Seminars and Colloquia by Series

The Clemens conjecture

Series
Student Algebraic Geometry Seminar
Time
Thursday, November 8, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stephen McKean – Georgia Tech
In 1986, Herb Clemens conjectured that on a general quintic threefold, there are finitely many rational curves of any given degree. In this talk, we will give a survey of what is known about this conjecture. We will also highlight the connections between enumerative geometry and physics that arise in studying the quintic threefold.

An Introduction to Étale Cohomology

Series
Student Algebraic Geometry Seminar
Time
Thursday, October 25, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Minahan – Georgia Tech
We will discuss some basic concepts in étale cohomology and compare them to the more explicit constructions in both algebraic geometry and algebraic topology.

The Littlewood-Richardson Rule

Series
Student Algebraic Geometry Seminar
Time
Thursday, October 18, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor Gunn – Georgia Tech
We will go over a short proof of the Littlewood-Richardson Rule due to Stembridge as well as some related combinatorics of tableaux.

Symmetric functions and representations of the symmetric group

Series
Student Algebraic Geometry Seminar
Time
Thursday, October 11, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor Gunn – Georgia Tech
I will discuss some elementary theory of symmetric functions and give a brief introduction to representation theory with a focus on the symmetric groups. This talk relates to the discussion of Schubert calculus in the intersection theory reading course but can be understood independent of attending the reading course.

An Introduction to Spectral Sequences

Series
Student Algebraic Geometry Seminar
Time
Thursday, October 4, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Minahan – Georgia Tech
We discuss the construction of spectral sequences and some of their applications to algebraic geometry, including the classic Leray spectral sequence. We will draw a lot of diagrams and try to avoid doing anything involving lots of indices for a portion of the talk.

Enriching Bézout’s Theorem

Series
Student Algebraic Geometry Seminar
Time
Thursday, September 27, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stephen McKean – Georgia Tech
Bézout’s Theorem is the classical statement that generic curves of degree c and d intersect in cd points. However, this theorem requires that we work over an algebraically closed field. Using some tools from A^1-algebraic topology, we will give an arithmetic generalization of Bézout’s Theorem. We will also describe the geometric implications of this generalization over the reals.

Matroids and Grassmannians

Series
Student Algebraic Geometry Seminar
Time
Thursday, September 20, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor Gunn – Georgia Tech
We will give a brief introduction to matroids with a focus on representable matroids. We will also discuss the Plücker embedding of the Grassmannian.

An Introduction to Tropical Geometry

Series
Student Algebraic Geometry Seminar
Time
Thursday, September 13, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor Gunn – Georgia Tech
Tropical geometry is a blend of algebraic geometry and polyhedral combinatorics that arises when one looks at algebraic varieties over a valued field. I will give a 50 minute introduction to the subject to highlight some of the key themes.

Some properties in Betti tables of Stanley-Reisner ideals

Series
Student Algebraic Geometry Seminar
Time
Thursday, September 6, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jaewoo Jung – Georgia Tech
One way to analyze a (finitely generated) module over a ring is to consider its minimal free resolution and look at its Betti table. The Betti table would be obtained by algebraic computations in general, but in case of the ideal (consists of relations) is generated by monomial quadratics, we can obtain Betti numbers (which are entries of the Betti table) by looking at the corresponding graphs and its associated simplicial complex. In this talk, we will introduce the Stanley-Reisner ideal which is the ideal generated by monomial quadratics and Hochster’s formula. Also, we will deal with some theorems and corollaries which are related to our topic.

Graph Profiles via Sum of Squares

Series
Student Algebraic Geometry Seminar
Time
Friday, April 20, 2018 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jose Acevedo – Georgia Tech
In this talk we show how to obtain some (sometimes sharp) inequalities between subgraph densities which are valid asymptotically on any sequence of finite simple graphs with an increasing number of vertices. In order to do this we codify a simple graph with its edge monomial and establish a nice graphical notation that will allow us to play around with these densities.

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