I will show how the effective action can be calculated by summing over 1 particle irreducible graphs.

In this talk we will introduce W-types and discuss several examples of inductive types.

We will recall the notion of Chow group of a scheme briefly and motivate the need for the notion of Equivariant Chow groups. We give a definition of the latter which closely resembles the Borel construction of Equivariant Cohomology groups via certain approximation of the universal G-bundle. We will prove that such construction is well defined and see some examples. We will end the talk with a discussion of functoriality of flat pullbacks and proper pushforwards in the equivariant context.

TBA

The index theorem of Atiyah and Singer is a milestone of modern mathematics. This result which computes the virtual dimension of the space of solutions of an elliptic operator in topological terms, has its roots in classical results like Gauss-Bonnet and Riemann-Roch theorems. I shall trace some of these roots, going back all the way to a statement in Euclid's Elements! Any proof of the index theorem involves some heavy doses of analysis as well as geometry and topology. I shall briefly indicate the original cobordism proof, and then will focus on a more modern heat equation proof and its ramifications.