# Department of **Mathematics**

## Directory

## Frank Thorne

Title: |
Associate Professor |

Department: |
Mathematics College of Arts and Sciences |

Email: |
thorne@math.sc.edu |

Phone: |
803-777-7527 |

Office: |
LeConte 317O |

Office Hours: |
Tue 11:30-12:30, Thu/Fri 9:00-10:00 |

Resources: |
My Website Curriculum Vitae [pdf] Department of Mathematics |

#### Education

Ph.D., Mathematics, University of Wisconsin, 2008

B.A., Mathematics, Rice University, 1999

#### Experience

Assistant/Associate Professor, University of South Carolina, 2011-

Postdoctoral Scholar, Stanford University, 2008-2011

#### Courses Taught

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)

#### Research

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

#### Selected Publications

- 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.