KARTIK PRASANNA
Work Address:
Department of Mathematics,
University of Michigan,
530 Church Street,
Ann Arbor, MI 48109.
Contact information:
(734) 764-0364 (w)
E-mail: kartikp@umich.edu
Citizenship
Indian citizen, US permanent resident.
Education
Princeton University, Princeton, NJ.
Ph.D. in Mathematics, November 2003. Advisor: Prof. Andrew Wiles.
Indian Institute of Technology, Bombay.
M.Sc. in Mathematics, July, 1998.
Masters thesis under the supervision of Prof. V.Srinivas (Tata Institute) and Prof. J.K.Verma.
Employment
September 2015 - present, Professor, University of Michigan.
September 2009 - August 2015, Associate Professor, University of Michigan.
August 2006 - July 2009, Assistant Professor, University of Maryland. (On leave of absence,
academic year 2006-2007)
September 2003 - June 2006, Hedrick Assistant Professor, UCLA.
Visiting
Positions
April - August 2007, Mcgill University and CRM, Montreal.
Feb - March 2007, Tata Institute of Fundamental Research, Mumbai.
Sep 2006 - Jan 2007, University of Paris, 13
Administrative
service
Director of graduate admissions, University of Michigan, 2015 - 2016.
Executive committee, University of Michigan, 2013 - 2014.
Personnel committee, University of Michigan, 2010 - 2012.
Editorial
service
Awards and
Distinctions
Associate editor, Advances in Mathematics.
Simons Fellow in mathematics
Academic year 2014-15.
von Neumann fellowship, Institute for Advanced Study
Academic year 2014-15.
Robert Sorgenfrey Distinguished Teaching Award
UCLA, June 2005.
Institute Silver Medal for the Highest graduating Math Major
Indian Institute of Technology, Bombay, July 1998.
International Mathematics Olympiad 1992-1993 (Indian team)
Bronze medallist, 1993.
Indian National Mathematics Olympiad 1992
Ranked 5th.
National Talent Search Scholar, India, 1990
Grants
Simons Foundation (Simons fellowship), 2014-15, $ 97,441.
NSF Grant, Arithmetic of Automorphic forms: cycles, periods and p-adic L-functions, DMS
1160720, 2012-2015, $ 400,000.
NSF Grant, FRG: Collaborative Research: Automorphic forms, Galois representations, periods and p-adic L-functions, DMS 0854900, 2009-2013. $ 275,171.
NSF Grant, Algebraic cycles, L-functions and rational points on elliptic curves, DMS
1015173; previously NSF Grant DMS-0801191, 2008-2012, $ 125,993.
Research
Interests
Shimura varieties, automorphic forms, theta correspondences, special values of L-functions,
p-adic L-functions, algebraic cycles.
Publications
1. Integrality of a ratio of Petersson norms and level-lowering congruences.
Ann. of Math., 163, (2006), no. 3, 901-967.
2. Arithmetic aspects of the theta correspondence and periods of modular forms.
Eisenstein Series and Applications, Progress in Math. Vol 258, Birkhauser 2008,
251-269.
3. Arithmetic properties of the Shimura-Shintani-Waldspurger correspondence (with an appendix by Brian Conrad).
Invent. Math., 176 (2009), no. 3, 521-600.
4. On p-adic properties of central L-values of quadratic twists of an elliptic curve.
Canad. J. Math, Vol. 62 (2), 2010 pp. 400-414.
5. On the Fourier coefficients of modular forms of half-integral weight.
Forum Math., Volume 22 (2010), Issue 1, pp. 153-177.
6. p-adic Rankin L-series and rational points on CM elliptic curves, with M. Bertolini and H.
Darmon.
Pacific Journal of Math, (Jonathan Rogawski Memorial Issue), Vol. 260, No. 2., 2012,
pp. 261-303.
7. Chow-Heegner points on CM elliptic curves and values of p-adic L-functions, with M.
Bertolini and H. Darmon.
IMRN, vol 2014 (2014), 745-793.
8. Generalized Heegner cycles and Rankin L-series, with M. Bertolini and H. Darmon and
an appendix by Brian Conrad.
Duke Math Journal 162 (2013), no. 6, pp. 1033-1148.
9. p-adic L-functions and Euler systems: a tale in two trilogies, with M.Bertolini, F. Castella,
H. Darmon, S. Dasgupta and V. Rotger.
Survey article to appear in LMS Durham Symposium on Automorphic Forms and Galois
representations, 40 pages.
