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.