Associate Professor, University of South Carolina, 2011-
Postdoctoral Scholar, Stanford University, 2008-2011
Math 141, Calculus I
Math 142, Calculus II
Math 374, Discrete Structures
Math 531, Foundations of Geometry
Math 544, Linear Algebra
Math 546H, Algebraic Structures I
Math 547H, Algebraic Structures II
Math 574, Discrete Structures
Math 580, Elementary Number Theory
Math 701, Algebra I
Math 702, Algebra II
Math 735, Lie Groups
Math 782, Analytic Number Theory
Math 788, The Geometry of Numbers
Math 788, Elliptic Curves and Arithmetic Geometry
Math 788, Topics in Algebraic Number Theory
SCHC 212, The Mathematics of Game Shows
This is a new course which I developed from scratch, aiming to teach modeling, discrete math, and how to ask open-ended questions -- all in a fun setting that at least partially counts as "the real world". Notes (150 pp. PDF)
I am interested in analytic number theory and arithmetic statistics. One question that particularly interests me is: how are the discriminants of number fields distributed? Research on this topic involves copious amounts of analytic and algebraic number theory, representation theory, algebraic geometry, commutative algebra, and Fourier analysis. It is the relevance of so much of modern mathematics to this question that continues to drive my interest
- T. Taniguchi and F. Thorne, Orbital exponential sums for prehomogeneous vector spaces, American Journal of Math, in press.
- R. Lemke Oliver and F. Thorne, The number of ramified primes in fields of small degree, Proceedings of the American Mathematical Society 145 (2017), no. 8, 3201–3210.
- H. Cohen, S. Rubinstein-Salzedo, and F. Thorne, Identities for field extensions generalizing the Ohno-Nakagawa theorem, Compositio Mathematica 151 (2015), no. 11, 2059–2075.
- T. Taniguchi and F. Thorne, Secondary terms in counting functions for cubic fields, Duke Mathematical Journal, 162 (2013), no. 13, 2451-2508.