Aditya Dwivedi

I am a first‑year PhD student in Mathematics at the Indian Institute of Technology Bombay.

My research interests lie in homological algebra, category theory, K‑theory, and transcendental number theory.

I completed a BS‑MSc dual degree in Mathematics from IIT Bombay (CPI: 9.4/10, Mathematics: 9.8/10).

Interests

Homological Algebra, Category Theory, K‑theory, Transcendental Number Theory.

Erdős problem for formal power series ring and Mahler's classification
Aditya Dwivedi, Digvijay Tiwari
Draft available upon request.

Hochschild Homology and its Taylor Approximation (Jan 2026 – present)
Working towards an independent proof of the HKR theorem using category theory and algebraic topology.
Advisor: Prof. Rekha Santhanam, IIT Bombay
Master’s Thesis: Free resolutions and related invariants (Jul 2024 – May 2025)
Studied free resolutions, Betti numbers, and the work of Ananyan–Hochster on Stillman’s conjecture.
Advisor: Prof. Ananthnarayan Hariharan, IIT Bombay

(Apr 2026) Deformation of \(F\)-injectivity and other \(F\)-singularities – IIT Bombay
(Apr 2026) A proof of the HKR theorem for simplicial \(\mathsf{k}\)-vector spaces – IIT Bombay
(Apr 2025) Localisation of Model categories – IIT Bombay
(Apr 2025) Briançon‑Skoda theorem for F‑rational singularities – IIT Bombay
(Feb 2025) A proof of the classic Erdős‑Ko‑Rado theorem – IIT Bombay
(Jan 2025) A proof of the Hochschild‑Kostant‑Rosenberg theorem – IIT Bombay
(Jan 2025) A survey of Aṅkapāśa in Gaṇitakaumudī – IIT Gandhinagar (Invited)
(Nov 2024) Construction of Matsyameru in Gaṇitakaumudī – IIT Bombay
(Nov 2024) A survey of Manifold Calculus – IIT Bombay
(Oct 2024) A duality between Hilbert functions of Lex Ideals and quotients – IIT Bombay
(May 2024) Classification of the representations of the Unitary group – IIT Bombay
(Apr 2024) Asymptotics of Fourier transforms: some basic results – IIT Bombay
(Oct 2023) The absolute Galois group of \(\mathbb{Q}\) – IIT Bombay
(Aug 2023) A proof of the prime number theorem – IIT Bombay