A&C Seminar:  Fall 2008, Fridays, Milner 317, 3:00–3:50 p.m.

The Algebra and Combinatorics seminar is devoted to studying algebra, combinatorics, their interconnection, and their relations to mathematics and applications.

The seminar's organizer this semester is Aaron Lauve.

(Fall 2008 Calendar)    (Seminar history)    (About this page)

December 5	Federico Ardila (San Francisco State University)
3:00–3:50	Combinatorics and geometry of power ideals
	Abstract:   We investigate ideals in a polynomial ring which are generated by powers of linear forms. Such ideals are closely related to the theories of fat point ideals, Cox rings, and box splines. We pay special attention to a family of power ideals that arises naturally from a hyperplane arrangement A. We prove that their Hilbert series are determined by the combinatorics of A, and can be computed from its Tutte polynomial. We also obtain formulas for the Hilbert series of the resulting fat point ideals and zonotopal Cox rings. Our work unifies and generalizes results on power ideals obtained by Dahmen-Micchelli, de Boor-Ron, Holtz-Ron, Postnikov-Shapiro-Shapiro, and Sturmfels-Xu, among others. It also settles a conjecture of Holtz-Ron on the spline interpolation of functions on the lattice points of a zonotope. This is joint work with Alex Postnikov from MIT.

 
Fall 2008 Seminar Calendar

August 29	Organizational Meeting
3:00–3:50
September 5	Aaron Lauve (TAMU)
3:00–3:50	The Markoff condition and central words
September 12	Chris Hillar (TAMU)   Hurricane Ike'd
3:00–3:50	Polynomial recurrences and cyclic resultants
September 19	Stefan Forcey (Tennessee State University)
3:00–3:50	Positrons, polytopes, and antipodes.
September 26	Khaled Al-Takhman (Birzeit University & TAMU)
3:00–3:50	Corings and Comodules
October 3	Dmitri Nikshych (University of New Hampshire)
3:00–3:50	Weakly group-theoretical and solvable fusion categories
October 10	Alison Marr (Southwestern University, Texas)
3:00–3:50	A Magical Tour of Various Magic-Type Labelings
October 17	Deepak Naidu (TAMU)
3:00–3:50	Fusion subcategories of Rep(Dω(G))
October 24	Charles Doran (University of Alberta, Canada)
3:00–3:50	Algebraic Cycles, Regulator Periods, and Local Mirror Symmetry
October 31	Michael Anshelevich (TAMU)
3:00–3:50	Measures, orthogonal polynomials, and continued fractions
November 7	Sarah Witherspoon (TAMU)
3:00–3:50	Quantum Symmetric Algebras
November 14	Dimitrije Kostic
3:00–3:50	The Combinatorics of Integer Points in a Certain Polytope
November 19	Mitja Mastnak (Saint Mary's University)   Wed; 2:00; Milner 216
2:00–2:55	Hopf algebraic approach to the combinatorics of free probability
November 21	Scott Chapman (Sam Houston State University)
3:00–3:50	An Introduction to the Theory of Non-unique Factorizations
December 5	Federico Ardila (San Francisco State University)
3:00–3:50	Combinatorics and geometry of power ideals

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