Matthew Boylan

Title:	Professor Assistant Chair
Department:	Mathematics College of Arts and Sciences
Email:	boylan@math.sc.edu
Phone:	803-777-7542
Office:	LeConte 409
Office Hours:	M: 9 – 10 T: 10:30 – 11:30 W: 3 – 4
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

At U. of Illinois

Discrete Mathematics
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.

Department of Mathematics

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