Jay Shah


I am currently a Visiting Assistant Professor at the University of Notre Dame. I completed my PhD in 2017 at MIT under the direction of Clark Barwick. In Spring 2020, I will be a MSRI Postdoctoral Fellow in the program "Higher Categories and Categorification".

Research interests: Algebraic topology, higher category theory, algebraic K-theory, equivariant homotopy theory, motivic homotopy theory, stratified spaces, computational aspects of topology.

Email address: jshah3@nd.edu.

Office: 106 Hayes-Healy.

CV. Current as of December 25, 2019.


Papers:

Scheiderer motives and equivariant higher topos theory, with Elden Elmanto. December 2019. Submitted.

On the parametrized Tate construction and two theories of real p-cyclotomic spectra, with J.D. Quigley. September 2019. Submitted.

C_2-equivariant stable homotopy from real motivic stable homotopy, with Mark Behrens. August 2019. Submitted.

Algorithmic canonical stratifications of simplicial complexes, with Ryo Asai. August 2018. Submitted.

Parametrized higher category theory. My PhD thesis.

Parametrized higher category theory and higher algebra: Exposé II -- Indexed homotopy limits and colimits. This is a slightly modified version of my thesis. Submitted.

Categorifying rationalization, with Clark Barwick, Saul Glasman, Marc Hoyois, and Denis Nardin. October 2016. Accepted for publication in Forum of Mathematics, Sigma.

Parametrized higher category theory and higher algebra: Exposé I -- Elements of parametrized higher category theory, with Clark Barwick, Emanuele Dotto, Saul Glasman, and Denis Nardin. August 2016.

Parametrized higher category theory and higher algebra: A general introduction, with Clark Barwick, Emanuele Dotto, Saul Glasman, and Denis Nardin. August 2016.

Fibrations in ∞-category theory, with Clark Barwick. Published in the 2016 MATRIX Annals.

Spectral Mackey functors and equivariant algebraic K-theory, II, with Clark Barwick and Saul Glasman. Published in the Tunisian Journal of Mathematics.


Video:

The theory of real cyclotomic spectra, video of a lecture given in the "Current Directions in Homotopical Algebra" workshop, held at the Center for Geometry and Physics in Pohang, South Korea.

The genuine stabilization of a G-topos, video of a lecture given in the "Infinity-Categories, Infinity-Operads, and their Applications" CMO-BIRS workshop, held in Oaxaca, Mexico.


Slides:

Parametrized higher category theory. Slides for my talk at the MIT Topology seminar.

The theory of spectral Mackey functors. Slides for my talk at the 2017 YTM in Stockholm.