# Department of **Mathematics**

## Directory

## Matthew Boylan

Title: |
Professor |

Department: |
Mathematics College of Arts and Sciences |

Email: |
boylan@math.sc.edu |

Phone: |
803-777-7542 |

Office: |
LeConte 400C |

Office Hours: |
Tues: 10 – 11 Weds: 9 – 10 Thurs: 2 – 3 |

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

#### Education:

Ph.D Mathematics | University of Wisconsin at Madison | 2002 |

B.S. Mathematics | University of Wisconsin at Madison | 1999 |

#### Experience

2015 – present | Professor | University of South Carolina |

2017 – present | Director of Graduate Studies | University of South Carolina |

2009 – 2015 | Associate Professor | University of South Carolina |

2005 – 2009 | Assistant Professor | University of South Carolina |

2002 – 2005 | NSF VIGRE Visiting Research Assistant Professor | University of Illinois at Urbana-Champaign |

#### Courses Taught

##### At UofSC

Math 122: Calculus for Business Administration and Social Science

Math 141: Calculus I

Math 142: Calculus II

Math 241: Calculus III

Math 374: Discrete Structures

Math 531: Foundations of Geometry

Math 544: Linear Algebra

Math 546: Abstract Algebra I

Math 547: Abstract Algebra II

Math 550: Vector Calculus

Math 580: Number Theory

Math 701: Abstract Algebra I

Math 702: Abstract Algebra II

Math 780: Elementary Number Theory

Math 784: Algebraic Number Theory

Math 788B: Introduction to Modular Forms

Math 788E: Arithmetic of Elliptic Curves

Math 141: Calculus I

Math 142: Calculus II

Math 241: Calculus III

Math 374: Discrete Structures

Math 531: Foundations of Geometry

Math 544: Linear Algebra

Math 546: Abstract Algebra I

Math 547: Abstract Algebra II

Math 550: Vector Calculus

Math 580: Number Theory

Math 701: Abstract Algebra I

Math 702: Abstract Algebra II

Math 780: Elementary Number Theory

Math 784: Algebraic Number Theory

Math 788B: Introduction to Modular Forms

Math 788E: Arithmetic of Elliptic Curves

##### At U. of Illinois

Discrete Mathematics

Differential Equations

Mathematics for High School Teachers

Number Theory

Combinatorics

Differential Equations

Mathematics for High School Teachers

Number Theory

Combinatorics

#### Research

Dr. Boylan is a number theorist with a primary interest in modular forms and their
applications. He has given more than 50 invited talks away from his home institutions,
and his research has been funded by the National Science Foundation. Together with
colleagues at UofSC and Clemson, he is a co-founder and principal organizer of the
Palmetto Number Theory Series (PANTS) and he is a principal organizer for the Southeast Regional Meeting on Numbers (SERMON), both of which have benefitted from continuous funding by the National Science Foundation
and the National Security Agency.

#### Selected Publications

- M. Boylan. U_p-operators and congruences for Shimura images.
*Journal of Number Theory*, (2020) - M. Boylan and J. Webb. Congruences for the partition function modulo prime powers.
*Transactions of the American Mathematical Society*,**365**(2013), 2069 – 2206. - S. Ahglren and M. Boylan. Central critical values of modular L-functions and coefficients
of half-integral weight modular forms modulo l.
*American Journal of Mathematics***129**(2007), no. 2, 429 – 454. - M. Boylan. 2-adic properties of Hecke traces of singular moduli.
*Mathematics Research Letters*,**12**(2005), no. 4, 593 – 609. - S. Ahlgren and M. Boylan. Coefficients of half-integral weight modular forms modulo
l^j.
*Mathematische Annalen***331**(2005), no. 1, 219 – 241. - S. Ahlgren and M. Boylan. Arithmetic properties of the partition function.
*Inventiones Mathematicae***153**(2003), no. 3, 487 – 502.