People
Faculty
Professor Beasley studies formal aspects of quantum field theory and string theory. He works on gauge theory, as well as problems concerning manifolds with special holonomy.
Professor Braverman works in analysis on manifolds, index theory, and analytic torsion.
Professor Halacheva works in representation theory and low-dimensional topology, and the interplay of emerging geometric, combinatorial, and categorical structures within. Topics of her research include quantum groups and crystals, and the associated braid and cactus group actions; Rickard complexes and perverse equivalences on categorifications; dualities between Lie and diagram algebras; Schubert calculus; as well as a topological perspective on the Kashiwara-Vergne conjecture.
Professor Marian works on moduli theory in algebraic geometry.
Professor Toledano Laredo works in representation theory, particularly loop groups and quantum groups, and its relation to mathematical physics and algebraic geometry. One of the themes of his research has been to explore how quantum groups describe the branching behaviour, or monodromy of solutions of certain systems of differential equations in the complex domain.
Professor Weitsman works in quantum field theory, combinatorics, symplectic geometry, and the role of mathematical physics in geometry and topology.
Professor Yakimov works in the areas of Noncommutative Algebra, Cluster Algebras, Representation Theory, Triangulated Categories, Poisson Geometry and Integrable Systems. His work concerns the structure of monoidal triangulated categories, cluster structures on coordinate rings, categorifications and Poisson geometry of cluster algebras, representation of quantum groups, Poisson Lie groups and the bispectral problem.
Former RTG Faculty
Professor Castravet works in algebraic geometry, especially birational geometry and moduli spaces. She is also interested in arithmetic geometry, combinatorics, and computational algebraic geometry.
Professor Hogancamp’s research is centered on low-dimensional topology and categorification, and interfaces many other areas of mathematics, including representation theory, algebraic geometry, combinatorics and mathematical physics.
Professor King studies nilpotent orbits associated with semisimple Lie groups as symplectic manifolds and algebraic varieties. He investigates the interplay of these properties with issues in representation theory.
Professor Loseu works in Representation theory including that of reductive algebraic groups and Lie algebras, W-algebras, Symplectic reflection algebras, quantum groups and quantum Hamiltonian reductions. He is also interested in related subjects such as Kac-Moody categorifications, Hamiltonian group actions, Deformation quantization, combinatorics of crystals and geometry of symplectic resolutions of singularities.
Professor Macrì works in algebraic geometry, homological algebra and derived category theory, with applications to representation theory, enumerative geometry and string theory.