10. p-adic L-functions and the coniveau filtration on Chow groups, with M. Bertolini and H.
Darmon and an appendix by Brian Conrad.
Crelle, 66 pages, to appear.
Preprints:
11. Periods of quaternionic Shimura varieties. I., with A. Ichino.
Preprint, Dec 2015, 173 pages.
In preparation:
12. Automorphic cohomology, motivic cohomology and the adjoint L-function, with A.
Venkatesh.
13. Periods of quaternionic Shimura varieties. II, III, with A. Ichino.
14. On algebraic cycles attached to certain Rankin-Selberg L-functions, with A. Ichino.
15. Hodge classes on products of quaternionic Shimura varieties, with A. Ichino.
16. Cycles on unitary Shimura varieties and p-adic L-functions, with C. Skinner.
Professional
Service
Referee for JAMS, Ann. of Math., Inventiones, Journal of Algebra and Number theory, Duke
Mathematical Journal, Documenta Mathematica, Annales de L’Institut Fourier, Commentarii Math Helvetica, American Journal of Mathematics, Math. Zeitschrift, Math. Annalen,
Manuscripta Math; Reviewer for European Research Council Advanced Grants and served
on NSF panels.
Organized an FRG/RTG workshop on L-functions, Galois representations and Iwasawa theory, May 2011 with about 110 participants.
Invited Talks
At workshops, conferences and colloquiua:
Midwest Number theory conference, October 2015.
Colloquium, Tata Institute of Fundamental Research, August 2015.
Upstate New York Number theory conference, April 2015.
Workshop on the Kudla program, CRM Montreal, April 2015.
JHU-UMD Algebra and Number theory day, March 2015.
Meeting on Algebraic cycles and related topics (2 talks), Tata Institute of Fundamental Research, December 2014.
Colloque de mathématiques de Montréal CRM - ISM, Montreal, November 2014.
FRG workshop on Periods of automorphic forms and applications (2 talks), Stanford, June
2013.
Workshop on Rational points, Oxford, Sep 2012.
Conference in honor of Haruzo Hida’s 60th birthday, UCLA, June 2012.
Montreal-Toronto number theory weekend, Keynote talk, April 2012.
Banff workshop on Cycles on modular varieties, October 2011.
Arizona Winter School, course on Periods and special values of L-functions, March 2011.
Motives and Modular forms, a conference in honor of Don Blasius on his 60th birthday,
UCLA, November 2010.
RTG/FRG workshop on Modular/geometric Iwasawa theory and p-adic L-functions, UCLA,
June 2010 (2 talks)
Atkin Memorial conference, University of Illinois at Chicago, May 2010.
Advanced Course on Algebraic Cycles, Modular Forms, and Rational Points on Elliptic
Curves ( 8 hours), CRM, Barcelona, Dec 2009.
Explicit Methods in number theory, Oberwolfach, July 2009.
Palmetto Algebra and Number theory seminar (Plenary talk), Clemson University, Feb 2009.
Colloquium, University of Michigan, Nov. 2008
International conference on major developments in number theory: Selmer Groups, Lfunctions, and Galois Deformations, UCLA, March 2008, 2 talks.
International colloquium on Cycles, motives and Shimura varieties, Tata Institute, Bombay,
Jan 2008.
Colloquium, University of Wisconsin, Oct. 2007.
Colloquium, Indian Institute of Technology, Bombay, March 2007.
International conference on arithmetic algebraic geometry, El Escorial, Spain, Aug. 2006.
Colloquium: University of Montreal, Feb. 2006.
Colloquium: University of Illinois, Urbana-Champaign, Feb. 2006.
Colloquium: Univ. of Illinois, Chicago, Jan. 2006.
Colloquium: Univ. of Utah, Jan. 2006.
Colloquium: Univ. of California, Santa Cruz, Jan. 2006.
Colloquium: Tata Institute, Bombay, Dec. 2005.
Conference on L-functions, Kyushu University, Fukuoka, Japan, Feb. 2006.
Conference on Eisenstein series and applications, American Institute of Mathematics, Aug.
2005.
Number theory/automorphic forms seminars:
University of Chicago number theory seminar, April 2016.
Northwestern number theory seminar, April 2016.
Stanford University number theory seminar, April 2016.
