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Research Seminars: Algebra and Combinatorics


Spring 2017

Time & Location: All talks are on Thursdays in Gibson 400A at 12:45 PM unless otherwise noted.
Organizer: Tai Ha


January 19

Topic

Speaker - Institution

Abstract:  TBA


January 26

Introduction to the Hodge Conjecture

Al Vitter - TULANE UNIVERSITY

Abstract

 

This will be the first of probably 2 talks. The Hodge Conjecture concerns smooth (non-singular) complex projective varieties. It relates the purely algebraic structure of the variety to its topological/complex-analytic structure via its cohomology groups. I will begin by discussing in a relatively untechnical way, some of the mathematics needed to state clearly the Hodge Conjecture. Then I will concentrate on some aspects that  bring out (hopefully) the subtlety and importance of the conjecture.

February 2

Introduction to the Hodge Conjecture (part 2)

Al Vitter - Tulane University

Abstract

 

This will be a continuation of my first talk. I will state the Hodge Conjecture and then talk about some aspects that show its subtlety and importance. The Hodge Conjecture concerns smooth (non-singular) complex projective varieties. It relates the purely algebraic structure of the variety to its topological/complex-analytic structure via its cohomology groups. I will begin by discussing in a relatively untechnical way, some of the mathematics needed to state clearly the Hodge Conjecture.


February 9

Classification of spherical diagonal actions of reductive groups

Mahir Bilen Can - Tulane University

Abstract

In this talk we present our recent progress on the diagonal actions of a reductive groups on product varieties of the form X_1 x X_2, where X_1 is a symmetric space and X_2 is a partial flag variety. In particular, we classify all such actions.


February 16

Classification of spherical diagonal actions of reductive groups, Part II.

Mahir Bilen Can - Tulane University

Abstract

In this talk we present our recent progress on the diagonal actions of a reductive groups on product varieties of the form X_1 x X_2, where X_1 is a symmetric space and X_2 is a partial flag variety.  In particular, we classify all such actions.

 


February 23

Topic

Speaker - Institution

Abstract:  TBA


March 2

The depth function of ideals in polynomial rings.

Tai Huy Ha - Tulane University

Abstract

We shall discuss what could be the depth function of an ideal in a polynomial ring. That is, for which function f(n), there exists an ideal I in a polynomial ring R such that depth R/I^n = f(n) for all n > 0.


March 9

A DYNAMIC BUCHBERGER ALGORITHM

Prof. John Perry - University of Southern Mississippi

Abstract


Gröbner bases are a major tool in commutative algebra, typically computed using the Buchberger algorithm. This algorithm is “static” in that it works with a fixed term ordering, required as input along with the ideal’s generators. In many cases, however, a “dynamic” Buchberger algorithm is more appropriate: it requires only the generators as input, and returns both a basis and an ordering that guarantees the Gröbner property. It computes the ordering by the guidance of a criterion inspired by an invariant of an ideal. This talk describes the algorithm, the traditional criterion to guide computation, and a new criterion.

March 16

Topic

Speaker - Institution

Abstract:  TBA


March 23

Algebra & Combinatoric seminar

Points, symbolic powers and a conjecture by G. V. Chudnovsky.

Paolo Mantero - University of Arkansas

Abstract

What is the smallest possible degree of an equation passing at least m times through t given points in the complex projective space P^N? The answer is not known (except in few special cases), however the complex analyst G. V. Chudnovsky in 1979 conjectured a lower bound, which until last year was only known to hold for points in P^2, general points in P^3 and certain extremal configurations in P^N.
In this talk we will survey the evolving framework of conjectures and results around the above question, and prove Chudnovsky's conjecture for any set of very general points in P^N.

 


March 30

Topic

Speaker - Institution

Abstract:  TBA


April 6

Topic

Speaker - Institution

Abstract:  TBA


April 13

Topic

Speaker - Institution

Abstract:  TBA


April 20

Topic

Prof. Fabrizio Zanello - Michigan Tech University (Host: Tai H  Ha)

Abstract:  TBA


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