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Hire Dr. Rahul K.

India

USD 200 /hr

Research Consultant | Algebraic Geometry · Commutative Algebra · Homological & Categorical Methods

Profile Summary

Master Profile Summary I am a research consultant specializing in algebraic geometry, commutative algebra, and their deep interactions with allied fields. My expertise spans: Commutative Algebra (100% pure) – symbolic and ordinary powers, associated primes, integral closure, blowup algebras, depth and dimension theory. Algebraic Geometry with Homological Algebra – derived categories, Ext/Tor functors, duality, spectral sequences, sheaf cohomology. Algebraic Geometry with Category Theory – stacks, functorial approaches, localization, categorical equivalences, higher categories. Algebraic Geometry with Algebraic Topology – motivic cohomology, K-theory, topological invariants of schemes. Étale Topology & Cohomology – Grothendieck topologies, étale fundamental groups, descent methods. Arithmetic & Number Theory Links – Diophantine geometry, schemes over integers, Galois cohomology, Langlands connections. Geometric Representation Theory – Satake correspondence, Springer theory, character sheaves, equivariant derived categories. Homotopy & Homology – chain complexes, simplicial methods, derived functors, applications in algebraic geometry and topology. What I Offer Drafting and structuring research papers for submission to Q1 journals. Mathematical consulting: theorem development, proof refinement, example construction, counterexample analysis. Technical editing & LaTeX support: bibliographies, cross-referencing, diagram creation, error-free typesetting. Publication strategy: aligning manuscripts with the expectations of journals such as Journal of Algebra, JPAA, Compositio, Selecta Mathematica, and Springer/Elsevier/AMS titles. Why Work With Me Ph.D.-level specialization in algebraic geometry, commutative algebra, and homological methods. Experience with Q1 journal standards and referee-style feedback. Ability to bridge multiple domains, ensuring your manuscript is both technically rigorous and well-positioned for acceptance.

Subject Matter Expertise

• ☆ Applied Mathematics
• ☆ Mathematical Models
• ☆ Mathematical Optimization
• ☆ Mathematics Education
• ☆ Mathematical Control Theory
• ☆ Computational Sciences
• ☆ Mathematical Physics
• ☆ Differential Equations
• ☆ Chaos Theory
• ☆ Group Theory
• ☆ Mathematical Wavelets
• ☆ Computational Mathematics
• ☆ Stochastic Processes
• ☆ Game Theory
• ☆ Pure Mathematics
• ☆ Fractals
• ☆ Number Theory
• ☆ Categorical Algebra
• ☆ Algebra
• ☆ Calculus
• ☆ Mathematical Analysis
• ☆ Geometry
• ☆ Mathematical Logic
• ☆ Topology
• ☆ Graph Theory
• ☆ Discrete Mathematics
• ☆ Integral Equations

Services

• Writing
• Consulting

Writing Technical Writing, Creative Writing, General Proofreading & Editing

Consulting Scientific and Technical Consulting

Work Experience

Independent Consultant

Independent Consultant

January 2025 - Present

Research Scholar

Sharda University

January 2025 - Present

Education

PhD

Sharda University

January 2025 - Present

Ph.D. (Mathematics)

Sharda University

January 2025 - December 2028

MSc (Mathematics)

Lovely Professional University

June 2022 - July 2026

M.Sc.

Lovely Professional University

June 2022 - June 2024

B.Tech. (CSE)

University of Mumbai

July 2009 - June 2012

Certifications

• NA

  NA

  January 2025 - January 2025

Publications

PREPRINT

Rahul Kundnani, Khushwant Virdi, Shri Kant, Khursheed Alam (2025). Minimal Automaton and Asymptotics for the Parity of Zeckendorf Digit Sums .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Néron Models over $\Spec\mathbb{Z}$: Prime-to-$p$ Isogeny Extension, Semicontinuity of Component Groups, Cohomological Inertia, Hecke-Orbit Uniformity, and Height Gaps .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Segal Sheafification and Refinement-Invariant Descent .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Zariski Density of Associated Graded Primes and Degree--1 Torsion in Special Fibers of Rees Algebras .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Cohomological Detection of Good Reduction on Tame Moduli Stacks: Nearby Cycles, $N=0$, and a Stacky Néron--Ogg--Shafarevich Criterion .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Cohomological Monodromy and Component-Group Corrections for Elliptic Curves with Bad Reduction: A Uniform $\ell$-Independent Lefschetz--Conductor Framework via Néron Models and Moduli Stacks .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Explicit Conductors and Nearby Cycles for Strictly Semistable Varieties over Local Fields .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Frobenius Slope Envelopes and Ramification Bounds in Mixed Characteristic .

Rahul Kundnani, Shri Kant, Khurheed Alam (2025). Slope--Weight Coincidence Loci in $p$-adic Hodge Theory and Applications to Modularity Lifting .

Rahul Kundnani, Shri Kant, Khursheed Alam (2025). Asymptotic Syzygy Growth and Depth Stability Along Integral-Closure Filtrations .