Spring 2007

**Wednesday 1/24**

No seminar**Wednesday 1/31**

Anne Shiu (UC Berkeley)

*Geometry of Rank Tests*__Abstract:__Convex rank tests are coarsenings of the hyperplane arrangement associated to the symmetric group. Semigraphoids are combinatorial structures that correspond to squares and hexagons on a polytope known as the permutohedron. These objects - convex rank tests and semigraphoids - are equivalent, and this result allows us to answer a question posed by Postnikov, Reiner, and Williams. No prior knowledge of hyperplane arrangements or permutohedra will be assumed.

This work originated in collaboration with the Pourquié lab at the Stowers Institute in Kansas City. We describe the experiments conducted to identify the molecular components of biological clocks, and explain how the convex rank test called the cyclohedron test contributes to time course microarray data analysis.**Wednesday 2/7**

No seminar**Wednesday 2/14**

Manoj Kummini

*Toric Varieties I***Wednesday 2/21**

Manoj Kummini

*Toric Varieties II***Wednesday 2/28**

Manoj Kummini

*Toric Varieties III***Wednesday 3/7**

Brandon Humpert

*k-Orientable Graphs***Wednesday 3/14**

Jeremy Martin

*Hyperplane Arrangements***Wednesday 3/21**

No seminar - Spring Break**Wednesday 3/28**

Bridget Franklin

*Building Codes from Difference Sets*(Undergraduate Honors presentation)**Wednesday 4/4**

Jenny Buontempo

*Tableau Cycling and Catalan Numbers***Wednesday 4/11**

Tom Enkosky

*Shellable and Cohen-Macaulay posets***Wednesday 4/18**

Tom Enkosky

Title TBA**Wednesday 4/25**

Ezra Miller (University of Minnesota)

*Combinatorics of permutations from determinantal ideals*__Abstract:__Ideals generated by minors in rectangular matrices filled with variables are classical, particularly when the minors are all of those having some fixed size. I'll talk about a more general class of determinantal ideals, where the sizes of the minors in certain subrectangles can vary. These ideals are naturally indexed by permutations in S_n, and we'll see just how richly the combinatorics and algebra interact. The algebraic results concern primality, Gröbner bases, Hilbert series, multidegrees, and Cohen-Macaulayness; the combinatorics inlcudes antidiagonals and planar diagrams of permutations, as well as Schubert and Grothendieck polynomials. I will assume that you've seen things like Gröbner bases, (multi)graded rings, and Hilbert series, but little else; the rest will be introduced from scratch.**Wednesday 5/2**

William Espenschied

Tropical Arithmetic**Wednesday 5/9**

William Espenschied

Tropical Geometry

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Last updated Fri 5/11/07 5:00 PM