Jeremy Rouse

Department of Mathematics

Wake Forest University

340 Manchester Hall

P.O. Box 7388

Winston-Salem, NC 27109

(336) 758-4159

rouseja 'at' wfu dot edu

http://www.wfu.edu/~rouseja

- Professor, Wake Forest University, July 2022-present.
- Associate Professor, Wake Forest University, July 2015-June 2022.
- Assistant Professor, Wake Forest University, July 2010-June 2015.
- J. L. Doob Research Assistant Professor, August 2007-August 2010, University of Illinois, Urbana-Champaign.

- Ph.D. in Mathematics, University of Wisconsin, Madison, 2007 Field: Number Theory
- M.A. in Mathematics, University of Wisconsin, Madison, 2005.
- B.S. in Mathematics, Harvey Mudd College, 2003 High Distinction
- Budapest Semesters in Mathematics, Spring 2002

Minor: Analysis

Honors in Mathematics

- Modular and Automorphic Forms.
- L-functions.
- Elliptic Curves and Abelian Varieties.
- Quadratic Forms.

For online access to published versions of the articles below, see this page.

- P. Clark, P. Pollack, J. Rouse, K. Thompson, 'Densities of sets of integers represented by quadratic forms', accepted for publication in
*Journal of Number Theory*. - J. Rouse, K. Thompson, 'Quaternary quadratic forms with prime discriminant', accepted for publication in
*Acta Arithmetica*. - X. Lang, J. Rouse, 'Rational points on
x ', submitted.^{3}+ x^{2}y^{2}+ y^{3}= k - J. Rouse, A. Sutherland, D. Zureick-Brown, 'l-adic images of Galois for elliptic curves over Q,
*Forum of Mathematics, Sigma***10**(2022), Paper No. e62. (Code is available here.) - A. Newton, J. Rouse, 'Integers that are sums of two rational sixth powers,
*Canadian Mathematical Bulletin***66**(2023), no. 1, 166-177. (Code is available here.) - A. Bourdon, D. Gill, J. Rouse, L. Watson, 'Odd degree isolated points on
X with rational_{1}(N)j -invariant', accepted for publication in*Research in Number Theory*. (Code is available here.) - M. Cerchia, J. Rouse, 'Uniform bounds on the image of the arboreal Galois representation attached to non-CM elliptic curves',
*Proceedings of the American Mathematical Society***149**(2021), no. 2, 583-589. - J. Holley-Reid, J. Rouse,
'The number of representations of
*n*as a growing number of squares', accepted for publication in*Involve*. - C. Donnay, S. R. Garcia, J. Rouse, 'p-adic quotient sets II: quadratic forms',
*Journal of Number Theory***201**(2019), 23-39. - K. Liang, J. Rouse, 'The density of odd order reductions for elliptic curves with a rational points of order 2',
*International Journal of Number Theory***15**(2019), no. 8, 1547-1563. - J. Rouse,
'Integers represented by positive-definite quadratic forms and Petersson inner products',
*Acta Arithmetica***187**(2019), no. 1, 81-100. - S. Binegar, R. Dominick, M. Kenney, J. Rouse, A. Walsh,
'An Elliptic Curve Analogue to the
Fermat Numbers',
*Involve***12**(2019), no. 3, 427-449. - J. DeBenedetto, J. Rouse, 'Quadratic forms representing all integers coprime to 3',
*Ramanujan Journal***46**(2018), no. 2, 431-446. - G. Dresden, K. Hess, S. Islam, J. Rouse, A. Schmitt, E. Stamm,
T. Warren, P. Yue, 'When is
*a*the sum of two squares?',^{n}+ 1*Involve***12**(2019), no. 4, 585-605. - B. Goddard, J. Rouse, 'Sum of two repdigits a square,'
*Integers***17**(2017), Paper No. A24. - J. Patsolic, J. Rouse, 'Trinomials defining quintic number fields,'
*International Journal of Number Theory***13**(2017), no. 7, 1881-1894. - A. Block Gorman, T. Genao, H. Hwang, N. Kantor, S. Parsons, J. Rouse,
'The density of primes dividing a particular non-linear recurrence sequence',
*Acta Arithmetica***175**(2016) no. 1, 71-100. - B. Davis, R. Kotsonis, J. Rouse, 'The density of primes dividing a term in the Somos-5 sequence,'
*Proceedings of the American Mathematical Society, Series B***4**(2017), 5-20. - J. Rouse, Y. Yang, 'Three consecutive almost squares,'
*International Journal of Number Theory***12**(2016), no. 4, 969-978. - J. Rouse, D. Zureick-Brown, 'Elliptic curves over Q and 2-adic images of Galois,'
