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Leslie D. Saper, Professor and Director of Undergraduate Studies

Leslie D. Saper
Contact Info:
Office Location:  110 Physics
Office Phone:  (919) 660-2843
Email Address: send me a message
Web Page:

Teaching (Fall 2015):

  • Math 690-10.01, Algebraic Topology II Synopsis
    Physics 205, WF 08:30 AM-09:45 AM
Teaching in Previous Semesters
Office Hours:

Tuesdays and Fridays, 2:00 - 3:30, and by appointment.

Ph.D.Princeton University1984
B.S., M.S.Yale University1979

Research Interests: Locally symmetric varieties, Number theory and 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)

  • Joshua Cruz  
Postdocs Mentored

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. L. Ji, K. Murty, L. Saper, and J. Scherk, The Fundamental Group of Reductive Borel-Serre and Satake Compactifications, The Asian Journal of Mathematics, vol. 19 no. 3 (2015), pp. 465-486 [arXiv:1106.4810], [available here]  [abs]
  2. Leslie D. Saper, $\mathscr L$-modules and micro-support, Annals of Math. (Accepted, latest revision 1/05) [arXiv:math/0112251]
  3. Leslie D. Saper, L2-cohomology of locally symmetric spaces. I, Pure and Applied Mathematics Quarterly, vol. 1 no. 4 (2005), pp. 889–937 [MR2201005], [arXiv:math/0412353]
  4. Leslie D. Saper, $\mathscr L$-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], [arXiv:math/0112250]  [abs]
  5. Leslie D. Saper, Geometric rationality of equal-rank Satake compactifications, Math. Res. Lett., vol. 11 no. 5 (2004), pp. 653–671 [MR2106233], [arXiv:math/0211138]  [abs]
Selected Invited Lectures

  1. Perverse sheaves and the reductive Borel-Serre compactification, November 21-23, 2014, Conference on Hodge Theory and L2-cohomology, Johns Hopkins University, Baltimore    
  2. Raghunathan's Vanishing Theorem and Applications, December 28, 2011, Conference on Cohomology of Arithmetic Groups, Tata Institute for Fundamental Research, Mumbai, India    
  3. Cohomology of Locally Symmetric Spaces and the Moduli Space of Curves, June 09, 2011, Workshop on Arithmetic Groups vs. Mapping Class Groups, Mathematisches Forschungsinstitut Oberwolfach, Germany [abstract]    
  4. The congruence subgroup kernel and the reductive Borel-Serre compactification, March 1, 2011, Algebraic Geometry and Number Theory seminar at John Hopkins University, Baltimore    
  5. Self-dual sheaves and L2-cohomology of locally symmetric spaces, June 24, 2010, Conference on Spectral Analysis on Noncompact Manifolds at the Hausdorff Center for Mathematics, Bonn, Germany    
  6. Cohomology of Locally Symmetric Spaces, February 17, 2009, Colloquium at University of Michigan, Ann Arbor [slides]    
  7. $\mathscr L$-modules and the cohomology of locally symmetric spaces, December 15, 2008, International conference on Repr√©sentations des groupes de Lie et applications, Institut Henri Poincar√©, Paris, France    
  8. Cohomology of compactifications of locally symmetric spaces, September 8, 2008, Workshop on Topology of Stratified Spaces, Mathematical Sciences Research Institute, Berkeley    
  9. Quadratic Reciprocity from Euler to Langlands, September 28, 2007, Graduate/faculty Seminar, Duke University, [abstract]    
  10. 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    
  11. 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]    
  12. L2-Harmonic Forms on Locally Symmetric Spaces, January 19, 2006, Colloquium at Tata Institute for Fundamental Research, Mumbai, India [slides]    
  13. 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    
  14. 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]    
  15. 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]    
  16. 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    
  17. L2-cohomology of Algebraic Varieties, August 23, 1990, Invited Address, International Congress of Mathematicians, Kyoto, Japan
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
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