Leslie D. Saper, Professor and Associate Chair

Contact Info:

Office Location:	110 Physics Bldg
Office Phone:	(919) 660-2843
Email Address:
Web Page:	https://www.math.duke.edu/faculty/saper

Teaching (Fall 2008):

• MATH 121.01, INTRO ABSTRACT ALGEBRA Synopsis

  Physics 119, TuTh 08:30 AM-09:45 AM

Teaching in Previous Semesters

Office Hours:

Mondays, 10:30 - 12:00, Thursdays 2:00 - 3:30, and by appointment

Education:

Ph.D.	Princeton University	1984
B.S., M.S.	Yale University	1979

Specialties:

Geometry
Topology

Research Interests: Locally symmetric varieties, Automorphic forms,
L²-cohomology and intersection cohomology, Geometrical analysis of singularities

A central theme in mathematics has been the interplay between topology and analysis. One subject here is the representation of topological invariants (such as cohomology) by analytic means (such as harmonic forms). For compact manifolds this is the well-known Hodge-deRham theory. Professor Saper studies generalizations of these ideas to singular spaces, in particular complex algebraic varieties. In these cases, an appropriate replacement for ordinary cohomology is Goresky and MacPherson's intersection cohomology, while on the analytic side it is natural to impose L²-growth conditions.

When one deals with varieties defined by polynomials with coefficients in the rationals, or more generally some finite extension, this theory takes on number theoretic significance. Important examples of such varieties are the locally symmetric varieties. One may reduce the defining equations modulo a prime and count the number of resulting solutions; all this data is wrapped up into a complex analytic function, the Hasse-Weil zeta function. This should be viewed as an object on the topological side of the above picture. On the analytic side, Langlands has associated L-functions to certain automorphic representations. The issue of whether one may express the Hasse-Weil zeta function in terms of automorphic L-functions, and the relation of special values of these functions to number theory, are important fundamental problems which are motivating Professor Saper's research.

Curriculum Vitae

Current Ph.D. Students   (Former Students)

• Oliver Gjoneski  

Postdocs Mentored

• Jonathan Hanke (August 23, 2003 - August 31, 2007)  

Recent Conferences Organized

1. Workshop on Locally Symmetric Spaces, co-organizer with S. Kudla, J. Rohlfs, and B. Speh, Banff International Research Station, May 18, 2008 - May 23, 2008

Recent Publications   (More Publications)

1. Leslie D. Saper, -modules and micro-support, Annals of Math. (Accepted, latest revision 1/05) [math.RT/0112251]
2. Leslie D. Saper, L²-cohomology of locally symmetric spaces. I, Pure and Applied Mathematics Quarterly, vol. 1 no. 4 (2005), pp. 889–937 [MR2201005], [math.RT/0412353]
3. Leslie D. Saper, -modules and the conjecture of Rapoport and Goresky-MacPherson, in Formes Automorphes (I) -- Actes du Semestre du Centre Émile Borel, printemps 2000, Astérisque, edited by J. Tilouine, H. Carayol, M. Harris, M.-F. Vignéras, vol. 298 (2005), pp. 319--334, Société Mathématique de France [MR2141706], [math.RT/0112250]  [abs]
4. Leslie D. Saper, Geometric rationality of equal-rank Satake compactifications, Math. Res. Lett., vol. 11 no. 5 (2004), pp. 653–671 [MR2106233], [math.RT/0211138]  [abs]
5. Leslie D. Saper, On the cohomology of locally symmetric spaces and of their compactifications, in Current developments in mathematics, 2002, edited by David Jerison, George Lusztig, Barry Mazur, Tom Mrowka, Wilfried Schmid, Richard Stanley, & S.-T. Yau, Current developments in mathematics, 2002 (2003), pp. 219–289, Int. Press, Somerville, MA (reprinted in Lie Groups and Automorphic Forms, edited by L. Ji, et al., AMS/IP Studies in Advanced Mathematics, vol. 37, 2006.) [MR2062320], [math.RT/0306403]  [abs]

Selected Invited Lectures

1. Quadratic Reciprocity from Euler to Langlands, September 28, 2007, Graduate/faculty Seminar, Duke University, [abstract]    
2. Geometry and Topology of Locally Symmetric Spaces, January 8, 2007, Conference on Geometry, Topology, and their Interactions in honor of Farrell-Jones, Instituto de Matemáticas Unidad Morelia, Mexico    
3. Cohomology of Locally Symmetric Spaces, July 17 - August 4, 2006, International conference and instructional workshop on discrete groups, Morningside Center of Mathematics, Chinese Academy of Science, Beijing, China [slides]    
4. L²-Harmonic Forms on Locally Symmetric Spaces, January 19, 2006, Colloquium at Tata Institute for Fundamental Research, Mumbai, India [slides]    
5. L²-cohomology of locally symmetric spaces, International Conference In Memory of Armand Borel: Algebraic groups, arithmetic groups, automorphic forms and representation theory, 26 - 30 July, 2004, Center of Mathematical Sciences at Zhejiang University, China    
6. Cohomology of compactifications of locally symmetric spaces, 16 - 30 December 2003, a series of 4 talks at the Graduate School of Mathematical Sciences, University of Tokyo, Japan [talk 1, talk 2, talk 3, talk 4]    
7. On the Cohomology of Locally Symmetric Spaces and of their Compactifications (two lectures), 15-17 November 2002, Conference on Current Developments in Mathematics 2002, Harvard University, [talk 1,talk 2]    
8. Rapoport's conjecture on the intersection cohomology of the reductive Borel-Serre compactification, April 25, 2000, Conference on Galois representations and automorphic representations, Institut Henri Poincaré, Paris, France    
9. L₂-cohomology of Algebraic Varieties, August 23, 1990, Invited Address, International Congress of Mathematicians, Kyoto, Japan    

Recent Grant Support

• Cohomology of Locally Symmetric Spaces and Applications to Number Theory, National Science Foundation, DMS-05-02821, 2005/07-2008/06.