In this talk the algorithm for bounding x-degrees of right-hand factors will be introduced. I will focus on the notion of generalized exponents, which plays a crucial role in the algorithm. Generalize... More

I'll talk about the problem of finding the algebraic integer of smallest Mahler measure in a given number field. (Where this integer is not a root of unity and is a primitive element.) I'll begin wit... More

This is an ATE exam.

One of Thurston’s many amazing ideas are his hyperbolic gluing equations. Roughly speaking, given an ideally triangulated 3-manifold M, one can construct a set of complex polynomial equations whose ... More

We describe a generalization of the Segre zeta function defined by Aluffi to subschemes of projective bundles. Given a rational map of projective bundles P(F) to P(E) induced by a surjection of the un... More

We will discuss some old and new conjectures about the colored Jones polynomial.

These include the volume conjecture, AJ conjecture, slope conjecture, and strong slope conjecture.

The vo... More

In Geometric and Combinatorial Group Theory, we study finitely generated groups by relating them with their geometric counterparts, Cayley Graphs, endowed with a metric, the so called the word metric.... More

Last semester, I gave several talks introducing the non-Archimedean analytic background necessary for Katz, Rabinoff, and Zureick-Brown's proof that there exists a uniform bound on the number of ratio... More

For a finite separable field extension K/k, all subfields can be obtained by intersecting so-called principal subfields of K/k. The talk will present a way to quickly compute these intersections. If t... More

2-Stratifolds are a generalization of closed surfaces in that they contain simple closed curves where several sheets meet. Currently, there is no general classification of these spaces or their funda... More

We will start reading the paper by Bourgain, Katz and Tao on the so-called "sum-product" estimates.

We will present a new approach to the computation of the Segre class of a subscheme of projective space, based on the construction of a suitable Newton-Okounkov body. The result may be viewed as a co... More

Gromov introduced some procedures to turn a given polyhedron into a new one endowed with a piecewise Euclidean metric of non-positive curvature, while preserving some of its original topological featu... More