Sep 12 
Ivan Martino 
Algebraic Structures related to Matroid Theory (Winter is Coming)
abstract±
In this talk I will describe certain algebraic structures related to Matroid Theory. After defining a matroid over a ring, I will focus on matroids over a field $k$ and matroids over the integers $\mathbb{Z}$.
Poster.



Following seminar, we will go out for food and refreshment.

Sep 19 
Laure Flapan 
At 3:30, before seminar, we will have tea, coffee and cookies in the lounge.
Hodge groups, Hodge structures, and the Hodge Conjecture.
abstract±
I will introduce the Hodge group and discuss its usefulness in the context of the Hodge conjecture as well as, more generally, in other connections between topology and algebraic geometry.
Poster.

Sep 26 
Emily Barnard 
At 3:30, before seminar, we will have Ivan's cake in the lounge.
Counting and the Canonical Join Representation
abstract±
We will start the talk by considering some apparently unrelated counting problems.
Each of family of objects that we want to count has some extra structure: a partial order that turns out to be a lattice. I will explain how a certain ``factorization’’ of the elements in a lattice can help us count. This talk will be heavy on examples, and accessible to all.
Poster.

Oct 3 
Emanuele Macri 
The Genus of Space Curves and Stability in the Derived Category.
abstract±
In the first part of the talk, I will introduce a Conjecture by Hartshorne and Hirschiwitz on bounds for the genus space curves which are not contained in a surface of a given degree. For example, for curves not contained in a quadratic surface, this is nothing but the wellknown Castelnuovo bound.
In the second part of the talk, I will present how to approach this Conjecture by using derived categories (in a joint work in progress with Benjamin Schmidt), and where new ideas are needed to hopefully(!) complete this plan.
Poster.



Following seminar, we will go out for food and refreshment.

Oct 10 
Benjamin Sung 
There will be tea and cookies before the
talk in the department lounge.
Sheaf cohomology on CalabiYau
hypersurfaces in toric varieties and
Dbrane instantons
abstract±
Sheaf cohomology of divisors on a CalabiYau threefold yields
information about the zero mode spectrum of wrapped ED3
branes and hence the nonperturbative superpotential, which
has direct applications for moduli stabilization and axion
inflation. I will present a new technique and explicit formulas
for these computations based on joint work with Andreas
Braun, Cody Long, Liam McAllister, and Mike Stillman.
Poster.

Oct 17 
Chris McDaniel (Endicott College) 
From Watanabe's Bold Conjecture to Soergel's Categorification Theorem.
abstract±
In commutative algebra, Watanabe's Bold Conjecture asserts that every complete intersection can always embed into some quadratic complete intersection with the same socle degree. We will show that this Bold Conjecture holds for a class of complete intersections called coinvariant rings, with BottSamelson rings acting as the quadratic ones. BottSamelson rings seem to have been introduced by Soergel who succeeded in uncovering some of their remarkable properties, including his celebrated Categorification Theorem. In fact, Soergel's Categorification Theorem and the conjectures stemming from it are what eventually led Elias and Williamson to a proof of the notorious KazhdanLusztig positivity conjecture in representation theory. We will highlight some of these beautiful results of Soergel and EliasWilliamson, and of course describe their connection to Watanabe's Bold Conjecture.
Poster.

Oct 24 
Andrew Laurie (MIT) 
Solitons, bubbling, and blow up for geometric PDE's.
abstract±
Solitons (coherent solitary waves) are the building blocks of the globalintime dynamics and singularity formation for dispersive PDE. In the case of a globally defined solution, the soliton resolution conjecture asserts that as a solution evolves, it decomposes into a finite number of weakly interacting solitons plus a remainder exhibiting linear dynamics. In the case of a solution that develops a singularity by concentrating mass or energy, solitons often play the role of universal blowup profiles  zooming in on the solution near the singularity, the shape of a soliton comes into view. In this talk, we’ll mostly discuss the latter phenomena (which is often called bubbling) in the context of a model geometric PDE called the wave maps equation, which is a generalization of the free wave equation to manifold valued maps.
Poster.

Oct 31 
Valerio Toledano Laredo 
Pick Valerio's Brain
abstract±
Valerio Toledano Laredo works in representation theory, particularly loop groups and quantum groups. More recently, he has explored the semiclassical aspect of quantum groups and uncovered, in collaboration with Tom Bridgeland of Sheffield University, a novel [and fascinating] dictionary between wallcrossing in Algebraic Geometry and Stokes phenomena for differential equations with irregular singularities in the complex plane.
Poster.



Following seminar, we will go out for food and refreshment.

Nov 7 
Bena Tshishiku (Harvard) 
The "Dark Matter" Problem.
abstract±
The dark matter problem in lowdimensional topology is about surface bundles, mapping class groups, moduli spaces, and cohomology (and has nothing to do with cosmology). I will explain this problem and the circle of ideas around surrounding it.
Poster.

Nov 14 
Asilata Bapat (UGA) 
Examples of Compactifications of Quiver Varieties.
abstract±
I will start with a recent construction of McGerty and Nevins, which systematically produces compactifications of quiver varieties.
I will explain some variants of this construction, as well as work in progress on computing specific examples, including the Hilbert scheme of points on a plane.
Poster.

Nov 21 
Thanksgiving Break 

Nov 28 
Jonathan Mboyo Esole 
Representations and anomalies in presence of a nontrivial MordellWeil group
abstract±
In this talk, I will explore how the presence of a nontrivial MordellWeil group on an elliptic fibration affects its relative Mori cone.
I will also discuss how the MordellWeil group of the elliptic fibration modifies the structure of representations and anomalies in the dual gauge theory associated with the elliptic fibration.
Poster.

Dec 5 
Mustazee Rahman (MIT) 
On largest eigenvalues of bounded degree graphs
abstract±
Classical AlonBoppana theorem gives a sharp lower bound on the
second largest eigenvalue of a regular graph. Obtaining such bounds for nonregular
graphs is more complicated. I will explain some combinatorial and topological
ideas that allows for AlonBoppana type bounds for large, bounded degree graphs.
These bounds also apply to unimodular networks, which are a stochastic generalization
of finite graphs. In fact, the stochastic generalization plays a central role in
deducing such bounds for finite graphs.
Poster.



End of Semester (Seminar Resumes Spring 2018) 