Positroids, knots, and -Catalan numbers
P Galashin, T Lam - Duke Mathematical Journal, 2024 - projecteuclid.org
We relate the mixed Hodge structure on the cohomology of open positroid varieties (in
particular, their Betti numbers over C and point counts over F q) to Khovanov–Rozansky …
particular, their Betti numbers over C and point counts over F q) to Khovanov–Rozansky …
Affine Springer Fibers and Generalized Haiman Ideals (with an Appendix by Eugene Gorsky and Joshua P. Turner)
JP Turner - International Mathematics Research Notices, 2024 - academic.oup.com
Abstract We compute the Borel–Moore homology of unramified affine Springer fibers for
under the assumption that they are equivariantly formal and relate them to certain ideals …
under the assumption that they are equivariantly formal and relate them to certain ideals …
Shalika germs for tamely ramified elements in
O Kivinen, CC Tsai - arXiv preprint arXiv:2209.02509, 2022 - arxiv.org
Degenerating the action of the elliptic Hall algebra on the Fock space, we give a
combinatorial formula for the Shalika germs of tamely ramified regular semisimple elements …
combinatorial formula for the Shalika germs of tamely ramified regular semisimple elements …
On the Cohomology of Two Stranded Braid Varieties
T Scroggin - arXiv preprint arXiv:2312.03283, 2023 - arxiv.org
We compute the cohomologies of two strand braid varieties using the two-form present in
cluster structures. We confirm these results with proof using Alexander and Poincar\'e …
cluster structures. We confirm these results with proof using Alexander and Poincar\'e …
Fray functors and equivalence of colored HOMFLYPT homologies
L Conners - arXiv preprint arXiv:2405.00875, 2024 - arxiv.org
We construct several families of functors on the homotopy category of singular Soergel
bimodules that mimic cabling and insertion of column-colored projectors. We use these …
bimodules that mimic cabling and insertion of column-colored projectors. We use these …
Rational Cherednik Algebras and Torus Knot Invariants
X Ma - arXiv preprint arXiv:2402.18770, 2024 - arxiv.org
The HOMFLY polynomial of the $(m, n) $ torus knot $ T_ {m, n} $ can be extracted from the
doubly graded character of the finite-dimensional representation $\mathrm {L} _ {\frac {m}{n}} …
doubly graded character of the finite-dimensional representation $\mathrm {L} _ {\frac {m}{n}} …
Affine Springer Fibers and Generalized Haiman Ideals
JP Turner - arXiv preprint arXiv:2310.07215, 2023 - arxiv.org
We compute the Borel-Moore homology of unramified affine Springer fibers for $\mathrm
{GL} _n $ under the assumption that they are equivariantly formal and relate them to certain …
{GL} _n $ under the assumption that they are equivariantly formal and relate them to certain …
[PDF][PDF] Triply Graded Link Homology for Coxeter Braids on 4 Strands
JP Turner - arXiv preprint arXiv:2410.03068, 2024 - arxiv.org
arXiv:2410.03068v1 [math.GT] 4 Oct 2024 Page 1 TRIPLY GRADED LINK HOMOLOGY FOR
COXETER BRAIDS ON 4 STRANDS JOSHUA P. TURNER Abstract. We compute the triply …
COXETER BRAIDS ON 4 STRANDS JOSHUA P. TURNER Abstract. We compute the triply …
Matrix Factorizations and Khovanov Homology
A Wang - 2024 - scholarworks.umass.edu
In this thesis we develop a geometric interpretation for Rasmussen's spectral sequences
using a construction for Khovanov-Rozansky link homology developed by Oblomkov and …
using a construction for Khovanov-Rozansky link homology developed by Oblomkov and …