Location
LGRT 1555

Prof. Braden studies the topology of singular algebraic varieties, especially ones with a combinatorial nature such as toric varieties and Schubert varieties. He uses invariants like intersection cohomology to extract information about the combinatorial structure of polytopes and Coxeter groups from these varieties. A major theme in his work is lifting or "categorifying" relations and inequalities among combinatorial invariants by showing that they arise from canonical relations among topological invariants; an inequality might arise from showing that a map of cohomology groups is an injection, for instance. These relations are studied by working equivariantly, using the symmetries imposed by large groups acting on the varieties.

Education

Ph.D. Massachusetts Institute of Technology, 1995

Cambridge University (part III of mathematics tripos), 1991

B.A. University of Chicago, 1990

RESEARCH INTERESTS

Topology of algebraic varieties; Representation Theory; Combinatorics

Selected Publications

  • T. Braden, J. Huh, J. Matherne, N. Proudfoot and B. Wang, A semi-small decomposition of the Chow ring of a Matroid, Adv. Math, 409 Part A (2022), article 108646.
  • T. Braden, A. Licata, N. Proudfoot and B. Webster, Quantizations of conical symplectic resolutions II: category O and symplectic duality, Astérisque 384 (2016), 75-179.
  • T. Braden, N. Proudfoot and B. Webster, Quantizations of conical symplectic resolutions I: local and global structure, Astérisque 384 (2016), 1–73.
  • T. Braden, A. Licata, N. Proudfoot and B. Webster, Gale duality and Koszul duality, Adv. Math. 225 (2010), no. 4, pp. 2002-2049.
  • T. Braden and N. Proudfoot, The hypertoric intersection cohomology ring, Invent. Math. 177 (2009), no. 2, 337--379.
  • T. Braden and V. Lunts, Equivariant-constructible Koszul duality for dual toric varieties, Adv. Math. 201 (2006), no. 2, 408-453.
  • T. Braden, Hyperbolic localization of intersection cohomology, Transform. Groups 8, no. 3, (2003), 209-216.
  • T. Braden and S. Billey, Lower bounds for Kazhdan-Lusztig polynomials from patterns, Transform. Groups 8, no. 4, (2003), 321-332.
  • T. Braden and R. MacPherson, From moment graphs to intersection cohomology, Math. Ann. 321 (2001), no. 3, 533-551.
  • T. Braden and R. MacPherson, Intersection homology and a conjecture of Kalai, Comment. Math. Helv. 74 (1999), no. 3, 442--455.