ALGECOM-10


 

 

 




Algebra, Geometry and Combinatorics Day (AlGeCom) is a one day, informal meeting of mathematicians from the University of Illinois, Purdue University, IUPUI, Loyola University Chicago, and nearby universities, with interests in algebra, geometry and combinatorics (widely interpreted).

Further details will be posted here as they become available. Or you may contact the University of Illinois organizers Hal Schenck and Alexander Yong, or the Purdue organizers Uli Walther and Saugata Basu or IUPUI organizer Evgeny Mukhin or the Loyola organizer Peter Tingley.

Date:   Saturday May 24, 2014

Location: Department of Mathematics at University of Illinois at Urbana-Champaign

Conference: 245 Altgeld Hall.

Poster session and coffee breaks: 239 Altgeld Hall.


For a map, click here

Parking on campus lots is free on Saturdays. The closest one is lot C3
here on this map




Speakers  and schedule:

Coffee and pastries          9-10am

 

Victor Reiner (Minnesota) 10-11h

Title:  Combining q-analogues and t-analogues

Abstract.  Together with my colleagues Dennis Stanton and Joel Lewis, we have found several
results for the symmetric group S_n having q-analogues for the general linear group
GL( n, F_q ).  Often the symmetric group result also has a t-analogue, where t is
now a grading variable coming from invariant theory, and the q-analogue becomes a
(q,t)-analogue for GL( n , F_q ). Here the q and the t play asymmetric roles!

This talk will discuss some theorems of this nature, along with some
conjectures.



Thomas Lam (Michigan) 11:30h-12:30h

Title:  Dimers and the canonical basis

Abstract:  Let G be a planar bipartite graph embedded in a disk, with
boundary vertices on the boundary of the disk.  I will talk about
algebraic aspects of perfect matchings of G, or equivalently, the
"dimer model".  I will explain how canonical bases from representation
theory can be applied to the study of dimers.




Lunch          12h30-2:00h


Karola Meszaros (Cornell) 2:00h-3:00h

Title: H-polynomials of triangulations of flow polytopes (and more)

Abstract: The h-polynomial of a simplicial complex is a way of encoding the
number of faces of each dimension. I will introduce a multivariate generalization
of the h-polynomials of unimodular triangulations of flow polytopes. The
inspiration for this generalization lies in the subdivision algebra of flow
polytopes, whose relations prescribe a way of subdividing flow polytopes. The
multivariate generalization of the h-polynomials can be used to prove certain
nonnegativity properties in the subdivision and related algebras. Included will be
a discussion of earlier significant results regarding flow polytopes and their
implications for the generalized h-polynomials.




Poster session and afternoon tea:   3:00h-5:00h (fresh coffee at 3 1/4h)












-----------------------------------------------------------------------------------------------------------------

Parking:

Lodging: We suggest the Hampton Inn. The Hampton is also holding 10 rooms; checking in on 5/23 and checking out on 5/25 under the
name Algecom. All rooms still available on 4/23 will be released.


Alternatives:


Banquet: 5:15pm at Mandarin Wok (403 E. Green St, Urbana).