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Research Seminars: Algebra and Combinatorics

Fall 2020

Time & Location: All talks are on Wednesday in Zoom Meeting at 3:00 PM unless otherwise noted.
Organizer: Mahir Can

Archives

 

November 4

Title: Overview of tropical algebra and geometry - part 1

Kalina Mincheva | Tulane University

Abstract:

In this talk we will give an overview of the field of tropical mathematics. Tropical geometry provides a new set of purely combinatorial tools to approach classical problems in algebraic geometry.  The fundamental objects in tropical geometry are tropical varieties -- combinatorial ``shadows" associated to more traditional geometric objects, algebraic varieties. Until recently, the theory has focused on the geometric aspects of tropical varieties as opposed to the underlying algebra, largely due the lack of tropical analogues to commutative algebra tools. In the talk we will discuss various limitations of the approach which we try to overcome using tropical algebra methods. We will also point out some of the inherent difficulties in working with an idempotent (tropical) algebra and will introduce algebraic objects that carry geometric information.

Time: 3:00

Recording of the Talk:   https://tulane.zoom.us/rec/share/nNY1kcs2F5l3oUIGFITKSUiOWPEEME_V8vPHbmW...

 

November 11

Title: Applications of tropical algebra methods - part 2

Kalina Mincheva | Tulane University

Abstract:

We present results on the properties of the algebraic objects introduced in the previous talk. We discuss the resulting analogues to classical theorems and aspects of dimension theory both for (tropical) ideals and congruences. We also describe connections to algebraic geometry via the theory of tropical schemes and ideals, focusing on recent results on tropical counterparts of vector bundles.

Time: 3:00

Recording of the Talk:  https://tulane.zoom.us/rec/share/6F9ayR7yzDETIpAqDJBGjlVJ0pbqAOjUHafir-L...

 

November 18

Title: From Posets to Equivariant Group Embeddings

Mahir Can | Tulane University

Abstract:

In this talk we will introduce and discuss a class of affine equivariant embeddings of algebraic groups.  More precisely, we will consider the algebraic monoid structure of an incidence algebra. Specializing to the solvable case, we will give a complete classification of the toric incidence monoids.  In addition, we will discuss the automorphism groups of incidence monoids.

Time: 3:00