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Research Seminars: Algebra and Combinatorics


Fall 2016

Time & Location: All talks are on Thursdays in Gibson 414 at 2:00 PM unless otherwise noted.
Organizer: Tai Ha


September 8

Topic

Speaker - Institution

Abstract:  TBA


September 15

Topic

Speaker - Institution

Abstract:  TBA


September 22

Topic

Speaker - Institution

Abstract:  TBA


September 29

Infinite-Dimensional Reductive Monoids Associated to Highest Weight Representations of Kac-Moody Groups

Zhenheng Li - University of South Carolina, Aiken (Host: Mahir Can)

Abstract

We show in this talk how to construct a monoid from a highest weight representation of a Kac-Moody group over the complex numbers. The unit group of the monoid is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We then show that this monoid has similar properties to those of a J-irreducible reductive linear algebraic monoid. More specifically, the monoid is unit regular and has a Bruhat decomposition, and the idempotent lattice of the generalized Renner monoid of the Bruhat decomposition is isomorphic to the face lattice of the convex hull of the Weyl group orbit of the highest weight.


October 6

Topic

Speaker - Institution

Abstract:  TBA


October 13

Topic

Speaker - Institution

Abstract:  TBA


October 20

Verifiability of Stillman's Question

Arindam Banerjee - Purdue University

Abstract

Stillman's question asks whether one can find an upper bound for protective dimension of homogeneous ideals depending only on the degree sequence of its generating set, independent of the number of variables in the polynomial ring.  it is believed that this question has a positive answer and many researchers have proved it for different special cases in recent years. In this joint work with Giulio Caviglia, we study a variant of this question; i.e, we ask if one conjectures a bound for a a fixed degree sequence, whether that can be algorithmically verified. We answer this in affirmative and in the process we also prove some other related and interesting results.

 


October 27

Topic

Laura Matusevich - Texas A&M

Abstract:  TBA


November 3

Topic

Speaker - Institution

Abstract:  TBA



November 10

Local Cohomology of Powers of Monomial Idealsopi

Jonathan Montaño - UNIVERSITY OF KANSAS

 

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November 17

Towards a Deformation Theory for Complex G2 Manifoldsc

Mahir Can - Tulane University

Abstract

In differential geometry a G2 manifold is a seven dimensional manifold with a metric whose holonomy group is contained in the exceptional Lie group G2.

This topic is a highly active branch of mathematics and it has organic ties to mathematical physics.

In this talk we will make an introduction to some universal algebro-geometric objects associated with G2-manfiolds. We do not assume any background in algebraic geometry.


December 1

Towards a deformation theory in complex G2 manifolds, part II

Mahir Can - Tulane University

Abstract

Part II.

In differential geometry a G2 manifold is a seven dimensional manifold with a metric whose holonomy group is contained in the exceptional Lie group G2.


This topic is a highly active branch of mathematics and it has organic ties to mathematical physics.

In this talk we will make an introduction to some universal algebro-geometric objects associated with G2-manfiolds. We do not assume any background in algebraic geometry.

 

December 8

Some Algebraic Properties of Toric Edge Rings

Selvi Beyarslan - Tulane University

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