# Alex ChandlerUniversity of Vienna | UniWien · Faculty of Mathematics

Alex Chandler

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

Education

January 2011 - May 2014

January 2011 - May 2014

## Publications

Publications (7)

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.

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...

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...

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.

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...

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...

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)