Global Springer theory

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Geometric representations of graded and rational Cherednik algebras (2014, methodology): “1) for P = Pi, we reduce to a calculation for groups of semisimple rank one, and can be checked in the same way as in [37].”
DAHA and iterated torus knots (2014, methodology): “The latter paper, where the connection with the affine Springer fibers was established, provides a certain link to the theory of DAHA modules [45; 49], though we cannot relate this to our using DAHA.”
Riemann–Hilbert for tame complex parahoric connections (2010, background): “without the weights) have been studied algebraically recently by Yun [ 28 ], and, in eect, the local picture of such Higgs bundles was studied by Kazhdan and Lusztig [18] in 1988.”
Torus knots and the rational DAHA (2012, methodology): “For torus knots, we conjecture that this grading coincides with the grading induced by the filtrationF• onHm/n. ACKNOWLEDGEMENTS We are grateful to M. Aganagic, R. Bezrukavnikov, I. Cherednik, D.-E. Diaconescu, V. Ginzburg, L. Göttsche, I. Grojnowski, S. Gukov, T. Hausel,M. Khovanov, A. Kirillov Jr”
Affine permutations and rational slope parking functions (2014, unknown): “rticular, if m = kn±1), then the Poincare polynomial of´ Fm~n is given by the following simple formula: ∞ Q k=0 tk dimHk ‰F m~nŽ = Q f∈PFm~n t2∑if(i). It had been provenby Varagnolo, Vasserot and Yun [32, 33] that the cohomologyof afﬁne Springer ﬁbers Fm~n carry the action of double afﬁne Hecke alge”