Matthew G. Boylan: Curriculum Vitae

Matthew G. Boylan

Associate Professor
Department of Mathematics
University of South Carolina
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Contact Information:

Address: Department of Mathematics Office: 402 LeConte College

University of South Carolina

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 - August 2009,
University of South Carolina.
Associate Professor, August 2009 -,
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:

elliptic modular forms.
Maass forms.
algebraic number theory.
partitions and q-series.

Grant support:

2011 - 2012 National Science Foundation Grant DMS-1101301, Palmetto Number Theory Series (PI), $11,223.
2010 - 2011 National Security Agency Grant, Palmetto Number Theory Series (PI), $15,513.
2010 - 2011 National Science Foundation Grant DMS-1001553, Palmetto Number Theory Series (PI), $13,423.
2009 - 2012 National Science Foundation Grant DMS-0901068, Harmonic Maass Forms (PI), $121,000.
2009 - 2010 National Science Foundation Grant DMS-0901732, Palmetto Number Theory Series (co - PI), $11,096.
2008 - 2009 National Security Agency Grant, Palmetto Number Theory Series (PI), $10,070.
2008 - 2009 National Science Foundation Grant DMS-0801150, Palmetto Number Theory Series (PI), $7950.
2007 - 2008 National Science Foundation Grant DMS-0703547, Palmetto Number Theory Series (co - PI), $7413.
2006 - 2009 National Science Foundation Grant DMS-0600400, Modular Forms and Number Theory (PI), $109,930.

Publications:

[1]	Congruences for $_2F_1$ hypergeometric functions over finite fields. Ramanujan Journal 5 (2001), no. 4, 385-390.
[2]	Swinnerton-Dyer type congruences for certain Eisenstein series. q-series with applications to Combinatorics, Number Theory, and Physics (Urbana, IL, 2000), 93-108, Contemporary Mathematics, 291, Amer. Math. Soc., Providence, RI, 2001.
[3]	Parity of the partition function in arithmetic progressions, II. (with K. Ono) Bulletin of the London Mathematical Society 33 (2001), no. 5, 558-564.
[4]	Congruences for $2^t$-core partition functions. Journal of Number Theory 92 (2002), no. 1, 131-138.
[5]	Exceptional congruences for the coefficients of certain eta-product newforms. Journal of Number Theory 98 (2003), no. 2, 377-389.
[6]	Arithmetic properties of the partition function. (with S. Ahlgren) Inventiones Mathematicae 153 (2003), no. 3, 487-502.
[7]	Exceptional congruences for powers of the partition function. Acta Arithmetica 111 (2004), no. 2, 187-203.
[8]	Coefficients of half-integral weight modular forms modulo $\ell^j$. (with S. Ahlgren) Mathematische Annalen 331 (2005), no. 1, 219-241.
[9]	2-adic properties of Hecke traces of singular moduli. Mathematics Research Letters 12 (2005), no. 4, 593-609.
[10]	Non-vanishing of the partition function modulo small primes. International Mathematics Research Notices (2006), Art. ID 46120, 17 pp.
[11]	Central critical values of modular $L$-functions and coefficients of half-integral weight modular forms modulo $\ell$. (with S. Ahlgren) American Journal of Mathematics 12 (2007), no. 2, 429-454.
[12]	Odd coefficients of weakly holomorphic modular forms. (with S. Ahlgren) Mathematics Research Letters 15 (2008), no. 3, 409 - 418.
[13]	Arithmetic properties of certain level one mock modular forms. International Journal of Number Theory, 6 (2010), no. 1, 185 - 202.
[14]	Quadratic AGM and p-adic limits arising from modular forms. (with S. Garthwaite) Bulletin of the London Mathematical Society, 42 (2010), no. 3, 527 - 537.
[15]	On the vanishing of Fourier coefficients of certain genus zero newforms. (with S. Garthwaite and J. Webb) International Journal of Number Theory, 7 (2011), no. 5, 1229 - 1245.
[16]	The partition function modulo prime powers. (36 pages) (with J. Webb) Transactions of the American Mathematical Society, accepted for publication.

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.
January 2009: "Mock modular forms on SL_2(Z)",
AMS Special Session on Automorphic and Modular Forms in Number Theory,
Washington, D.C.
October 2009: "The arithmetic-geometric mean and p-adic limits of modular forms",
AMS Special Session on Modular and Automorphic Forms, Boca Raton, FL.
December 2009: "The arithmetic-geometric mean and p-adic limits of modular forms",
International Conference on Number Theory, SASTRA University, Kumbakonam, India.

