# Tom Braden

Professor; Director, Graduate Program

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.

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Education

Ph.D. Massachusetts Institute of Technology, 1995

Cambridge University (part III of mathematics tripos), 1991

B.A. University of Chicago, 1990

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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.