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/equivariant/motivic homotopy theory, Equivariant Algebra, Algebraic K-Theory, TQFTs, Higher category theory, Homotopy Type Theory and Categorical Logic. Currently, my thesis work revolves around Topological Jacobi forms and equivariant TMF computations. Apart from that, I am also involved in some Picard group computations of invertible modules over E_n^{hC_2}, 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 towards the general Mahowald-Ravenel redshift phenomena of the Mahowald invariant, which was work under the guidance of J.D. Quigley, Freed-Hopkins theory, and HoTT semantics, which was under the guidance of Ulrik Buchholtz.

I also find Applied Category Theory, in general, really interesting.

Apart from these 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 that can be pursued.

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.)