shadow_tr

Research Seminars: Algebraic Geometry

Fall 2018

Time & Location: All talks are on Monday in Gibson Hall 325 at 3:00 P.M. unless otherwise noted.
Organizer: Mahir Can


September 15

Topic

Yildiray OzanInstitution

Abstract: TBA

Gibson Hall 325

Time 11:00am


September 17

Variations on the $S_n$-module $Lie_n$

Sheila SundaramPierrepont School

Abstract:

Sheila Sundaram


October 29

Catalan Functions and k-Schur functions

Anna PunDrexel University

Abstract:

Li-Chung Chen and Mark Haiman studied a family of symmetric functions called Catalan (symmetric) functions which are indexed by pairs consisting of a partition contained in the staircase (n-1, ..., 1,0) (of which there are Catalan many) and a composition weight of length n. They include the Schur functions ,the Hall-Littlewood polynomials and their parabolic generalizations. They can be defined by a Demazure-operator formula, and are equal to GL-equivariant Euler characteristics of vector bundles on the flag variety by the Borel-Weil-Bott theorem. We have discovered various properties of Catalan functions, providing a new insight on the existing theorems and conjectures inspired by Macdonald positivity conjecture.

 A key discovery in our work is an elegant set of ideals of roots that the associated Catalan functions are k-Schur functions and proved that graded k-Schur functions are G-equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We exposed a new shift invariance property of the graded k-Schur functions and resolved the Schur positivity and k-branching conjectures by providing direct combinatorial formulas using strong marked tableaux. We conjectured that Catalan functions with a partition weight are k-Schur positive which strengthens the Schur positivity of Catalan function conjecture by Chen-Haiman and resolved the conjecture with positive combinatorial formulas in cases which capture and refine a variety of problems.

 This is joint work with Jonah Blasiak, Jennifer Morse and Daniel Summers. https://arxiv.org/abs/1804.03701



October 22

The Variety of Polarizations

Aram BinghamTulane University

Abstract:

aram_b

 


Date

Topic

SpeakerInstitution

Abstract: TBA


Date

Topic

SpeakerInstitution

Abstract: TBA


Date

Topic

SpeakerInstitution

Abstract: TBA


Date

Topic

SpeakerInstitution

Abstract: TBA


Date

Topic

SpeakerInstitution

Abstract: TBA


Date

Topic

SpeakerInstitution

Abstract: TBA


Date

Topic

SpeakerInstitution

Abstract: TBA



Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu