Rahul Kundnani
Also known as: Kundnani Rahul Thakurdas, R T Kundnani, R Thakurdas K, R K Thakurdas
Sharda University, Lovely Professional University, University of Mumbai
0009-0002-8759-9986
About
Rahul Thakurdas Kundnani is an active researcher in modern Algebraic Geometry and its deep interconnections with Commutative Algebra, Homological Algebra, Category Theory, and Number Theory. His work explores structural and homological phenomena within schemes, derived categories, and stacks, emphasizing how algebraic and categorical methods unify cohomological, arithmetic, and geometric frameworks.
His current research investigates the behavior of primary and integral-closure filtrations, the asymptotic growth of syzygies, and derived functorial invariants governing stability phenomena in non-reduced and equivariant geometries. He is particularly interested in geometric categorification, equivariant derived categories, and representation-theoretic structures underlying moduli and character sheaves.
Rahul also works at the interface of Algebraic and Étale Topology, developing analogies between homotopy-theoretic and arithmetic constructions. His interests extend into Quantum Topology and the formulation of algebraic and categorical models for quantum cryptography and counter-intelligence systems, where motivic and derived methods provide new structural insight into information and symmetry.
He has authored several advanced papers linking derived geometry, Rees algebras, valuation theory, and motivic homology, demonstrating new conceptual bridges between geometric representation theory and homological stability. His broader aim is to advance a unified vision where algebraic geometry serves as the central language connecting topology, arithmetic, and quantum computation.
Employment
-
Sharda University Research Scholar2025 - Present
Education
-
Sharda University Ph.D.2025 - 2028
-
Lovely Professional University MSc2022 - 2026
-
University of Mumbai B.Tech.2009 - 2012
Projects & Funding
Projects & funding information is unavailable.
Publications (19)
- Prime-to-\(p\) Isogenies, Component Groups, and Cohomological Inertia for Néron Models Save
- Degree-One Boundary Decompositions for Hodge-Type Shimura Varieties at Hyperspecial Level Save
- EQUIVARIANT DERIVED CATEGORIES, QUOTIENT STACKS, AND GEOMETRIC CATEGORIFICATION OF REPRESENTATIONS Save
- Artin and Swan Conductors via Nearby Cycles for Strictly Semistable Varieties over Local Fields Save
- Cohomological Monodromy, Vanishing Cycles, and Component--Group Corrections for Elliptic Curves with Bad Reduction:\\ A Uniform $\ell$--Independent Lefschetz--Conductor Framework via N\'eron Models, Nearby Cycles, and Frobenius Geometry Save
- Asymptotic Syzygy Growth and Depth Stability Along Integral-Closure Filtrations Save
- Homological Ramification Filtrations in Residually Transcendental Valued Function Fields Save
- Filtered Homological Newton Stratifications and Factorization Stability over Valuation Rings Save
- Vanishing of Boundary Chern Classes under Derived Base Change on Toroidal Compactifications Save
- Homological Obstructions to Integral Closure in Simple Extensions of Valuation Rings Save