A proof of the shuffle conjecture
E Carlsson, A Mellit - Journal of the American Mathematical Society, 2018 - ams.org
We present a proof of the compositional shuffle conjecture by Haglund, Morse and Zabrocki
[Canad. J. Math., 64 (2012), 822–844], which generalizes the famous shuffle conjecture for …
[Canad. J. Math., 64 (2012), 822–844], which generalizes the famous shuffle conjecture for …
[HTML][HTML] Refined knot invariants and Hilbert schemes
E Gorsky, A Neguţ - Journal de mathématiques pures et appliquées, 2015 - Elsevier
We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic
and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's …
and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's …
Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux
A Anokhina, A Mironov, A Morozov… - Advances in High …, 2013 - Wiley Online Library
If a knot is represented by an m‐strand braid, then HOMFLY polynomial in representation R
is a sum over characters in all representations Q∈ R⊗ m. Coefficients in this sum are traces …
is a sum over characters in all representations Q∈ R⊗ m. Coefficients in this sum are traces …
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
A Oblomkov, J Rasmussen, V Shende - Geometry & Topology, 2018 - msp.org
We conjecture an expression for the dimensions of the Khovanov–Rozansky HOMFLY
homology groups of the link of a plane curve singularity in terms of the weight polynomials of …
homology groups of the link of a plane curve singularity in terms of the weight polynomials of …
Knot homology and refined Chern–Simons index
M Aganagic, S Shakirov - Communications in Mathematical Physics, 2015 - Springer
We formulate a refinement of SU (N) Chern–Simons theory on a three-manifold M via an
index in the (2, 0) theory on N M5 branes. The refined Chern–Simons theory is defined on …
index in the (2, 0) theory on N M5 branes. The refined Chern–Simons theory is defined on …
Toric braids and (m, n)-parking functions
A Mellit - Duke Mathematical Journal, 2021 - projecteuclid.org
We find a geometric interpretation of the A q, t algebra, the algebra which appeared in the
previous work of Erik Carlsson and the author on the proof of the shuffle conjecture. This …
previous work of Erik Carlsson and the author on the proof of the shuffle conjecture. This …
Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology
E Gorsky, A Neguţ, J Rasmussen - Advances in Mathematics, 2021 - Elsevier
We construct a categorification of the maximal commutative subalgebra of the type A Hecke
algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal …
algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal …
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 …
A closed formula for the evaluation of foams
LH Robert, E Wagner - Quantum Topology, 2020 - ems.press
A closed formula for the evaluation of foams Page 1 Quantum Topol. 11 (2020), 411–487 DOI
10.4171/QT/139 Quantum Topology © European Mathematical Society A closed formula for …
10.4171/QT/139 Quantum Topology © European Mathematical Society A closed formula for …
On the computation of torus link homology
B Elias, M Hogancamp - Compositio Mathematica, 2019 - cambridge.org
On the computation of torus link homology Page 1 On the computation of torus link
homology Ben Elias and Matthew Hogancamp Compositio Math. 155 (2019), 164–205. doi:10.1112/S0010437X18007571 …
homology Ben Elias and Matthew Hogancamp Compositio Math. 155 (2019), 164–205. doi:10.1112/S0010437X18007571 …