# Department of **Mathematics**

## Directory

## Frank Thorne

Title: |
Professor |

Department: |
Mathematics College of Arts and Sciences |

Email: |
thorne@math.sc.edu |

Phone: |
803-777-7527 |

Office: |
LeConte 447 |

Office Hours: |
Mon 4-5 and Tue 9-10 and 4-5, held in a location TBD. Message me to coordinate a time and place. |

Resources: |
My Website Curriculum Vitae [PDF] |

### Research Interests

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

### Education

- Ph.D. in Mathematics,
*University of Wisconsin*, (2008) - B.A. in Mathematics,
*Rice University*(1999)

### Experience

- Professor,
*University of South Carolina*(2023 – present) - Assistant/Associate Professor,
*University of South Carolina*, (2011 – 2023) - 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

### 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.