Notes on Equivariant

Notes on Mirror Symmetry

1 Equivariant Cohomology 1 1.1 Group cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Equivariant cohomology of topological spaces . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Equivariant vector bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Equivariant pushforward . . . . . . . . . . . . . . . . . . . . . . . ....

Notes on Equivariant D-modules

A Short Note on Models for Equivariant Homotopy Theory

These notes explore equivariant homotopy theory from the perspective of model categories in the case of a discrete group G. Section 2 reviews the situation for topological spaces, largely following [May]. In section 3, we discuss two approaches to equivariant homotopy theory in more general model categories. Section 4 discusses some examples to which the material from Section 3 applies. In part...

Ring structures of mod p equivariant cohomology rings and ring homomorphisms between them

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

Notes on Cherednik Algebras and Algebraic Combinatorics, Montreal 2017

These are the notes for a short course given at the summer school Equivariant Combinatorics at the CRM in Montreal. The notes contain somewhat more material than was practical to cover in the course. The intended audience was graduate students and researchers in algebraic combinatorics with no prior experience with Cherednik algebras, but who are interested in the algebraic combinatorics having...