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.
June 2008: "Theta cycles in the study of partition congruences",
University of Wisconsin at Madison, REU seminar.
April 2009: "Modular forms and partitions",
Bucknell University, Department colloquium.
April 2009: "Hecke operators in the study of harmonic Maass forms",
Bucknell University, Number theory seminar.
June 2009: "Quadratic AGM and p-adic limits of modular forms",
University of Wisconsin at Madison, REU seminar.
September 2009: "Modular forms and partitions",
Georgia Southern University, Department colloquium.
February 2010: "Quadratic AGM and p-adic limits of modular forms",
University of Florida, Number theory seminar.
February 2010: "Modular forms and partitions",
University of Florida, Department colloquium.
September 2010: "Quadratic AGM and p-adic limits of modular forms",
Emory University, Number theory seminar.
November 2010: "Quadratic AGM and p-adic limits of modular forms",
Brigham Young University, Number theory seminar.
August 2011: "The partition function modulo prime powers",
Emory University, Number theory seminar.

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.
September 2009: "Quadratic AGM and p-adic limits of modular forms",
Palmetto Number Theory Series X, Savannah, GA.

Teaching:

University of Wisconsin at Madison:
- Calculus teaching assistant: Fall 2001, Spring 2002.
University of Illinois at Urbana-Champaign:
- Differential equations and orthogonal functions (Math 285): Fall 2002.
- Mathematics for high school teachers (Math 305): Spring 2003.
- Number theory: Fall 2003 (Math 353), Spring 2005 (Math 453).
- Discrete math: Spring 2004 (Math 213).
- Combinatorics: Fall 2004 (Math 413).
University of South Carolina:
- Undergraduate algebra I (Math 546): Fall 2009.
- Undergraduate algebra II (Math 547): Spring 2010.
- Graduate algebra I (Math 701): Fall 2012.
- Graduate algebra II (Math 702): Spring 2013.
- Algebraic number theory (Math 784): Spring 2008, Spring 2010.
- Arithmetic of elliptic curves (Math 788E): Fall 2008.
- Calculus I (Math 141): Fall 2005.
- Calculus II (Math 142): Fall 2010, Spring 2011.
- Calculus for business administration and social science (Math 122): Fall 2008.
- Discrete structures (Math 374): Spring 2009.
- Foundations of Geometry (Math 531): Fall 2011.
- Introduction to modular forms (Math 788B): Fall 2006, Spring 2012.
- Linear algebra (Math 544): Spring 2006, Spring 2007, Fall 2007, Fall 2010.
- Number theory (Math 580): Fall 2009.
- Vector calculus (Math 241): Spring 2009, Fall 2011.
- Vector analysis (Math 550): Spring 2011.

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.
At the University of South Carolina:
- Fall 2005 -: 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.
- Special Session on "Modular Forms, Elliptic Curves, and Related Topics,"
  Fall 2011 Southeast Sectional Meeting of the AMS, Winston-Salem, NC,
  co-organizer with Jeremy Rouse.
- Palmetto Number Theory Series (PANTS):
  I (Fall 2006), IV (Fall 2007), VIII (Fall 2008), XI (Fall 2009), XIV (Fall 2010),
  co-organizer with Michael Filaseta.

Professional Service:

American Mathematical Society Southeast Section Program Committee (2010 - 2012);
Chair: 2011 - 2012.
Referee work (59 articles): Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, Acta Arithmetica, Advances in Mathematics, American Mathematical Monthly, Annals of Combinatorics, Canadian Journal of Mathematics, Discrete Mathematics, Electronic Journal of Combinatorics, Fields Institute Communications Series, 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, Monatshefte fur Mathematik, Proceedings of the American Mathematical Society, Ramanujan Journal, Rocky Mountain Journal of Mathematics, Transactions of the American Mathematical Society.
Review work: Mathematical Reviews (2002-present): 65 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 (2009), Pradipto Banerjee (2010).
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 (2011; Visiting Assistant Professor, Wake Forest University), Kenny Brown (in-progress).

Honors and Awards:

Phi Beta Kappa, University of Wisconsin at Madison, 1998.
NSF VIGRE Graduate Student Fellow, University of Wisconsin at Madison, 1999-2001.
Selfridge Prize for Excellence in Mathematics Presentation, 2003 West Coast Number Theory Conference.
Incomplete List of Teachers Ranked as Excellent by Their Students, University of Illinois at Urbana-Champaign, Fall 2004.
2005 - 2006 American Mathematical Society Project NExT Fellow (New Experiences in Teaching).
2011 University of South Carolina Rising Star Award.

Back to Home Page of Matt Boylan

Last modified on August 15, 2011.

Address:	Department of Mathematics	Office:	402 LeConte College
	University of South Carolina
	1523 Greene St.	Fax:	(803) 777-3783
	Columbia, SC 29208	E-mail:	boylan@math.sc.edu

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

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.