Geometry Seminar
Spring 2008
Fridays at 4 pm in Milner 216

Format: Talks are 50-60 minutes, with the option to continue after a short break.
* List below includes Department Colloquia and Frontiers Lectures with geometric content.

* Approximately once a month the geometry group meets with the physics department for a joint Geometry & String Theory seminar.

January 18

January 25

February 1
Geometry & String Theory Seminar
D. Morrison (Duke U. & U.C. Santa Barbara)

February 7 (Department Colloquium)
Sebastian Casalaina-Martin
Curves, abelian varieties, and the moduli of cubic threefolds.
A result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this talk I will discuss the possible degenerations of these abelian varieties, and give a description of the compactification of the moduli space of cubic threefolds obtained in this way. The relation between this compactification and those constructed in the work of Allcock-Carlson-Toledo and Looijenga-Swierstra will also be considered, and is similar in spirit to the relation between the various compactifications of the moduli spaces of low genus curves. This is joint work with Radu Laza.

February 8

February 15

February 22--24
Texas Geometry and Topology Conference at Texas Tech.

February 29
R. Harvey (Rice U.)
Potential theory in a general geometric setting.

March 7
Geometry & String Theory Seminar
Tony Pantev (U. Penn.)
Mirror symmetrry for del Pezzo surfaces
I will review recent progress in mirror symmetry for del Pezzo surfaces, and will describe a joint work in progress with D.Auroux, L.Katzarkov, and D.Orlov giving an explicit formula for the mirror map in the del Pezzo case. I will also discuss non-trivial tests on Kontsevich's homological mirror symmetry conjecture in this setting.

March 14
No seminar, Spring Break.

March 21
Sabin Cautis (Rice U.)
Knot invariants using algebraic geometry.
I will describe an algebraic geometer's view of knot invariants. This includes a geometric construction of knot invariants such as Khovanov homology by looking at certain flag-like varieties.

March 28
N. R. Wallach (U.C. San Diego)
Euler polynomials, Hilbert polynomials and Hilbert series.
The Euler polynomial of degree n has as its k-th coefficient the number of permutations of n with exactly k descents. We show how to use these polynomials to relate the Hilbert polynomial and the Hilbert series for projective imbeddings with normal cones. For homogeneous (under an affine algebraic group) projective varieties we demonstrate how these results can be used to derive explicit formulas for degrees and Hilbert series. This is joint work with Benedict Gross.

April 4
Geometry & String Theory Seminar (in ENPH 501)
Ilarion Melnikov (U. Chicago)
Half-twisted sigma models and generalized Gromov-Witten invariants.
It is well known that certain twisted quantum field theories compute generating functions for Gromov-Witten invariants of a large class of interesting spaces: e.g. projective toric varieties or hypersurfaces therein. These twisted theories may often be deformed to half-twisted models. In this talk I will describe the deformed theories and present computational techniques that lead to a generalization of the well-known generating functions of genus zero Gromov-Witten invariants for projective toric varieties. I will also describe work in progress to extending these techniques to Calabi-Yau three-folds.

April 11--13
Texas Algebraic Geometry Seminar, Rice University.

April 18

April 25