Contact Information:

Address:	Department of Mathematics	Office:	400G LeConte College
	University of South Carolina	Phone:	(803) 777-8874
	1523 Greene St.	Fax:	(803) 777-3783
	Columbia, SC 29208	E-mail:	boylan@math.sc.edu

Biographical Information:

Citizenship:	U.S.A.
Date of Birth:	10/9/76.
Place of Birth:	Stevens Point, Wisconsin.

Professional Positions

• NSF VIGRE Visiting Research Assistant Professor, August 2002-August 2005,
  University of Illinois at Urbana-Champaign.

• Palmetto Assistant Professor, August 2005- ,
  University of South Carolina.

Education:

Ph.D.,	August 2002, Pure Mathematics,
	University of Wisconsin at Madison.
	Advisor: K. Ono.
B.S.,	May 1999, Pure Mathematics,
	University of Wisconsin at Madison.

Research Interests:

• classical modular forms
• Maass forms
• algebraic number theory
• partitions

Publications

Invited Conference Talks

• March 2002: "Exceptional congruences for modular form coefficients,"
  AMS Special Session on Number Theory, Atlanta, GA.
• October 2002: "Arithmetic properties of the partition function,"
  AMS Special Session on Arithmetic Algebraic Geometry, Madison, WI.
• May 2003: "Arithmetic properties of the partition function,"
  AMS Special Session on q-Series and Partitions, San Francisco, CA.
• November 2003: "Coefficients of half-integral weight modular forms modulo $\ell^j$,"
  Integers Conference 2003, Carrollton, GA.
• November 2004: "Arithmetic properties of the partition function,"
  Conference on Additive Number Theory, Gainesville, FL.
• March 2005: "Non-vanishing of central critical values of modular L-functions modulo $\ell$",
  AMS Special Session on L-functions, Bowling Green, KY.
• April 2006: "Non-vanishing of the partition function modulo small primes",
  AMS Special Session on Number Theory, South Bend, IN.
• April 2006: "Non-vanishing of the partition function modulo small primes",
  AMS Special Session on q-Series and Partitions, San Francisco, CA.
• October 2006: "Non-vanishing of the partition function modulo small primes",
  21st Annual Clemson University Mini-Conference on Combinatorics and Optimization,
  Clemson, SC.
• October 2007: "Odd coefficients of weakly holomorphic modular forms",
  Integers Conference 2007, Carrollton, GA.
• January 2008: "Odd coefficients of weakly holomorphic modular forms",
  AMS Special Session on Automorphic Forms and Related Topics, San Diego, CA.
• March 2008: "Mock modular forms on SL_2(Z)",
  Conference on Partitions, q-series, and Modular Forms, Gainesville, FL.
• March 2008: "Eulerian series and modularity",
  MAA Special Session on Combinatorial Number Theory, Charleston, SC.
• May 2008:
  The Hawaii Workshop on the Arithmetic of Modular Forms, Manoa, HI.

Invited Seminar and Colloquium Talks

• February 2004: "Coefficients of half-integral weight modular forms modulo $\ell^j$,"
  University of Wisconsin at Madison, Number theory seminar.
• October 2004: "Half-integral weight modular forms with few non-vanishing coefficients modulo $\ell$,"
  University of Wisconsin at Madison, Number theory seminar.
• October 2004: "Non-vanishing of central critical values of modular L-functions modulo $\ell$",
  Purdue University, Number theory seminar.
• November 2004: "Non-vanishing of central critical values of modular L-functions modulo $\ell$",
  Texas A&M University, Number theory seminar.
• January 2005: "Arithmetic properties of the Fourier coefficients of modular forms",
  University of Oregon, Department colloquium.
• January 2005: "Arithmetic properties of the Fourier coefficients of modular forms",
  University of South Carolina, Department colloquium.
• January 2005: "Arithmetic properties of the Fourier coefficients of modular forms",
  University of Pittsburgh, Department colloquium.
• February 2005: "Arithmetic properties of the Fourier coefficients of modular forms",
  Texas A&M University, Department colloquium.
• February 2005: "Arithmetic properties of the Fourier coefficients of modular forms",
  University of Colorado, Department colloquium.
• February 2005: "Arithmetic properties of the Fourier coefficients of modular forms",
  University of Iowa, Department colloquium.
• April 2005: "Non-vanishing of central critical values of modular L-functions modulo $\ell$",
  Johns Hopkins University, Number theory seminar.
• October 2005: "Non-vanishing of central critical values of modular L-functions modulo $\ell$",
  University of Georgia, Number theory seminar.
• October 2005: "Modular forms and partitions",
  University of Georgia, VIGRE Seminar.
• February 2006: "Modular forms and partitions",
  Furman University, Department colloquium.
• April 2006: "Arithmetic properties of the partition function",
  Clemson University, Number theory seminar.
• April 2006: "Non-vanishing of p(n) modulo 3",
  Penn State University, Number theory seminar.
• June 2006: "Ramanujan's congruences",
  University of Wisconsin at Madison, REU seminar.
• June 2006: "Ramanujan's congruences",
  Clemson University, REU seminar.
• March 2008: "Mock modular forms on SL_2(Z)",
  Texas A&M University, Number theory seminar.
• Fall 2008:
  Washington & Lee University, Department colloquium.