*Research in Number Theory*,**1**(2015). - J. Rouse, J. J. Webb, 'Spaces of modular forms spanned by eta-quotients,'
*Advances in Mathematics*,**272**(2015), 200-224. - J. Rouse, J. Thorner, 'The explicit Sato-Tate conjecture and densities pertaining to Lehmer-type questions,'
*Transactions of the American Mathematical Society***369**(2017) no. 5, 3575-3604. - P. Cubre, J. Rouse, 'Divisibility
properties of the Fibonacci entry point,'
*Proceedings of the American Mathematical Society*,**142**(2014), no. 11, 3771-3785. - M. Jones, J. Rouse, 'Solutions of the cubic
Fermat equation in quadratic fields,'
*International Journal of Number Theory*,**9**(2013), no. 6, 1579-1591. - J. Rouse, F. Thorne, 'On the existence of large degree Galois representations for fields of small discriminant,'
*Pacific Journal of Mathematics***271**(2014), no. 1, 243-256. - J. Rouse, 'Quadratic forms representing all odd positive integers,'
*American Journal of Mathematics***136**(2014), no. 6, 1693-1745. - J. Rouse, 'Explicit bounds for sums of
squares,'
*Mathematical Research Letters*,**19**(2012), no. 2, 359-376. - P. Jenkins, J. Rouse, 'Bounds for coefficients
of cusp forms and extremal lattices,'
*Bulletin of the London Mathematical Society*,**43**(2011), no. 5, 927-938. - B. Reznick, J. Rouse, 'On the sums of two cubes,'
*International Journal of Number Theory*,**7**(2011), no. 7, 1863-1882. - S. Ahlgren, J. Rouse, 'Congruences for newforms and the index of
the Hecke algebra,'
*Proceedings of the American Mathematical Society***139**(2011), no. 4, 1247-1261. - B. Kim, J. Rouse, 'Explicit bounds for the number of
*p*-core partitions,'*Transactions of the American Mathematical Society*,**366**(2014), no. 2, 875-902. - S. Ahlgren, J. Rouse,
'Critical
*L*-values of level p newforms (mod p),'*International Mathematics Research Notices*(2010), no. 9, 1575-1606. - S. Ahlgren, D. Choi, J. Rouse, 'Congruences
for level four cusp forms,'
*Mathematical Research Letters*,**16**(2009), no. 4, 683-701. - S. Ahlgren, N. Masri, J. Rouse, 'Vanishing
of modular forms at infinity,'
*Proceedings of the American Mathematical Society*,**137**(2009), 1205-1214. - J. Rouse, 'Bounds
for the
coefficients of powers of the Δ-function,'
*Bulletin of the London Mathematical Society*,**40**(2008), 1081-1090. - R. Jones, J. Rouse, 'Galois Theory
of
Iterated Endomorphisms,'
*Proceedings of the London Mathematical Society*,**100**, no. 3, (2010), 763-794. - J. Rouse, 'Atkin-Serre
Type
Conjectures for Automorphic Representations on
*GL(2)*,'*Mathematical Research Letters*,**14**(2007), no. 2, 189-204. - K. Bringmann, K. Ono, J. Rouse, 'Traces of
Singular Moduli on Hilbert Modular Surfaces,'
*International Mathematics Research Notices*,**47**(2005), 2891-2912. - J. Rouse, 'Zagier
Duality for the Exponents
of Borcherds Products for Hilbert Modular Forms,'
*Journal of the London Mathematical Society*,**73**(2006), 339-354. - J. Rouse, 'Vanishing and
Non-Vanishing of
Traces of Hecke Operators,'
*Transactions of the American Mathematical Society***358**(2006), no. 10, 4637-4651. - J. Rouse,
'Hypergeometric
Functions and Elliptic
Curves,'
*Ramanujan Journal***12**(2006), 197-205. - P. Anderson, A. Benjamin, J. Rouse,
'Combinatorial
Proofs of
Fermat's, Lucas's, and Wilson's Theorems,'
*The American Mathematical Monthly***112**(2005) No. 3, pg. 266-268. - A. Benjamin, J. Rouse,
'When Does
F divide_{m}^{L}F ? A Combinatorial Solution,'_{n}*Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications*.*Congressus Numerantium*,**194**(2009), 53-58. - A. Benjamin, J. Rouse, J. Quinn,
'Fibinomial
Identities,'
*Applications of Fibonacci Numbers, Volume 9*, Kluwer Academic Publishers, (2004), pp. 19-24. - A. Benjamin, J. Rouse,
'Recounting
Binomial Fibonacci
Identities,'
*Applications of Fibonacci Numbers, Volume 9*, Kluwer Academic Publishers, (2004), pp. 25-28.

