Hi, Soumya here!

I’m currently doing Masters in Mathematics at Indian Statistical Institute, Kolkata. My interest in research in Algebraic Topology, particularly I’m interested in Equivariant Stable Homotopy Theory.

The motivation behind this blog was to share my thoughts on mathematics and my experiences. I should thank Bikram for helping me setting up the website, particularly helping me setting up $\LaTeX$ without which this website wouldn’t have been fruitful.

Projects

Master’s Project at Indian Statistical Institute (ISI), Kolkata2025 Fall
I am currently doing my master’s project on Equivariant Stable Homotopy Theory under Professor Samik Basu. The goal of the project is to understand equivariant infinite loopspaces and cohomology operations on them. For this, we frist study Segal’s infinite loop space machinery from his paper Categories and Cohomology Theories to recognize spaces arising from symmetric monoidal categories as infinite loop spaces. We are also reading Peter May’s Algebraic Approach to Steenrod Operations to understand Dyer-Lashoff operations and then we want to study $C_2$-equivariant Steenrod operations following the ideas of Hu and Kriz, and equivariant Segal’s loopspace machinery following the ideas of Shimakawa.
Seminar on the Kervaire Invariant One Problem at Indian Statistical Institute (ISI), Kolkata2025 Fall
This is an ongoing reading seminar on Kervaire Invariant One Problem organised by Professor Samik Basu. The goal of the seminar is to understand the slice spectral sequence and learn major tools in Equivariant Stable Homotopy Theory following the works of Hill, Hopkins and Ravenel. The reading seminar will mostly focus on the proof of the periodicity theorem and the gap theorem.
Future Research Talent (FRT) at Australian National University (ANU), Canberra2024 Summer
I did a reading project on Equivariant Stable Homotopy Theory and Slice Spectral Sequence for Atiyah Real K-Theory. The goal of the project was to understand the construction of the Stable Homotopy Category both in the equivariant and the nonequivariant setup using the language of Model Categories. The main focus was to understand the Slice Spectral Sequence, a computational tool in Equivariant Stable Homotopy Theory popularised by Hill, Hopkins, and Ravenel in their proof of On the non-existence of elements of Kervaire invariant one. We ended the project looking at Dugger’s computation of homotopy groups of KR spectrum. (detailed project report can be found here).
Algebraic Geometry Seminar on Intersection Homology Theory at Indian Statistical Institute (ISI), Bengaluru2024 Spring
I am participating the Algebraic Geometry Reading Seminar on Intersection Homology Theory organised by Professor Charanya Ravi and Professor Jishnu Biswas from Indian Statistical Institute, Bangalore. More details about the seminar can be found over here.
Seminar on Riemann Surfaces at Indian Statistical Institute (ISI), Bengaluru2024 Spring
I participated in the Reading Seminar on Riemann Surfaces, organized by Professor B. Sury. The seminar was planned to introduce Riemann surfaces to students who had taken a course in complex analysis. We discussed about Céch Cohomology and concluded the seminar with some applications of Riemann Roch Theorem.
Visiting Scientist Research Program (VSRP) at Tata Institute of Fundamental Research (TIFR), Mumbai2023 Summer
I did an online reading project on Categorical Approach to Covering Spaces under Professor Anand Sawant, following the book Algebraic Topology by Tammo tom Dieck. (detailed project report can be found here).
Reading Project. New Mexico State University2023 Summer
I did an online reading project under Professor Prasit Bhattacharya on Homotopy Theory and Homology Theory, following the book A Concise Course in Algebraic Topology by Peter J. May. The project aimed to build a foundation for the construction of a Stable Homotopy Category.

Talks

  • Master’s Project End-semestral Talk at ISI, Kolkata. Equivariant Segal Infinite Loopspace Machine. (note)
  • Master’s Project Mid-semestral Talk at ISI, Kolkata. $\Gamma$-spaces and Connections with Category of Spectra. (notes)
  • FRT Presentation at ANU, Canberra. Equivariant Postnikov Tower and Homotopy Spectral Sequence. (notes)
  • Algebraic Topology Group at ISI, Kolkata. James space as a model for $\Omega\Sigma X$. (notes)
  • Intersection Homology Theory at ISI, Bengaluru. Pseudomanifolds and Intersection Homology. (notes)
  • Riemann Surfaces Seminar at ISI, Bengaluru. Céch Cohomology. (notes).
  • VSRP Presentation at TIFR, Mumbai. The Seifert-van Kampen Theorem for Fundamental Groupoid. (notes).
  • Limit Math Camp Talk. Mathematicians’ Dream of Doing Surgeries. (notes and YouTube link).
  • Math Club Talk at ISI, Bengaluru. What is Stable Homotopy Theory? (notes and YouTube link).

Activities

2025 SummerUndergraduate Directed Group Reading Project (UDGRP)
I was mentor of the Galois Theory summer reading project. It was a group reading project particularly intended for first and second-year undergraduates. The study of symmetries of roots of a polynomial is the proper setting for motivating Galois Theory, the goal of the project was to in built these ideas following the Morandi’s book on Fields and Galois Theory.
2023 SummerUndergraduate Directed Group Reading Project (UDGRP)
I was mentor of the Algebraic Topology summer reading project during 2023 Summer break. It was a group reading project particularly intended for first and second-year undergraduates. The goal of the project was to motivate the subject of Algebraic Topology through fundamental examples and exercises.
2022 WinterWinter Reading Project (WRP)
I was mentor of the Topology and Topological Groups winter reading project. It was a group reading project particularly intended for the first and second year undergraduates.