Alex Chandler

Alex Chandler
University of Vienna | UniWien · Faculty of Mathematics

Doctor of Philosophy in Mathematics

About

7
Publications
223
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2
Citations
Introduction
Khovanov homology, triply graded link homology, Macdonald polynomials, Verlinde algebras, open book decompositions
Additional affiliations
May 2019 - present
University of Vienna
Position
  • PostDoc Position
Description
  • Conducting research as part of the group "Macdonald Polynomials and Related Structures in Geometry" under Anton Mellit.
June 2014 - March 2019
North Carolina State University
Position
  • Graduate Teaching Assistant
Description
  • Presentation of lectures, supervision of group work, writing and grading exams for Math 141 (Single Variable Calculus) Math 242 (Multi Variable Calculus).
January 2011 - May 2014
Michigan State University
Position
  • Undergraduate Teaching Assistant
Description
  • Supervisor of the math learning center.
Education
January 2011 - May 2014
Michigan State University
Field of study
  • Mathematics and Physics
January 2011 - May 2014
Michigan State University
Field of study
  • Mathematics and Physics

Publications

Publications (7)
Article
Using the tools of algebraic Morse theory, and the thin poset approach to constructing homology theories, we give the categorification of Whitney’s broken circuit theorem for the chromatic polynomial, and for Stanley’s chromatic symmetric function.
Article
In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is, links whose Khovanov homology is supported on two adjacent diagonals, are known to contain only $\mathbb {Z}_2$ torsion. In this paper, we prove a local version of this result. If the Khovanov homology of a link is supported on two ad...
Preprint
Full-text available
In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for graphs to a homological setting, and its Frobenius characteristic is a q,t generalization of the chromatic symmetric function. We exhibit three pairs of graphs where each pai...
Preprint
Full-text available
Using the tools of algebraic Morse theory, and the thin poset approach to constructing homology theories, we give a categorification of Whitney's broken circuit theorem for the chromatic polynomial, and for Stanley's chromatic symmetric function.
Preprint
Full-text available
Motivated by generalizing Khovanov's categorification of the Jones polynomial, we study functors $F$ from thin posets $P$ to abelian categories $\mathcal{A}$. Such functors $F$ produce cohomology theories $H^*(P,\mathcal{A},F)$. We find that CW posets, that is, face posets of regular CW complexes, satisfy conditions making them particularly suitabl...
Preprint
Full-text available
In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are known to only contain $\mathbb{Z}_2$ torsion. In this paper, we prove a local version of this result. If the Khovanov homology of a link is supported in two adja...
Preprint
Full-text available
In the spirit of Bar Natan's construction of Khovanov homology, we give a categorification of the Vandermonde determinant. Given a sequence of positive integers $\vec{x}=(x_1,...,x_n)$, we construct a complex of colored smoothings of the $2$-strand torus link $T_{2,n}$ in the shape of the Bruhat order on $S_n$, and apply a TQFT to obtain a chain co...

Projects

Project (1)