- Japheth Varlack (Wake Forest Graduate Student), Fall 2022-present.
- Rachel (Ruiqi) Lin (Wake Forest Undergraduate), Summer 2022-present.
- Ariella Lee (Wake Forest Graduate Student), Summer 2020-Spring 2021.
- Shawn (Xiaonan) Lang (Wake Forest Undergraduate), Summer 2020-present.
- Alexis Newton (Wake Forest Graduate Student), Fall 2018-Spring 2020.
- Jiayi Li (Wake Forest Undergraduate), Fall 2018-Fall 2019.
- Haochen Wu (Wake Forest Undergraduate/Graduate Student), Fall 2018-Spring 2021.
- Michael Cerchia (Wake Forest Graduate Student), Fall 2017-Summer 2019.
- Ke Liang (Wake Forest Undergraduate), Fall 2017-Summer 2018.
- Marie Mickley (Wake Forest Undergraduate), Fall 2017-Spring 2018.
- Skye Binegar, Randy Dominick, Chris Donnay, Havi Ellers, Meagan Kenney, Kate O'Connor, Alex Walsh, Erin Wood (WADE Into Research REU), Summer 2017.
- John Holley-Reid (Wake Forest Undergraduate), Spring 2017-Summer 2019.
- Madeleine Barowsky, Will Damron, Kylie Hess, Andres Mejia, Freddy Saia, Nolan Schock, Emily Stamm, and Terrin Warren (WADE Into Research REU), Summer 2016.
- John Byrum (Wake Forest Undergraduate), Fall 2015-Spring 2016.
- Nick Clinch (Wake Forest Undergraduate), Fall 2015-Spring 2016.
- Sarah Blackwell, Alexi Block Gorman, Gabe Durham, Tyler Genao, Heesu Hwang, Noam Kantor, Sarah Parsons, and Tiffany Treece (WADE Into Research REU), Summer 2015.
- Bryant Davis and Rebecca Kotsonis (Wake Forest Undergraduates), Summer 2014-Spring 2015.
- Keenan Curtis (Wake Forest Undergraduate), Fall 2013-Spring 2014.
- Yilin Yang (Wake Forest Undergraduate), Summer 2013 and Fall 2013-Spring 2014.
- Jesse Patsolic (Wake Forest Graduate Student), Fall 2012-Spring 2014.
- Rowland Carlson (Wake Forest Undergraduate), Summer 2012.
- Greg Cordo (Wake Forest Undergraduate), Fall 2011-Spring 2012.
- Jesse Thorner (Wake Forest Graduate Student), Fall 2011-Spring 2013.
- Justin DeBenedetto (Wake Forest Undergraduate/Graduate Student), Summer 2011 and Fall 2012-Spring 2015.
- Marvin Jones (Wake Forest Graduate Student), Spring 2011-Spring 2012.
- Paul Cubre (Wake Forest Graduate Student), Spring 2011-Spring 2012.
- Jeff Mudrock (UIUC Undergraduate), 2009-2010.
- Byungchan Kim (UIUC Graduate Student), Fall 2009.
- Jonah Sinick (UIUC Graduate Student), Summer 2008.
- Shanshan Ding (Columbia Undergraduate), Adam Merberg (Brown Undergraduate), Summer 2007.
- Carl Erickson (Stanford Undergraduate), Alison Miller (Harvard Undergraduate), Aaron Pixton (Princeton Undergraduate), Richard Gottesman (Brown Undergraduate), KwokFung Tang (University of Chicago Undergraduate), Summer 2006.
- Po-Ru Loh (Caltech Undergraduate), Robert Rhoades (Bucknell Undergraduate), Summer 2005.

