Leslie Saper
Professor of Mathematics
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 wellknown HodgedeRham 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 L²growth 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 HasseWeil zeta function. This should be viewed as an object on the topological side of the above picture. On the analytic side, Langlands has associated Lfunctions to certain automorphic representations. The issue of whether one may express the HasseWeil zeta function in terms of automorphic Lfunctions, and the relation of special values of these functions to number theory, are important fundamental problems which are motivating Professor Saper's research.
Office Hours
(on Zoom) Wednesdays 10:30 am – 11:30 am, Thursdays 2:00 pm – 3:00 pm, and by appointment.
Current Appointments & Affiliations

Education, Training, & Certifications



Selected Grants



Recent Courses

Advising & Mentoring

Ph.D. Students Supervised:
 Mingxue (Dena) Zhu Ho, Realizing Hecke Actions on Modular Forms via Cohomology of Dessins d'Enfants (February 2018  June 2021)
 Josh Cruz, Examples of the Local L^{2}Cohomology of Algebraic Varieties (April 9, 2015  May 15, 2020)
 Oliver Gjoneski, Cohomology of Arithmetic Groups, and MultiVariable Period Polynomials Associated to Cusp Forms, (January, 2007  May 15, 2011)
 Dan Yasaki, On the Existence of Spines for Qrank 1 Groups, (January 1, 2001  May 15, 2005)
 Charles Vuono, The Kodaira Embedding Theorem for Kähler Varieties with Isolated Singularities, (September 1, 1989  May 31, 1992)
Undergraduate Theses Directed:
 Kyle Casey, Siegel Modular Forms, (October 30, 2014  May 15, 2016)
 Alexander Wertheim, Complex Multiplication on Elliptic Curves, (April 4, 2013  May 15, 2014)
 Brandon Levin, Class Field Theory and the Problem of Representing Primes by Binary Quadratic Forms, (November 29, 2004  May 15, 2007)
Graduate Mentoring: one entering graduate student each year as assigned by the Director of Graduate Studies
Undergraduate Major Advising: three to four undergraduate majors each year as assigned by the Director of Undergraduate Studies
Other undergraduate mentoring through a AWM mentoring group.
Postdoctoral Mentoring: usually one per year



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