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Link homology

An online research community sponsored by the

 

American Institute of Mathematics, San Jose, California

organized by

Nicolle Gonzalez, Eugene Gorsky, Matthew Hogancamp, Oscar Kivinen, and Alexei Oblomkov

The Link Homology Research Community, sponsored by AIM and the NSF, revolves around the recent developments in the intersection of categorification, Khovanov-Rozansky homology, affine Springer fibers, Hilbert schemes and link homology, and combinatorics. In particular, Khovanov-Rozansky homologies were computed explicitly for all torus links, and the answer is best expressed in terms of combinatorics of q,t-Catalan numbers and Macdonald polynomials. We plan to study possible expansions of this result to other classes of links, and to connect it to other algebraic and geometric models for link homology involving Hilbert schemes of points, affine Springer fibers and braid varieties. More abstract questions such as categorification of the skein algebras and modules, and their relation to the categorifications of the Heisenberg and elliptic Hall algebras will be also studied.

The Community will include several activities oriented at current graduate students and early career researchers. Among our main goals are writing expository articles and surveys that will aid newcomers interested in these recent developments. Such surveys would clarify the connections between the different results and conjectures, and streamline and organize the proofs of important results which are currently scattered across several papers.

We have a community agreement.

If you would like to participate, please apply by filling out the on-line form. Applications are open to all, and we especially encourage women, underrepresented minorities, and researchers from primarily undergraduate institutions to apply.




For more information email research@aimath.org