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Thursday, November 15, 2018 - 13:30 ,
Location: Skiles 006 ,
Marcel Celaya ,
Georgia Tech ,
Organizer: Trevor Gunn

Thursday, November 8, 2018 - 13:30 ,
Location: Skiles 006 ,
Stephen McKean ,
Georgia Tech ,
Organizer: Trevor Gunn

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.

Thursday, October 25, 2018 - 13:30 ,
Location: Skiles 006 ,
Daniel Minahan ,
Georgia Tech ,
Organizer: Trevor Gunn

We will discuss some basic concepts in étale cohomology and compare them
to the more explicit constructions in both algebraic geometry
and algebraic topology.

Thursday, October 18, 2018 - 13:30 ,
Location: Skiles 006 ,
Trevor Gunn ,
Georgia Tech ,
Organizer: Trevor Gunn

We will go over a short proof of the Littlewood-Richardson Rule due to Stembridge as well as some related combinatorics of tableaux.

Thursday, October 11, 2018 - 13:30 ,
Location: Skiles 006 ,
Trevor Gunn ,
Georgia Tech ,
Organizer: Trevor Gunn

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.

Thursday, October 4, 2018 - 13:30 ,
Location: Skiles 006 ,
Daniel Minahan ,
Georgia Tech ,
Organizer: Trevor Gunn

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.

Thursday, September 27, 2018 - 13:30 ,
Location: Skiles 006 ,
Stephen McKean ,
Georgia Tech ,
Organizer: Trevor Gunn

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.

Thursday, September 20, 2018 - 13:30 ,
Location: Skiles 006 ,
Trevor Gunn ,
Georgia Tech ,
Organizer: Trevor Gunn

We will give a brief introduction to matroids with a focus on representable matroids. We will also discuss the Plücker embedding of the Grassmannian.

Thursday, September 13, 2018 - 13:30 ,
Location: Skiles 006 ,
Trevor Gunn ,
Georgia Tech ,
Organizer: Trevor Gunn

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.

Thursday, September 6, 2018 - 13:30 ,
Location: Skiles 006 ,
Jaewoo Jung ,
Georgia Tech ,
Organizer: Trevor Gunn

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.