- Instructor, WFU MTH 745, Spring 2012.
- Instructor, WFU MTH 722, Spring 2012.
- Instructor, WFU MTH 721, Fall 2011, Fall 2023.
- Instructor, WFU MTH 346/646, Fall 2011, Fall 2015, Fall 2017.
- Instructor, WFU MTH 345/645, Spring 2011, Spring 2013, Spring 2014, Spring 2016, Spring 2017, Spring 2020, Spring 2021, Summer 2023.
- Instructor, WFU MTH 321, Fall 2018, Spring 2019, Spring 2020.
- Instructor, WFU MTH 311, Spring 2022, Spring 2023.
- Instructor, WFU MTH 243, Fall 2014, Fall 2018.
- Instructor, WFU MTH 165, Fall 2010, Fall 2011, Fall 2013, Fall 2014, Fall 2015, Fall 2017, Fall 2018, Fall 2019, Fall 2020, Fall 2021, Spring 2023, Fall 2023.
- Instructor, WFU MTH 121, Spring 2015, Spring 2017, Fall 2017, Spring 2018, Spring 2019, Fall 2019, Fall 2021.
- Instructor, WFU MTH 117, Fall 2013, Spring 2020.
- Instructor, WFU MTH 113, Spring 2011, Spring 2012, Spring 2013, Fall 2014, Fall 2015, Fall 2020, Spring 2021, Fall 2023.
- Instructor, WFU MTH 112, Fall 2010, Spring 2016, Summer 2021.
- Instructor, WFU MTH 111, Fall 2013, Spring 2014.
- Instructor, UIUC Math 231, Spring 2010.
- Instructor, UIUC Math 453, Spring 2010.
- Instructor, UIUC Math 241 honors section, Fall 2009.
- Instructor, UIUC Math 181, Spring 2009.
- Instructor, UIUC Math 595, introduction to modular forms, Spring 2009.
- Instructor, UIUC Math 453, Fall 2008.
- Instructor, independent study in modular forms, Spring 2008.
- Instructor, UIUC Math 241 honors section, Spring 2008.
- Instructor, UIUC Math 213, Fall 2007.
- Instructor, UW-Madison Summer Enhancement Program in Algebra, Summers of 2005, 2006, and 2007.
- Instructor, UW-Madison NSF REU in Number Theory, Summers of 2005, 2006, and 2007.
- Teaching Assistant, UW-Madison Math 222 WES, Spring 2007.
- Teaching Assistant, UW-Madison Math 221 WES, Fall 2006.
- Teaching Assistant, UW-Madison Math 221, Fall 2005.
- Student Facilitator, Harvey Mudd College Academic Excellence Program, Math 11-12, Fall 2002.
- Grader and Tutor, various undergraduate math classes at Harvey Mudd College, Fall 2000-Spring 2003.
- Private Tutor.

- National Security Agency Grant for the 2016 Automorphic Forms Workshop, $14,400.
- National Science Foundation Grant, 2015-2018, DMS-1461189, REU Site: Wake/Davidson Experience In Number Theory Research (PI, with co-PI Katherine Thompson), $258,354.
- 2014 TLC Teaching Innovation Award.
- CRADLE IV Fellow, 2013-2015.
- A.J. Sterge Faculty Fellow, 2013-2016 and 2020-2023.
- List of Teachers Ranked as Excellent By Their Students, Spring 2010, Math 453.
- National Science Foundation Grant, 2009-2012, DMS-0901090, The distribution of Fourier coefficients of modular forms and arithmetic applications (PI), $83,651.
- Project NExT Fellow, 2008-2009.
- University Housing's Favorite Instructor Award, Spring 2007.
- Outstanding teaching evaluations, Fall 2006, Spring 2007.
- NDSEG Fellowship, sponsored by the Department of Defense and the Office of Naval Research, 2003-2006.
- Honorable mention in the 2002 William Lowell Putnam Mathematical Competition.
- Top 500 in the William Lowell Putnam Mathematical Competition, 1999, 2000, 2001.
- Dean's List at Harvey Mudd College, 2000-2003.

