Algebra and Combinatorics Seminar
The current seminar's organizers are
ChunHung Liu and
Catherine Yan.

Date Time 
Location  Speaker 
Title – click for abstract 

01/27 3:00pm 
BLOC 302 
Ayah Almousa University of Minnesota 
GLequivariant resolutions over Veronese subrings
We construct explicit GLequivariant minimal free resolutions of certain (truncations of) modules of relative invariants over Veronese subrings in arbitrary characteristic. The free modules in the resolution correspond to certain skew Schur modules associated to "ribbon" or "skewhook" diagrams, and the differentials at each step are surprisingly uniform. We then utilize the uniformity of these resolutions to explicitly compute information about tensor products, Hom, and Tor between these modules and show that they also have rather simple descriptions in terms of ribbon skewSchur modules.
I will emphasize the hidden role of symmetric function theory in detecting the answer to this question and guiding our intuition to build new tools to prove our results in arbitrary characteristic. This is joint work with Mike Perlman, Sasha Pevzner, Vic Reiner, and Keller VandeBogert. 

02/10 3:00pm 
BLOC 302 
Laura Matusevich Texas A&M University 


02/17 3:00pm 
BLOC 302 
Mahrud Sayrafi University of Minnesota 
Bounding the Multigraded Regularity of Powers of Ideals
Building on a result of Swanson, CutkoskyHerzogTrung and Kodiyalam described the surprisingly predictable asymptotic behavior of CastelnuovoMumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller. 

03/24 3:00pm 

Avery St. Dizier UIUC 


03/31 3:00pm 
BLOC 302 
Hongdi Huang Rice University 


04/05 3:00pm 
BLOC 302 
Yuri Bahturin Memorial University of Newfoundland 
From groups to algebras and back
We analyze and extend the classical Malcev correspondence between the divisible torsionfree nilpotent groups and rational nilpotent Lie algebras. The new setting is arbitrary finitedimensional nilpotent algebras. We prove the implicit function theorem for the polynomial functions on such algebras. This allows us to produce various correspondences between these algebras and (quasi)groups, each built on the same underlying set. Applications are provided for the
commensurators of nilpotent groups, filiform Lie algebras and partially
ordered algebras.
(joint work with Alexander Olshanskii) 

04/14 3:00pm 
BLOC 302 
Lauren Snider Texas A&M University 


04/21 12:40pm 
BLOC 302 
Jesus de Loera University of California, Davis 
(Colloquium)


04/28 3:00pm 
BLOC 302 
Patricia Klein Texas A&M University 
