Jay Shah

Affiliate Professor

Education

Ph.D in Mathematics, Massachusetts Institute of Technology, 2017
B.S., in Mathematics, University of Chicago, 2012

Research Groups

Algebra and Algebraic Geometry, Topology

Research Area

Algebraic Topology and Higher Category Theory

Bio

Research Interests

I work in the areas of algebraic topology, homotopy theory, and higher category theory. Currently, I am especially interested in the higher categorical and algebraic structures one encounters in equivariant homotopy theory and analogous settings. My thesis established a theory of indexed infinity-categories, focusing on the notion of indexed homotopy limits and colimits; specializing the base infinity-category to the orbit category of a finite group, one obtains equivariant applications. Subsequent to this and in joint work with Barwick, Dotto, Glasman, and Nardin, I am developing infinity-categorical foundations for equivariant higher algebra. For example, we introduce and study a notion of G-symmetric monoidal infinity-category which is a homotopical enhancement of a structure studied by Hopkins and Hill. Geometrically, our viewpoint is informed by stratified homotopy theory; for instance, in a certain precise sense one may view the slice filtration of G-spectra introduced in the seminal work of Hill, Hopkins, and Ravenel as a perversity filtration. Apart from this, I am pursuing some other projects in equivariant homotopy theory and motivic homotopy theory.
 

Selected Publications

  • Parameterized higher category theory and higher algebra: Expos´e II - Parameterized homotopy limits and colimits. In preparation.
  • Categorifying rationalization (with C. Barwick, S. Glasman, M. Hoyois, and D. Nardin). October 2016. arXiv:1610.07162. Not yet submitted for publication.
  • Parameterized higher category theory and higher algebra: Expos´e I - Elements of parameterized higher category theory (with C. Barwick, E. Dotto, S. Glasman, and D. Nardin). August 2016. arXiv:1608.03657. Not yet submitted for publication.
  • Parameterized higher category theory and higher algebra: a general introduction (with C. Barwick, E. Dotto, S. Glasman, and D. Nardin). August 2016. arXiv:1608.03654. Not yet submitted for publication.
  • Fibrations in 1-category theory (with C. Barwick). August 2016. arXiv:1607.04343. Submitted for publication to the MATRIX conference proceedings.

Email: jshah3@nd.edu
Office: 255 Hurley Bldg

Website