- The failure of injectivity in number theory, colloquium, Tulane University, February 3, 2022.
- Elliptic curves and Galois representations, Five College Number Theory Seminar, October 12, 2021.
- l-adic images of Galois for elliptic curves over Q, VaNTAGe seminar, June 22, 2021.
- How often is the order odd modulo a prime?, algebra seminar, University of Connecticut, February 24, 2021.
- Provably finding rational points on curves, Hudson colloquium, Georgia Southern University, November 4, 2020.
- Integers represented by positive-definite quadratic forms and Petersson inner products, algebra seminar, Vanderbilt University, October 13, 2020.
- The failure of injectivity in number theory, colloquium, University of South Carolina, October 1, 2020.
- Integers represented by positive-definite quadratic forms and Petersson inner products, algebra seminar, University of Virginia, September 4, 2020.
- Integers represented by positive-definite quadratic forms and Petersson inner products, algebra seminar, Emory University, November 5, 2019.
- Integers represented by quadratic forms, number theory seminar, Brigham Young University, March 12, 2019.
- Elliptic curves over Q and 2-adic images of Galois, number theory seminar, Duke University, March 2, 2016.
- Quadratic forms representing all odd positive integers, Graduate Student colloquium, Duke University, October 21, 2015.
- Elliptic curves over Q and 2-adic images of Galois, Wesleyan University Algebra Seminar, April 3, 2015.
- Integers represented by quadratic forms, Wesleyan University Colloquium, April 2, 2015.
- Quadratic forms representing all odd positive integers, Duke University, November 14, 2012.
- Quadratic forms representing all odd positive integers, University of North Carolina-Greensboro, October 3, 2012.
- Quadratic forms representing all odd positive integers, University of North Carolina-Chapel Hill, October 2, 2012.
- Quadratic forms representing all odd positive integers, Quebec-Vermont Number Theory Seminar, September 27, 2012.
- Quadratic forms representing all odd positive integers, University of South Carolina, February 14, 2012.
- Quadratic forms representing all odd positive integers, Emory University, February 2, 2012.
- Primes dividing recurrence sequences, Clemson University, March 10, 2011.
- On sums of two cubes, University of South Carolina, March 2, 2011.
- More modular forms, Wake Forest University, October 25, 2010.
- Introduction to modular forms, Wake Forest University, October 18, 2010.
- Galois theory of iterated endomorphisms, Emory University, October 5, 2010.
- Sums of two cubes and elliptic surfaces, University of Illinois, Urbana-Champaign, May 4, 2010.
- The index of the Hecke algebra in weight 4, University of Illinois, Urbana-Champaign, February 18, 2010.
- Explicit bounds for the number of
*p*-core partitions, University of Illinois, Urbana-Champaign, December 3, 2009. - Critical
*L*-values of level*p*newforms (mod*p*), University of Wisconsin-Madison, November 12, 2009. - Theorems and conjectures about elliptic curves and
*L*-functions, University of Illinois, Urbana-Champaign, October 13, 2009. - The Birch and Swinnerton-Dyer Conjecture, University of Illinois, Urbana-Champaign, April 7, 2009.
- Primes dividing recurrence sequences, University of Illinois, Urbana-Champaign, January 20, 2009.
- Modular forms with coefficients supported on finitely many square classes (mod l), University of Illinois, Urbana-Champaign, October 7, 2008.
- Bounds for the coefficients of powers of the $\Delta$-function, University of Wisconsin-Madison, May 1, 2008.
- Lehmer's Conjecture, University of Illinois, Urbana-Champaign, February 7, 2008.
- Bounds for the coefficients of powers of the $\Delta$-function, University of Illinois, Urbana-Champaign, October 11, 2007.
- Iterated endomorphisms of abelian algebraic groups, University of Illinois, Urbana-Champaign, September 4, 2007.
- Almost-square primes, University of Wisconsin-Madison, January 31, 2006.
- Traces of singular moduli on Hilbert modular surfaces, University of Wisconsin-Madison, November 10, 2005.
- The arithmetic of Borcherds products for Hilbert modular forms, University of Wisconsin-Madison, January 27, 2005. v
- Vanishing and non-vanishing of traces of Hecke operators, University of Illinois, Urbana-Champaign, September 21, 2004.
- Vanishing and non-vanishing of traces of Hecke operators, University of Wisconsin-Madison, September 9, 2004.

