Research Interests

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 USC 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.

Education

• Ph.D. in Mathematics, University of Wisconsin at Madison (2002)
• B.S. in Mathematics, University of Wisconsin at Madison (1999)

Experience

• Professor, University of South Carolina (2015 – present)
• Director of Graduate Studies, University of South Carolina (2017 – present)
• Associate Professor, University of South Carolina (2009 – 2015)
• Assistant Professor, University of South Carolina (2005 – 2009)
• NSF VIGRE Visiting Research Assistant Professor, University of Illinois at Urbana-Champaign (2002 – 2005)

Courses Taught

At USC

• 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

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.