Ishan Panpaliya

Award-winning mathematics student researcher with a focus on number theory and cryptography. Demonstrates exceptional problem-solving abilities and strong communication skills. Committed to achieving excellence in all projects. Actively seeking part-time research scientist or summer internship opportunities in mathematical sciences.

1. On the atomicity of one-dimensional monoid algebras (2024) arXiv: arXiv:2411.16151

• Investigates atomicity and the ascending chain condition (ACCP) in one-dimensional monoid algebras, strengthening previous results and showing atomic behavior under certain rational Puiseux monoids. (arXiv)

2. On the ascent of almost and quasi-atomicity to monoid semidomains (2025) arXiv: arXiv:2501.04990

• Studies how almost atomicity and quasi-atomicity properties in commutative monoids behave when extended to polynomial rings and monoid domains, including examples showing limits of such ascent properties. (arXiv)

3. On GL-domains and the ascent of the IDF property (2025) arXiv: arXiv:2504.10722

• Defines and characterizes GL-domains and studies whether the irreducible divisor finiteness (IDF) property ascends to polynomial extensions, answering open questions about this behavior. (arXiv)

4. The average genus number for pure fields of prime degree (2025) arXiv: arXiv:2507.14317

• Multiauthor paper) Investigates average genus numbers in pure number fields of prime degree—a topic in algebraic number theory.