26 citations · 157 across the 26 of their papers we have counts for
6 papers · 1 filter
Hilbert schemes and -ification of Khovanov-Rozansky homology
Eugene Gorsky, Matthew Hogancamp
We define a deformation of the triply graded Khovanov-Rozansky homology of a link depending on a choice of parameters for each component of , which satisfies link-spli…
An involutive upsilon knot invariant
Matthew Hogancamp, Charles Livingston
Using the theory of involutive Heegaard Floer knot theory developed by Hendricks-Manolescu, we define two involutive analogs of the Upsilon knot concordance invariant of Ozsvath-St…
Categorical diagonalization
Ben Elias, Matthew Hogancamp
This paper lays the groundwork for the theory of categorical diagonalization. Given a diagonalizable operator, tools in linear algebra (such as Lagrange interpolation) allow one to…
A DG-extension of symmetric functions arising from higher representation theory
Andrea Appel, Ilknur Egilmez, Matthew Hogancamp +1
We investigate analogs of symmetric functions arising from an extension of the nilHecke algebra defined by Naisse and Vaz. These extended symmetric functions form a subalgebra of t…
Khovanov-Rozansky homology and higher Catalan sequences
Matthew Hogancamp
We give a simple recursion which computes the triply graded Khovanov-Rozansky homology of several infinite families of knots and links, including the and tor…
Idempotents in triangulated monoidal categories
Matthew Hogancamp
In these notes we develop some basic theory of idempotents in monoidal categories. We introduce and study the notion of a pair of complementary idempotents in a triangulated monoid…