Notre Dame Math Graduate Student Seminar, 2009-2010

All talks are at 4:15 in HH231 unless otherwise noted.

Previous Semesters

To volunteer to give a talk, or for anything else regarding the seminar, contact Megan Patnott.

Schedule

Abstracts

September 7, 2009

Speaker

Liviu Nicolaescu

Title

Knots and their curvatures

Abstract

I will discuss an old result of John Milnor stating roughly that if a closed curve in space is not too curved then it cannot be knotted.

September 21, 2009

Speaker

Megan Patnott

Title

An Introduction to Using Beamer

Abstract

Beamer is one of the more commonly used LaTeX packages for making presentations. We'll discuss the basics of using it, as well as a couple of useful tricks.

October 5, 2009

Speaker

Sarah Cotter

Title

Variations on a theme of Helly

Abstract

Helly's Theorem, proved by Eduard Helly in 1923, is a result in convex geometry dealing with the intersections of certain families of sets. While Helly's Theorem is rather useful on its own, by weakening its requirements we can broaden its applications to a surprising variety of problems. Topics covered may include (p, q)-properties, fractional Helly properties, VC dimension, the arrangement of sheep, art gallery problems, and robots.

November 9, 2009

Speaker

Bernadette Boyle

Title

Cayley-Bacharach Theorem through the ages

Abstract

Much of algebraic geometry focuses on the vanishing locus of systems of polynomials, as well as, the polynomials that vanish on a certain subspace. In this talk, I will discuss some of the major tools algebraic geometers use in studying these vanishing loci and polynomials while focusing on a classical result in algebraic geometry, the Cayley-Bacharach theorem. I will discuss several different formulations of the Cayley-Bacharach theorem from its earliest roots in Pappus' Theorem (4th century AD), through the twentieth century. This talk is based on the paper "Cayley-Bacharach Theorems and Conjectures" by D. Eisenbud, M.Green, and J. Harris.

November 23, 2009

Speaker

David Karapetyan

Title

On the Uniqueness of Solutions to the Burgers Equation in Sobolev Spaces

Abstract

It is shown that solutions to the Burgers initial value problem are unique in Sobolev Spaces $H^s$ for $s>3/2$. Using a modification of the Kato-Ponce commutator estimate, an energy estimate for the Burgers i.v.p is derived; an application of Gronwall's inequality then yields the desired result.
(See abstract as pdf.)

Previous Years

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