Algebra-Geometry-Combinatorics Seminar
Spring 2009
This seminar meets every Friday in the SFSU Mathematics Department (in Thornton Hall 211--directions to campus). For further information, please contact the seminar organizers (Federico Ardila, Matthias Beck, Joseph Gubeladze, and Serkan Hosten).
Dates for Spring 2009: Jan 30, Feb 13, Feb 20, Mar 20, May 1, May 4
30 January, 2009
3:10 p.m.
Brian Hopkins
Saint Peter's College
| Bulgarian solitaire and related operations on partitions |
| Given some coins split into piles, take one from each pile to create a new pile; repeat. This is the basis of the deterministic game Bulgarian solitaire, which can be cast as an operation on partitions. Where will you end up? What partitions will you never reach? We will survey results from the initial 1982 article through recent work and open questions. Also, the operation can be generalized to a family of operations from the Bulgarian solitaire move to conjugation. The same questions can be asked for all of these operators; a nice unifying solution to one such question will be presented. Proof techniques will include generating functions and combinatorial arguments on graphical representations of partitions. |
13 February, 2009
3:10 p.m.
Diane Maclagan
University of Warwick
| Polyhedral bounds on nef cones |
| The nef cone of a projective toric variety is a polyhedral cone associated to the polytope or polyhedral fan defining the toric variety. I will describe three combinatorially defined polyhedral cones associated to a polyhedral fan, which all equal the nef cone when the fan is the normal fan of a polytope, and introduce the question of understanding when these are equal. This is particularly interesting when the polyhedral fan is the space of phylogenetic trees, when the cones bound the nef cone of moduli space of genus zero curves with n marked points. This is joint work with Angela Gibney (Georgia). |
20 February, 2009
3:10 p.m.
Alan Stapledon
University of Michigan
| Ehrhart theory of Lawrence polytopes |
| Given a collection B = { b_1, ..., b_n } of non-zero vectors in Z^d, one can associate the f-vector and h-vector of the corresponding matroid, both of which encode the number of linearly independent collections of i elements in B, for 1<=i<=d. Analogously, one can associate to B a lattice polytope P, called a Lawrence polytope, and corresponding polynomials f_P (m) and delta_P(t), both of which encode the number of lattice points in all dilations of P. We will give an explicit description of delta_P(t) and, by considering a connection with the geometry of hypertoric varieties, deduce some non-trivial inequalities between its coefficients. |
13 March, 2009
3:10 p.m.
Maurice Rojas
Texas A&M University
1 May, 2009
No seminar.
MONDAY, 4 May, 2009
3:10 p.m.
Karola Meszaros
Massachusetts Institute of Technology
