4 papers
Spectral geometry of Khovanov Laplacians
Jernej Grlj, Aaron D. Lauda
For an oriented link diagram , the Khovanov cochain complex carries a canonical Hermitian inner product that defines a combinatorial Hodge Laplacian. Its kernel is naturally iso…
6-valent vertex in the web category and its categorification
Jernej Grlj, Mikhail Khovanov, Haihan Wu +1
We define a -rotationally invariant 6-valent vertex in the web category. When , we provide a categorification of the 6-valent vertex using $\mathf…
Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance
Jernej Grlj, Aaron D. Lauda
While persistent Laplacians (PL) offer a richer geometric representation of data than persistent homology, utilizing their full eigenspectrum for learning tasks is often hampered b…
Action of the Witt algebra on categorified quantum groups
Jernej Grlj, Aaron D. Lauda
We construct an action of the positive Witt algebra on the categorified quantum group associated to a simply-laced Lie algebra. In the type A case, we show that this action induces…