Jeremy Rouse

University of Illinois, Urbana-Champaign
Department of Mathematics
301 Altgeld Hall
1409 W. Green Street
Urbana, IL 61801
(217) 333-3504
jarouse at math dot uiuc dot edu
http://www.math.uiuc.edu/~jarouse

Professional Positions

• J. L. Doob Research Assistant Professor, August 2007-present, University of Illinois, Urbana-Champaign.

Education

• Ph. D. in Mathematics, University of Wisconsin, Madison, 2007
Field: Number Theory
Minor: Analysis

• M. A. in Mathematics, University of Wisconsin, Madison, 2005.
• B. S. in Mathematics, Harvey Mudd College, 2003
High Distinction
Honors in Mathematics

• Budapest Semesters in Mathematics, Spring 2002

Research Interests

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

Publications

• S. Ahlgren, J. Rouse, 'Critical L-values of level p newforms (mod p),' accepted for publication in International Mathematics Research Notices.
• S. Ahlgren, D. Choi, J. Rouse, 'Congruences for level four cusp forms,' Mathematical Research Letters, 16 (2009), no. 4, 683-701.
• N. Boston, M. Darnall, J. Getz, G. Mantilla, H. Nover, E. Ozman, R. Rhoades, J. Rouse, M. Ruiz, M.-H. Sengun, L. Solomou, S. Turkelli, M. Woodbury, 'The Proof of Fermat's Last Theorem,' submitted.
• 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 $\Delta$-function,' Bulletin of the London Mathematical Society, 40 (2008), 1081-1090.
• R. Jones, J. Rouse, 'Galois Theory of Iterated Endomorphisms,' accepted for publication in Proceedings of the London Mathematical Society.
• 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), 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_m^L divide F_n? A Combinatorial Solution,' Applications of Fibonacci Numbers, Volume 10, Kluwer Academic Publishers, (2006), pg. 35-41.
• 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.

Student Research Involvement

• Jeff Mudrock (UIUC Undergraduate), 2009-2010.
• 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.

Teaching/Mentoring

• 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.

Awards

• 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.

Seminars

• 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, Oct. 13, 2009.
• The Birch and Swinnerton-Dyer Conjecture, University of Illinois, Urbana-Champaign, Apr. 7, 2009.
• Primes dividing recurrence sequences, University of Illinois, Urbana-Champaign, Jan. 20, 2009.
• Modular forms with coefficieints supported on finitely many square classes (mod l), University of Illinois, Urbana-Champaign, Oct. 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, Feb. 7, 2008.
• Bounds for the coefficients of powers of the $\Delta$-function, University of Illinois, Urbana-Champaign, Oct. 11, 2007.
• Iterated endomorphisms of abelian algebraic groups, University of Illinois, Urbana-Champaign, Sept. 4, 2007.
• Almost-square primes, University of Wisconsin-Madison, Jan. 31, 2006.
• Traces of singular moduli on Hilbert modular surfaces, University of Wisconsin-Madison, Nov. 10, 2005.
• The arithmetic of Borcherds products for Hilbert modular forms, University of Wisconsin-Madison, Jan. 27, 2005.
• Vanishing and non-vanishing of traces of Hecke operators, University of Illinois, Urbana-Champaign, Sept. 21, 2004.
• Vanishing and non-vanishing of traces of Hecke operators, University of Wisconsin-Madison, Sept. 9, 2004.

Conferences

• 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).

Service

• Presentation to the UIUC MATRIX math club, November 18, 2009.
• Co-organizer, UIUC Number Theory Seminar, 2009-2010.
• Judge, Undergraduate Poster Session, 2009 AMS-MAA Joint Meetings, Washington DC.
• 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 Bulletin of the London Mathematical Society, Canadian Journal of Mathematics, Experimental Mathematics, Integers, International Journal of Number Theory, Involve, Mathematics of Computation, Mathematics Magazine, Proceedings of the American Mathematical Society, and The Ramanujan Journal.

Additional Information

• 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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