Algebra, Combinatorics, and Geometry

Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh. A number of the ongoing research projects are described below. The group also offers a PhD program.

PhD in mathematics with the the Algebra, Combinatorics, and Geometry Group >

Research

Arithmetic of Shimura Varieties
The theory of Shimura varieties lies at the intersection of number theory, algebraic geometry, and the theory of automorphic representations. It plays a key role in the Langlands program as a source of Galois representations attached to automorphic f
Combinatorial and Statistical Designs, Set and Graph Partitions
Combinatorial and Statistical Designs, Set and Graph Partitions
Cryptography and Quantum Computation
Kaveh has a side interest in applications of algebraic geometry and representation theory in cryptography and quantum computation.
Equivariant Cohomology
The equivariant cohomology along with the celebrated localization formula provides a strong tool in computing usual cohomology of a geometric object equipped with action of a group.
Formal Theorem Proving
In a formal proof, all of the intermediate logical steps of a proof are supplied. No appeal is made to intuition, even if the translation from intuition to logic is routine. Thus, a formal proof is less intuitive and yet less susceptible to logical e
Lie theory, Representation theory
Ion's main research area is Lie theory/representation theory. Most recently, he has been interested in Macdonald theory, which provides an uniform framework for the study of several questions regarding the spherical harmonic analysis of real/p-adic r
Motivic Integration and Representation Theory
Several years ago, M. Kontsevich created a new type of integration, called motivic integration, where the values of integrals are not numbers but geometric objects.
Newton-Okounkov Bodies
The theory of Newton-Okounkov bodies attempts to generalize the correspondence between toric varieties and convex polytopes, to arbitrary varieties (even without presence of a group action).
Non-Commutative Algebra and Geometry
Ion maintains an active interest in several topics in non-commutative algebra/geometry: deformation quantization, (finite dimensional) Hopf algebras, graded rings, and categories.
Sphere Packings and Discrete Geometry
The Kepler conjecture asks what is the densest packing of congruent balls in three-dimensional Euclidean space.
Symmetries and Dualities in Physics
Sati's research is interdisciplinary and lies in the intersection of geometry and mathematical/theoretical physics.

Contact Us

The Dietrich School of
Arts and Sciences
301 Thackeray Hall
Pittsburgh, PA 15260
Phone: 412-624-8375
Fax: 412-624-8397
math@pitt.edu

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