Other Talks

• May 2000: "Congruences for $2^t$-core partition functions,"
  Millenial Conference on Number Theory, Urbana, IL.
• October 2000: "Parity of the partition function in arithmetic progressions,"
  q-Series with Applications to Combinatorics, Number Theory, and Physics, Urbana, IL.
• December 2000: "Parity of the partition function in arithmetic progressions,"
  West Coast Number Theory Conference, San Diego, CA.
• May 2001: "Exceptional congruences for modular form coefficients,"
  Illinois Number Theory Conference, Urbana, IL.
• December 2001: "Exceptional congruences for modular form coefficients,"
  West Coast Number Theory Conference, Pacific Grove, CA.
• May 2002: "Exceptional congruences for modular form coefficients,"
  7th Meeting of the Canadian Number Theory Association, Montreal, Canada.
• October 2003: "Coefficients of half-integral weight modular forms modulo $\ell^j$,"
  Midwest Number Theory Conference for Graduate Students and Recent PhDs, Madison, WI.
• December 2003: "Coefficients of half-integral weight modular forms modulo $\ell^j$,"
  West Coast Number Theory Conference, Pacific Grove, CA.
• March 2004: "2-adic properties of traces of singular moduli,"
  18th Annual Workshop on Automorphic Forms and Related Topics, Santa Barbara, CA.
• April 2004: "Coefficients of half-integral weight modular forms modulo $\ell^j$,"
  Conference in Honor of Morris Newman's 80th Birthday, Santa Barbara, CA.
• June 2004: "2-adic properties of traces of singular moduli,"
  8th Meeting of the Canadian Number Theory Association, Toronto, Canada.
• December 2004: "2-adic properties of traces of singular moduli,"
  West Coast Number Theory Conference, Las Vegas, NV.
• December 2005: "Non-vanishing of central critical values of modular L-functions modulo $\ell$,"
  West Coast Number Theory Conference, Pacific Grove, CA.
• March 2006: "Non-vanishing of the partition function modulo small primes",
  Southeast Regional Meeting on Numbers, Greenville, SC.
• July 2006: "Non-vanishing of the partition function modulo small primes",
  9th Meeting of the Canadian Number Theory Association, Vancouver, Canada.
• April 2007: "Non-vanishing of weakly holomorphic modular form coefficients and applications",
  Southeast Regional Meeting on Numbers, Winston-Salem, NC.
• May 2007: "Coefficients of weakly holomorphic modular forms modulo $\ell$",
  Illinois Number Theory Fest, Urbana, IL.
• September 2007: "Odd coefficients of weakly holomorphic modular forms",
  Palmetto Number Theory Series III, Charleston, SC.
• April 2008: "Mock modular forms on SL_2(Z)",
  Southeast Regional Meeting on Numbers, Clemson, SC.

Teaching

• University of Wisconsin at Madison:
  • Calculus teaching assistant: Fall 2001, Spring 2002.

• University of Illinois at Urbana-Champaign:
  • Differential equations and orthogonal functions: Fall 2002.
  • Mathematics for high school teachers: Spring 2003.
  • Number theory: Fall 2003, Spring 2005.
  • Discrete math: Spring 2004.
  • Combinatorics: Fall 2004.

• University of South Carolina:
  • Calculus I: Fall 2005.
  • Linear algebra: Spring 2006, Spring 2007, Fall 2007.
  • Introduction to modular forms: Fall 2006.
  • Algebraic number theory: Spring 2008.
  • Arithmetic of ellptic curves: Fall 2008.
  • Calculus for business administration and social science: Fall 2008.

Other Professional Activities

• Seminar and conference organization (at the University of Illinois at Urbana-Champaign):
  • Fall 2003-Spring 2004: Math 500, graduate student seminar series,
    co-organizer with Patrick Bahls and Michael Bush.
  • Spring 2004: seminar on "Topics in Modular Forms and Number Theory,"
    co-organizer with Scott Ahlgren.
  • May 2004: Illinois Number Theory Conference,
    co-organizer with Scott Ahlgren.
  • Fall 2004: department number theory seminars,
    co-organizer with Alexandru Zaharescu.
  • Spring 2005: department number theory seminars,
    co-organizer with Bruce Berndt.
• Seminar and conference organization (at the University of South Carolina):
  • Fall 2005 - Spring 2006: department number theory seminar,
    co-organizer with Michael Filaseta.
  • Fall 2006 - Spring 2008: department number theory seminar,
    organizer.
  • Special Session on "Modular Forms and Analytic Number Theory,"
    Fall 2006 Southeast Sectional Meeting of the AMS, Fayetteville, AR,
    co-organizer with Gang Yu.
  • Fall 2006: Palmetto Number Theory Series (PANTS I),
    co-organizer with Nigel Boston and Michael Filaseta.
  • Fall 2007: PANTS IV,
    co-organizer with Michael Filaseta and Ognian Trifonov.

• Referee work (34 articles): Acta Arithmetica, American Mathematical Monthly, Annals of Combinatorics, Discrete Mathematics, Electronic Journal of Combinatorics, Integers, International Journal of Mathematics and Mathematical Sciences, International Journal of Number Theory, International Mathematics Research Notices, Involve, Israel Journal of Mathematics, Journal of Computational Mathematics and Optimization, Journal of Number Theory, Journal de Theorie des Nombres Bordeaux, Proceedings of the American Mathematical Society, Ramanujan Journal, Rocky Mountain Journal of Mathematics.

• Review work: Mathematical Reviews (2002-present): 47 reviews.

• Reviewer of National Science Foundation (NSF) and National Security Agency (NSA) grants: (2006-present).

• Advising:
  • Doctoral Defense Committees: Boon Pin Yeap (2003), Heekyoung Hahn (2004), Hamza Yesilyurt (2004), Dan Baczkowski (in progress).
  • 2005- : University of South Carolina Pi Mu Epsilon co-advisor with Maria Girardi and Ronda Sanders.
  • Master's Theses: Jonathan Mason (2007), Mohamad Youssef (2007), Jennifer Larson (2008).
  • Ph.D students: John Webb (in progress).

Honors and Awards