- 2023 Southeastern Regional Meeting on Numbers (SERMON), UNC Greensboro, Saturday, May 6, 2023.
- Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting, Simons Foundation, New York, January 11-12, 2023.
- 2023 Joint Math Meetings, January 4-7, 2023.
- PANTS XXXV, University of South Carolina, December 10-11, 2022.
- Modular Curves Workshop 2, MIT, November 5-9, 2022.
- 2022 Fall Eastern AMS Section Meeting, University of Massachusetts-Amherst, October 1-2, 2022. (invited talk)
- Modern breakthroughs in Diophantine problems, Banff International Research Station, June 20-24, 2022.
- AMS paraDIGMS 2022 spring conference, Online, April 28-May 1, 2022.
- Wake Forest University inclusive teaching conference, April 21, 2022.
- Modular curves workshop, MIT, March 21-25, 2022.
- AMS paraDIGMS 2021 fall conference, Online, October 28-31, 2021.
- 2021 AMS/MAA Joint Math Meetings, Online, January 6-9, 2021. (Invited talk)
- 2020 Fall Southeastern AMS Section Meeting, Online, October 10-11, 2020.
- CTNT 2020 Conference, University of Connecticut, June 12-14, 2020. (Plenary talk.)
- Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting, Simons Foundation, New York, Janaury 9-10, 2020.
- PANTS XXXIII, Clemson University, December 14-15, 2019. (Contributed talk.)
- Modular Forms, Arithmetic, and Women in Mathematics, Emory University, November 1-3, 2019. (Plenary talk.)
- SouthEastern Region Meeting on Numbers (SERMON 2019), UNC Greensboro, April 13-14, 2019.
- Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting, Simons Foundation, New York, January 10-11, 2019.
- PANTS 31, University of South Carolina, December 8-9, 2018.
- Torsion groups and Galois representations of elliptic curves, University of Zagreb, Croatia, June 25-29, 2018. (Contributed talk.)
- Early Career Research Workshop in coding theory, cryptography, and number theory, Clemson University, June 11-15, 2018. (Group leader.)
- SouthEastern Regional Meeting on Numbers (SERMON XXXI), East Tennesse State University, Johnson City, TN, March 10-11, 2018. (Contributed talk.)
- 2018 AMS/MAA Joint Math Meetings, San Diego, California, January 10-13, 2018. (Session co-organizer.)
- Conference on aspects of the algebraic and analytic theory of quadratic forms, University of Georgia, July 23-27, 2017. (Three invited talks.)
- 2017 Spring Eastern AMS Section Meetings, Hunter College, City University of New York, New York, May 6-7, 2017. (Invited talk)
- 2017 AMS/MAA Joint Math Meetings, Atlanta, Georgia, January 4-7, 2017. (Contributed talk)
- PANTS XXVI, University of North Carolina-Greensboro, September 17-18, 2016. (contributed talk)
- 30th Automorphic Forms Workshop, Wake Forest University, March 7-10, 2016. (Co-organizer)
- Lattices and Applications in Number Theory, Oberwolfach, Germany, January 17-23, 2016. (Invited talk)
- AMS/MAA Joint Meetings, Seattle, Washington, January 6-9, 2016. (Contributed talk)
- PANTS XXIV, Emory University, September 12-13, 2015.
- 29th Automorphic Forms Workshop, University of Michigan, March 2-March 5, 2015. (contributed talk)
- 2014 Fall Southeastern AMS Section Meeting, University of North Carolina at Greensboro, Greensboro, North Carolina, November 8-9, 2014. (invited talk)
- 2014 Fall Central AMS Section Meeting, University of Wisconsin Eau-Claire, Eau-Claire, Wisconsin, September 20-21, 2014. (invited talk)
- Building Bridges: 2nd EU/US Workshop on Automorphic Forms and Related Topics, University of Bristol, England, July 7-11, 2014. (contributed talk)
- Number Theory at Illinois: A Conference in Honor of the Batemans, June 5-7, 2014. (invited talk)
- 28th Automorphic Forms Workshop, Moab, Utah, May 12-16, 2014. (contributed talk)
- International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms, Puerto Natales, Chile, December 16-21, 2013. (invited talk)
- Palmetto Number Theory Series (PANTS) XX, Davidson College, September 7-8, 2013.
- 2013 Southeastern Regional Meeting on Numbers (SERMON), High Point University, April 13-14, 2013.
- 27th Automorphic Forms Workshop, University College Dublin, March 11-14, 2013 (contributed talk).
- AMS/MAA Joint Meetings, San Diego, California, January 9-12, 2013 (invited talk).
- 2012 Fall Western Section Meeting, University of Arizona, Tucson, AZ, October 27-28, 2012 (invited talk).
- Palmetto Number Theory Series (PANTS) XVIII, Wake Forest University, September 15-16, 2012 (co-organizer).
