at the

American Institute of Mathematics, San Jose, California

organized by

William Fulton, Rebecca Goldin, and Julianna Tymoczko

The goal of this conference is to relate the geometric and combinatorial aspects of what has been dubbed ''GKM'' theory by bringing researchers from combinatorics and geometry/topology together, so that workers in each of these fields can benefit from the insights and experience of those in the other. The conference will address open questions such as the following:

- Can the combinatorial techniques of GKM theory be extended to a wider class of spaces, even if the image of the inclusion map cannot be described? These families could include singular spaces, infinite dimensional spaces, stacky spaces (including Deligne-Mumford stacks), and spaces with specific kinds of group actions or geometric structures.
- For what larger class of manifolds than $G/P$ does the Kostant program extend? Resolving this would entail finding geometric reasons behind the combinatorial rules in $G/P$. What specific kinds of group actions or geometric structure would be required? Answering this question would allow us to apply these powerful combinatorial techniques to reveal geometric and algebraic structure (such as intersections and cohomology rings of all types) in a much broader context.
- Can the techniques of GKM theory be used to prove combinatorially positive results in Schubert calculus or its generalization in an appropriate geometric setting? A combinatorially positive result interprets structure constants in the cohomology ring as the cardinality of a set; an answer to this question might generalize combinatorial objects such as puzzles, cartons, or tableaux to an algorithm that counts paths within graphs, and give closed positive formulas for structure constants in an equivariant cohomology ring.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Equivariant Schubert calculus and jeu de taquin

by Hugh Thomas and Alexander Yong

Equivariant cohomology, syzygies and orbit structure

by Christopher Allday, Matthias Franz, and Volker Puppe, *Trans. Amer. Math. Soc. 366 (2014), no. 12, 6567-6589 * MR3267019

What is equivariant cohomology?

by Loring Tu, *Notices Amer. Math. Soc. 58 (2011), no. 3, 423-426 * MR2789121

Singularities of generalized Richardson varieties

by Sara Billey and Izzet Coskun

Patch ideals and Peterson varieties

by Erik Insko and Alexander Yong

Singularities of generalized Richardson varieties

by Sara Billey and Izzet Coskun