Dhruva Divate

Areas of Interest: Equivariant Homotopy Theory

Supervisor: Prof. J.P.C. GreenleesLink opens in a new window.

Thesis Title (submitted): Gorenstein Condition and Duality for Real Topological Hochschild Homology

Abstract: The ubiquity of Gorenstein rings has been noted by Bass in the context of algebraic geometry and the same is known in the context of algebraic topology due to the work of Dwyer, Greenlees, and Iyengar. Greenlees further proved that topological Hochschild homology $\mathrm{THH}(R;k)$ is Gorenstein when $R$ is regular and $k$ is a perfect field of positive characteristic. I examine the refinement of this result in $\mathbb{Z}/2$-equivariant setting for Real topological Hochschild homology of Dotto, Moi, Patchkoria, and Reeh in two cases and compute the $RO(Q)$-graded homotopy of relative norm of Yang in these cases, where $Q$ is a group of order 2. I further exhibit an example of Gorenstein ascent in the equivariant case.

Contact:

Dhruva dot Divate at warwick dot ac dot uk

or

dhruva at divate dot info