- 2012 Southeastern Regional Meeting on Numbers (SERMON), Western Carolina University, Cullowhee, NC, March 30-April 1, 2012 (contributed talk).
- Hawaii Conference on Algebraic Number Theory, Arithmetic Geometry and Modular Forms, University of Hawaii at Manoa, Honolulu, HI, March 6-8, 2012 (invited talk).
- 2012 Spring Western Section AMS Meetings, University of Hawaii at Manoa, Honolulu, HI, March 3-4, 2012 (invited talk).
- AMS/MAA Joint Meetings, Boston, Massachusetts, January 4-7, 2012 (invited talk and session co-organizer).
- 2011 Fall Southeastern Section AMS Meeting, Wake Forest University, Winston-Salem, NC, September 24-25, 2011 (special session co-organizer).
- Mathfest 2011, Lexington, KY, August 4-6, 2011.
- The 25th Annual Automorphic Forms Workshop, Oregon State University, March 23-26, 2011 (contributed talk).
- Palmetto Number Theory Series (PANTS) XV, Clemson University, Feb. 19-20, 2011 (contributed talk).
- The Number Theory of Partitions, Emory University, January 21-23, 2011 (invited talk).
- AMS/MAA Joint Meetings, New Orleans, Louisiana, January 6-9, 2011 (contributed talk).
- West Coast Number Theory Conference 2010, December 15-18, 2010 (contributed talk).
- Palmetto Number Theory Series (PANTS) XIII, UNC-Greensboro, Sept. 25-26, 2010 (contributed talk).
- AMS/MAA Joint Meetings, San Francisco, California, January 13-16, 2010 (contributed talk).
- MathFest 2009, Portland, OR, August 5-8, 2009.
- Graduate workshop on Zeta functions,
*L*-functions, and applications, Utah Valley University, Orem, Utah, June 1-4, 2009 (contributed talk). - 2009 Spring Central Section AMS Meeting, Urbana, IL, March 27-29, 2009.
- Illinois Number Theory Celebration, University of Illinois, Urbana, March 25-26, 2009.
- Arizona Winter School 2009, University of Arizona, Tucson, March 14-18, 2009.
- Conference on Quadratic Forms, Sums of Squares, Theta Functions, and Integral Lattices, University of Florida, Gainesville, March 11-15, 2009 (invited talk).
- AMS/MAA Joint Meetings, Washington DC, January 5-8, 2009 (invited talk).
- MathFest 2008, Madison, WI, July 31-August 2, 2008.
- Canadian Number Theory Association X Meeting, University of Waterloo, July 13-18, 2008 (contributed talk).
- 2008 Spring Eastern Section AMS Meeting, New York, March 15-16, 2008 (invited talk).
- Computing arithmetic spectra, AIM workshop, March 10-14, 2008.
- AMS/MAA Joint Meetings, San Diego, California, January 6-9, 2008 (invited talk).
- 2006 Fall Southeastern Section AMS Meeting, Fayetteville, November 3-4, 2006 (invited talk).
- 2006 Fall Western Section AMS Meeting, Salt Lake City, October 7-8, 2006 (invited talk).
- The 20th Annual Workshop on Automorphic Forms and Related Topics, The University of Colorado at Boulder, March 29-April 3, 2006.
- Workshop on Intersections of Arithmetic Cycles and Automorphic Forms, Le Centre de recherches mathématiques, Université de Montréal, December 12-16, 2005 (invited talk).
- Midwest Number Theory Conference for Graduate Students III, University of Wisconsin-Madison, November 5-6, 2005 (contributed talk).
- Singular Moduli and Equidistribution, NSF FRG Conference, University of Maryland, College Park, October 7-9, 2005 (contributed talk).
- Bretton Woods Workshop on Multiple Dirichlet Series, Bretton Woods, July 11-14, 2005.
- The 19th Annual Workshop on Automorphic Forms and Related Topics, University of North Texas, March 17-20, 2005 (contributed talk).
- Midwest Number Theory Conference for Graduate Students and Recent PhDs II, University of Illinois, Urbana-Champaign, February 5-6, 2005 (contributed talk).
- Conference on Additive Number Theory, University of Florida, Gainesville, November 17-20, 2004 (contributed talk).
- Arakelov Theory and Modular Forms, NSF FRG Conference, University of Wisconsin-Madison, September 16-19, 2004.
- Midwest Number Theory Conference for Graduate Students and Recent PhDs, University of Wisconsin-Madison, October 25-26, 2003.
- Southern California MAA Section Meeting, Harvey Mudd College, March 8, 2003.
- AMS/MAA Joint Meetings, Baltimore, Maryland, January 15-18, 2003 (invited talk).
- The Tenth International Conference on Fibonacci Numbers and Their Applications, Northern Arizona University, June 24-28, 2002 (contributed talk).
- AMS/MAA Joint Meetings, San Diego, California, January 6-9, 2002 (contributed talk).