Columbia-NYU Joint Number theory seminar, February 2015.
Kyoto University, May 2014.
University of Wisconsin, April 2014.
TIFR, August 2013 (series of 3 talks).
Stanford University, Feb 2013.
University of Chicago, Feb 2012.
Indian Institute of Technology, Bombay, August 2011.
Tata Institute of Fundamental Research, Mumbai, August 2011.
Princeton/IAS number theory seminar, March 2011.
Michigan State University, November 2010.
University of Chicago, April 2010.
Caltech, March 2010.
MIT (Boston College-MIT joint number theory seminar), Feb 2009.
Clemson University, Palmetto Algebra and Number theory seminar (Plenary talk), Feb 2009.
Johns Hopkins University, Mar. 2008.
NYU (New York Joint number theory seminar), Feb 2008.
Princeton University, Nov. 2007.
Univ. of Michigan, Nov. 2007.
Univ. of Wisconsin, Oct. 2007.
Mcgill University, Apr. and Aug. 2007 (3 talks).
TIFR, Mar. 2007 (2 talks).
Universite Paris-Sud, Nov. 2006.
Universite Paris 6-7, Oct. 2006.
Ohio State, May 2006.
Columbia University (New York Joint number theory seminar), March 2006.
MIT, Feb 2006.
University of Maryland, Nov. 2005.
Princeton University, Nov. 2005.
UCLA, Oct. 2005.
Mcgill University, Sep. 2004.
Caltech, Feb. 2004.
UC San Diego, Nov. 2003.
Univ. of Michigan, Mar. 2003.
Expository
talks
1. University of Michigan, What is Iwasawa theory ? , Nov. 2008.
2. Zhejiang University, Hangzhou, China, International summer school on Arithmetic, Geometry and Topology of Shimura varieties, 7 lectures on Complex multiplication and Shimura
curves, June 2005.
3. UCLA, Working seminar on π1 (P1 \ {0, 1, ∞}) (5 lectures, Spring 2004).
4. Princeton University, Working Seminars on Weil Conjectures (Fall 1999), Perverse sheaves
(Spring 2000), Canonical models of Shimura Varieties (Fall 2001).
5. Indian Institute of Technology, Bombay, Rational Points on Curves, Lecture Series, Autumn Semester 1997.
Teaching
and
Mentoring
Undergraduate classes:
University of Michigan:
Math 217: Linear Algebra. 2 sections, Fall 2015.
Math 494: Honors Algebra II, Winter 2014.
Math 493: Honors Algebra I, Fall 2013.
Math 115: Calculus I, Winter 2013.
Math 575: Number theory, Fall 2012.
Math 115: Calculus I, Fall 2011.
Math 412: Introduction to Modern Algebra, Winter 2010.
University of Maryland:
Linear Algebra, Fall 2007.
UCLA:
Ordinary differential equations, Spring 2006.
Abstract Algebra, Winter and Spring 2006.
Honors Linear Algebra, Spring 2005.
Finite Mathematics, Lower Division, Winter 2005.
Algebra, Upper division, Fall 2003, Fall 2004.
Complex Analysis, Upper division, Fall 2003.
Number theory, Upper division, Winter 2004.
Linear Algebra, Lower division, Spring 2004.
Princeton University:
Linear Algebra and Multivariate Calculus for Economists, Fall 2002 and Spring 2003.
Graduate classes:
Math 678: Rational points on elliptic curves, Winter 2014, Michigan.
Math 679: Elliptic curves, Fall 2011, Michigan.
Math 776: Class Field Theory, Winter 2011, Michigan.
Math 678: Introduction to Iwasawa theory, Fall 2009, Michigan.
Abstract Algebra, Fall 2008, Spring 2009, UMD.
Introduction to Iwasawa theory, Spring 2008, UMD.
Introduction to Arakelov theory, Fall 2005, UCLA.
Research Interation Teams:
Modular forms, Fall 2007, UMD.
Modular curves and Galois representations, Spring 2008, UMD.
Graduate students:
Graduated (with year of graduation and subsequent positions):
1. Hunter Brooks (2013), Postdoc at EPFL, Lausanne (2013-2017).
2. Ari Shnidman (2015), Postdoc at Boston College, (2015-2018).
Current students:
3. Adam Kaye
4. Suchandan Pal
5. Charlotte Chan
6. Brandon Carter