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Welcome!
I am Pankaj Singh, a mathematician and recent Ph.D. in Mathematics from the University of South Carolina (USC) in Columbia, South Carolina, where I was advised by Dr. Alexander Duncan.
My research is broadly in algebraic and arithmetic geometry and related areas, including number theory, commutative and non-commutative algebra, and representation theory, with a focus on rationality problems, algebraic tori and their torsors, and Brauer groups. I also enjoy computational approaches to algebra (experimentation in Python, SageMath, and Macaulay2).
I work actively in formalized mathematics and proof assistants (Lean 4 / Mathlib). Recent projects include a four-person formalization of the Lorenz-system trapping-region lemma at the ICARM Summer School on Formalization of Mathematics, where I co-authored reusable, Mathlib-candidate lemmas on preconnected sets, frontiers, and continuous first-exit times; an audit methodology for AI-generated Lean formalizations developed through M2PI (PIMS), and ongoing work on a research-level formalization of Kontsevich deformation quantization. I am eager to contribute to community libraries such as Mathlib and CSlib through focused formalization projects.
Relevant documents:
Curriculum Vitae (Academic) - (Drive link),
I am guided by the principles shared by Federico Ardila, which reflect a vision of inclusive and empowering mathematics:
Axiom 1: Mathematical potential is equally present in all groups, regardless of geographic, demographic, or economic boundaries.
Axiom 2: Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3: Mathematics is a powerful, malleable tool that different communities can shape and use to meet their own needs.
Axiom 4: Every student deserves to be treated with dignity and respect.
These principles shape how I approach learning, teaching, and engaging with mathematics.
Office: Leconte college Room 413
Contact: pksingh[at]email[dot]sc[dot]edu
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