- Presentation to the North Carolina Governor's school, July 23, 2016.
- Co-organizer, 2016 Automorphic Forms Workshop, Wake Forest University, March 7-10, 2016.
- Wake Forest library planning committee, Fall 2015-Spring 2019. (Chair from Fall 2017-present.)
- Presentation to the North Carolina Governor's school, July 25, 2015.
- Pro Mathematica Arte Council, 2015-present.
- Presentation to the North Carolina Governor's school, July 19, 2014.
- Active on MathOverflow.
- Career day presentation at Whitaker Elementary School, September 27, 2013.
- Presentation to the North Carolina Governor's school, July 13, 2013.
- Co-organizer of PANTS XVIII conference, Wake Forest University, September 15-16, 2012.
- Presentation to the North Carolina Governor's school, July 3, 2012.
- Co-organizer of MAA Invited Paper Session on Unsolved Problems, AMS-MAA Joint Meetings, Boston, MA, January 4-7, 2012.
- Co-organizer of Special Session Modular Forms, Elliptic Curves, and Related Topics, AMS Fall Southeastern Section Meeting, Wake Forest University, September 24-25, 2011.
- Presentation to the North Carolina Governor's school, June 21, 2011.
- Presentation to the UIUC MATRIX math club, November 18, 2009.
- Co-organizer, UIUC Number Theory Seminar, 2009-2010.
- Co-coordinator, Project NExT sessions, 2009 AMS-MAA Joint Meetings, Washington DC.
- UIUC Putnam committee, 2008-2010.
- Organizer, UIUC Number Theory Seminar, 2007-2008.
- Co-organizer of Midwest Number Theory Conference for Graduate Students III, November 2005.
- Co-organizer of Student Number Theory Seminar, Spring 2005.
- Speaker at East High School Math Week, 2005.
- Participant in Sidewalk Math, 2005.
- Reviewer for Mathematics Reviews.
- Refereeing for Acta Arithmetica, Algebra and Number Theory, American Mathematical Monthly, Bulletin of the Australian Mathematical Society, Bulletin of the London Mathematical Society, Canadian Journal of Mathematics, Experimental Mathematics, Integers, International Journal of Number Theory, Involve, Journal of Integer Sequences, Journal of Number Theory, Mathematics of Computation, Mathematics Magazine, Proceedings of the American Mathematical Society, Ramanujan Journal, Research in Number Theory, and Thai Mathematics Journal.
- Judge, Undergraduate Poster Session, AMS-MAA Joint Meetings, 2009 and 2012.
- NSF proposal panelist (twice).
- NSF proposal reviewer.

- Running.
- Studied French for four years. Studied in France during the summers of 1996, 1997.
- Interest in singing choral music. Participation (in various settings) from 1997-present.

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