Welcome to my directory page! I'm a Visiting Professor of Mathematics here at Oxford College, where I've been since 2017.
If you're an undergraduate student who successfully took Math 221 (linear algebra), and you're interested in learning more about knots from a mathematical standpoint (possibly for a summer research project), feel free to contact me.
PhD| Dartmouth College| 2016
MA| Dartmouth College| 2013
MA| Università degli Studi di Torino| 2011
BA| Università degli Studi di Torino| 2009
In the fall of 2019 I am teaching three sections of Math 111 - Calculus I; I am currently scheduled to teach two more sections of Math 111 and one section of Math 221Q in the spring semester. I am also overseeing one Oxford Research Scholar throughout the academic year, for 2 credit hours per term.
In past academic years at Oxford I have taught Math 111 - Calculus I (5 sections overall), Math 110 - Transition to Calculus (3 sections overall), Math 212 - Differential equations (3 sections overall) and Math 221Q - Linear algebra (1 section).
Emory students can access the online version of the Journal of Knot Theory and its Ramifications at this link (requires library login).
Joint Mathematics Meeting: Contributed paper session, Denver, CO, January 2020
I am a knot theorist, mainly interested in combinatorial invariants of knots. My thesis work revolved around generalizing three Vassiliev invariants of order one for virtual knots, first defined by A. Henrich, to the case of long and framed virtual knots; since then, I've generalized the polynomial invariant to the case of virtual tangles, and also given a couple of generalizations of the Affine Index Polynomial.
I am currently studying the properties of the new invariants I've defined, especially with regards to connected sum of tangles. I am also investigating GPV invariants of virtual knots, and their relation to Vassiliev invariants: it is known that every GPV invariant gives rise to a Vassiliev invariant, but little is known about the space of such extensions. With some collaborators, I'm also exploring the definition of GPV invariants for virtual string links (a special type of virtual tangles), as well as the relation between band-pass invariance and knot concordance for GPV invariants.
I get intuition for my research using Mathematica code; I am currently developing code (based on Bar-Natan's code) that evaluates a Gauss Diagram formula (another way of defining GPV invariants) on a given virtual knot, and that computes the dimension of the space of Vassiliev extensions of GPV invariants. If you're interested in the code feel free to contact me at firstname.lastname@example.org