Alternatively have a look at the program.

## Graded manifolds, Lie algebroids, and equivariant cohomology. Part 1

The goal of this minicourse is to explain how equivariant cohomology can be formulated in terms of differential graded manifolds and Lie algebroids. In this language, the constructions of the Weil and the BRST model, as well as the Mathai-Quillen isomorphism between them are concise, natural, and relatively straightforward. In Part 1 I start with a self-contained introduction to the basic notions of graded differential geometry, where the grading is over an arbitrary abelian group, typically $\mathbb{Z}$ or $\mathbb{Z}^2$.

## Graded manifolds, Lie algebroids, and equivariant cohomology. Part 2

The goal of this minicourse is to explain how equivariant cohomology can be formulated in terms of differential graded manifolds and Lie algebroids. In Part 2 we will see how the graded de Rham complex of a Lie algebroid gives rise to the Weil and the BRST models of equivariant cohomology.

## Graded manifolds, Lie algebroids, and equivariant cohomology. Part 3

## Graded manifolds, Lie algebroids, and equivariant cohomology. Part 4

## Graded manifolds, Lie algebroids, and equivariant cohomology. Last part.

## Towards higher geometric quantization

Manifolds equipped with a closed non-degenerate form of degree > 2 can be thought of as higher analogs of symplectic manifolds. In this talk, I will describe some work in progress on developing a geometric quantization procedure for such manifolds.

## Equivariant de Rham cohomology via gauged sigma models

## Equivariant de Rham cohomology via gauged sigma models II

## Differential K-theory from EFTs

I describe joint work with Arturo Prat-Waldron in constructing a model for differential K-theory from Euclidean Field theories.