Descent into the telescopically localised world
About
I am an Integrated Master’s student at the National Institute of Science Education and Research, Homi Bhabha National Institute, Bhubaneswar, India. My current thesis advisors are Chitrabhanu Chaudhuri and Lennart Meier.
I work in chromatic/motivic homotopy theory, Algebraic K-Theory, and Higher Category Theory. Currently, my thesis work revolves around (higher) Topological Jacobi forms and equivariant TMF computations. Apart from that, I am also involved in constructing motivic models of cyclotomic synthetic spectra, some THH computations, which will presumably shed some light on redshift phenomena and higher height cardinality computations in Ambidexterity.
In the past, I have organised seminars on Burklund-Yuan-Schlank’s Chromatic Nullstellensatz, which still makes the kid in me jump. I am also somewhat interested in Galois descent in telescopically localised algebraic K-theory and Freed-Hopkins reflection positivity and invertible phases, and recent progress after the resolution of THE Telescope conjecture.
Also, I have worked on a model for k-restricted unital infinity operads in the past, which was joint work with Yu Leon Liu. Apart from that, I also have some experience working on the general Mahowald-Ravenel redshift phenomena of the Mahowald invariant, under the guidance of J.D. Quigley, and on Freed-Hopkins theory and HoTT semantics, under the guidance of Ulrik Buchholtz.
I also find Applied Category Theory, in general, really interesting.
Apart from these, there are other ambitious projects and ventures that I wish to take up when my schedule permits, which, ofc, I don’t want to list. My view of Mathematics is broad, and I’m always open to ideas and themes coming from unknown waters in the unfathomable ocean of mathematics. I believe, after all, there are infinitely many things in the mathematical universe to pursue.
Aside from my primary preoccupations and interests, I’m also interested in Music, a hot mess of Schopenhauerian and Mainlaenderian Existentialist philosophy and, to some extent, Linguistics.
NOTE: I recently updated everything you see above. Thanks for stopping by. The stuff below, maybe later :P
Some stuff I’m currently reading or skimming, some of which I’m interested in finding time and energy to read. This is not exhaustive and in no order.
- The Chromatic Nullstellensatz arXiv
- PURITY IN CHROMATICALLY LOCALIZED ALGEBRAIC K-THEORY link
- Reflection positivity and invertible topological phases arXiv
- The motivic Mahowald invariant arXiv
- Generalised Mahowald Invariants: Thesis of J.D.Quigley link
- N_{\infty}-operads and associahedra arXiv
- Chromatic Cyclotomic Extensions arXiv
- Stable stems arXiv
- The Green book
- On topological cyclic homology arXiv
- TOPOLOGICAL HOCHSCHILD HOMOLOGY AND INTEGRAL p-ADIC HODGE THEORY arXiv
(Last updated on June 14, 2023)
(Note: I am not even trying to keep the above list updated because I just can’t and because it’s always an incomplete list. This is a mere expression of the flavour of things I am or am willing to spend my energy on at this moment.)