|
Tom Braden, Associate Professor |
 |
|
|
| Personal Webpage |
|
| Office | LGRT 1240 | | Phone | (413) 545-1732 | | Fax | (413) 545-1801 | | Email | braden <at> math.umass.edu | |
| Mailing Address |
| Department of Mathematics and Statistics |
| Lederle Graduate Research Tower |
| University of Massachusetts |
| Amherst, MA 01003-9305 |
|
|
| Office Hours: Tuesdays 2-3, Thursdays 3-4 |
| Courses |
| Fundamental Concepts of Mathematics and 1 credit co-seminar |
| Math 300.1 (MWF 10:10 - 11:00 am, LGRT 113) |
| |
| Affine and Projective Geometry |
| Math 461 (MWF 1:25 - 2:15 pm, LGRT 119) | | |
|
| 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 and singularities of algebraic varieties; intersection (co)homology and perverse sheaves; Schubert varieties, toric varieties, and their generalizations; connections to combinatorics and representation theory. |
|
| Prof. Braden studies the topology of singular algebraic varieties, especially 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. |
|
| Selected Publications |
| 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 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. |
|
