Research and Activities

On this page, I’ll upload my research works and keep them updated. I’ll also share any notes I’ve written, and in addition, I’ll be adding my talks and presentations here.

Recent Works

  1. Power Operations In Homology Of \(E_{\infty}\)-spaces- PDF.
  2. Braid Group action on \(D^b(\mathfrak{M}_{\eta})\)- PDF[arXiv:2510.15396]
  3. Revisiting Pontryagin's Proof of Stable Stems 1 and 2 PDF [arXiv:2503.11211]

Articles and Notes

  1. Applications of Cohomology operation in Homotopy theory - [PDF, html] This is my lecture notes of the talk delivered in the "What is...?" seminar organized by Mathclub, ISI Bangalore.
  2. Intersection homology - [PDF]. This pdf contains the materials of my two talks of Intersection homology seminar at ISI, Bangalore.
  3. Riemann Roch and Serre duality -[pdf] Here I have discussed about Riemann Roch theorem and it's application on Riemann surfaces including Moduli spaces. It was the contents for my talks of seminar on Riemann surfaces.
  4. Cohomology and Poincaré Duality - [PDF]
  5. Some Fixed point theorems - [PDF]
  6. Acyclic Model theorem and equivalence of homology theories -[PDF] This is part of my VSRP 2023 report.
  7. Künneth formula and Universal coefficient theorem - [PDF]
  8. Hahn Banach Separation and Riesz representation theorem - [PDF] This is not pure Analysis but convex Geometry. These were used in the functional analysis course (5th semester 2023, fall).
  9. The spaces of Lebesgue integrable functions \(L^1\) and \(L^2\) - [PDF]
  10. Notes on Complex analysis - [PDF]
  11. Notes on analysis of several variables - [PDF]
  12. One point compactification with examples - [PDF]
  13. Ordinal numbers and Cardinal numbers - [PDF]

Talks / Presentations

  1. (2025) On \(E_{\infty}\)-algebras and Power operations on it - Midsem Presentation, ISIK.
  2. (2025) Tentative Braid Group action on \(D^b(\mathfrak{M}_{\eta})\)- ANU, Canberra.
  3. (2025) Tangled in Three, Free in Four [Video] Limit 2025, ISI Bangalore.
  4. (2024) On Equivariant Stable Homotopy group of Sphere [Slides] Park City, PCMI(IAS) 2024
  5. (2024) What is cohomology [Video] 'What is ...?' seminar 2024,ISI Bangalore
  6. (2024) Intersection Homology and It's Properties - Intersection Homology seminar, ISI Bangalore, 2024.
  7. (2023) Jordan-Brouwer Separation theorem - VSRP,2023 Presentation, TIFR(Mumbai), Online.