Anish Chedalavada's Homepage

About Me:

I am a fifth year PhD student and Teaching Assistant in the Department of Mathematics at Johns Hopkins.

Research:

My current research focus is in spectral algebraic geometry and tensor-triangulated geometry. I am broadly interested in homotopy theory and the areas of geometry and algebra with which it interacts.

Preprints:

  1. Higher Zariski geometry, joint with Ko Aoki, Tobias Barthel, Tomer Schlank, and Greg Stevenson.
      We revisit the classical constructions of tensor-triangular geometry in the setting of stably symmetric monoidal idempotent-complete \(\infty\)-categories, henceforth referred to as 2-rings. In this setting, we produce a Zariski topology, a Zariski spectrum, a category of locally 2-ringed spaces (more generally \infty-topoi), and an affine spectrum-global sections adjunction, based on the framework of "\(\infty\)-topoi with geometric structure" as developed by Lurie in [DAGV]. Using work of Kock and Pitsch, we compute that the underlying space of the Zariski spectrum of a 2-ring recovers the Balmer spectrum of its homotopy category. These constructions mirror the analogous structures in the classical Zariski geometry of commutative rings (and commutative ring spectra), and we also demonstrate additional compatibility between classical Zariski and higher Zariski geometry. For rigid 2-rings, we show that the descent results of Balmer and Favi admit coherent enhancements. As a corollary, we obtain that the Zariski spectrum fully faithfully embeds rigid 2-rings into locally 2-ringed \infty-topoi. In an appendix, we prove a ``stalk-locality principle'' for the telescope conjecture in the rigid setting, extending earlier work of Hrbek.

In preparation:

Research Talks:

  1. A derived refinement of a classical reconstruction theorem in tt-geometry, Oberwolfach Workshop 2338a: Tensor-Triangular Geometry and Interactions. [Notes], [Extended Abstract for Oberwolfach Report].

Teaching:

Past teaching:

JH

UIC

Notes:

I maintain a list of talks along with notes from various reading seminars that I have participated in here.

Important Links: