Research

My research interests are broadly in algebra, number theory and algebraic geometry.

Recently I have been thinking about the local-global principles in Berkovich Theory and trying to obtain a period-index bound on complete non-Archimedean valued fields.

During the dual degree program at the University of Hyderabad, I did my MS Thesis on "Elements of Algebraic Number Theory".


Publications & Preprints

  • Strong u-invariant and Period-Index bound for complete ultrametric fields. Submitted. (arXiv version)

  • More publications upcoming. This tautological bullet point serves to ensure my website's CSS continues to function smoothly (unlike my garden).


Invited Talks

(*in reverse chronological order)

  • The Brauer Dimension of a Field, Special Session Talk for the AMS Special Session on Quaternions, at Joint Mathematics Meetings (JMM) 2025, Seattle, USA, January 2025.
  • Strong u-invariant and Period-Index Bounds, Zoom talk for Number Theory Seminar, The Ohio State University, December 2024.
  • Strong u-invariant and Period-Index Bounds, Talk at unQVNTS (Vermont) seminar, University of Vermont, October 2024.
  • Strong u-invariant and Period-Index Bounds, Talk at Algebra and Number Theory Seminar, Emory University, October 2024.
  • The Brauer Dimension of a Field, Special Talk, at ALGAR Summer School, University of Antwerp, Belgium, August 2024.
  • Twisted Number Field Counting, MAA Invited Paper Session on Rethinking Number Theory, at MAA MathFest, Indianapolis, August 2024.


Contributed Talks

(*in reverse chronological order)

  • Strong u-invariant for Complete Ultrametric Fields, AMS Contributed Papers on Topics in Algebra, JMM 2025.
  • A Twisted Variant of Malle’s Conjecture, AMS Contributed Paper Session on Number Theory and Field Theory III, JMM 2025.
  • (cancelled due to hurricane Helene) Strong u-invariant and Period-Index bound for complete ultrametic fields, Contributed Paper Session I, at Georgia Southern University for AMS Southeastern Sectional Meeting, October 2024.
  • (cancelled due to hurricane Helene) Twisted Number Field Counting, Contributed Paper Session I, at Georgia Southern University for AMS Southeastern Sectional Meeting, October 2024.
  • A Twisted Variant of Malle's Conjecture, Contributed Paper Session at Palmetto Number Theory Series (PANTS) XXXVIII, Wake Forest University, September 2024.
  • Twisted Number Field Counting, Graduate Student Conference in Algebra, Geometry, and Topology called GTA: Philadelphia 2024, Temple University in Philadelphia, May 2024.
  • Local-Global Principles Over The Years, Pre-talk for Igor Rapinchuk’s talk at Algebra and Number Theory Seminar, Emory University, October 2023.


Student Seminar Talks

(*in reverse chronological order)

  • Tidbits of Berkovich Spaces, RANT- Emory Student Seminar in Algebra and Number Theory, Atlanta, GA on April 18, 2024.
  • Basic Notions of Rigid Analytic Geometry, RANT- Emory Student Seminar in Algebra and Number Theory, Atlanta, GA on November 16, 2023.
  • What do Jabberwocky and Fava Beans have in common?, RANT- Emory Student Seminar in Algebra and Number Theory, Atlanta, GA on December 6, 2021.
  • Origami Constructible Numbers, RANT- Emory Student Seminar in Algebra and Number Theory, Atlanta, GA on February 16, 2021.
  • Class Number Formula, Final presentations for Masters’ Thesis, University of Hyderabad, India, September 15, 2020.


Contributed Course Talks

(*in reverse chronological order)

  • Extensions of Dedekind Domains and Discrete Valuations, for a course on Galois Cohomology, Emory University, March 29, 2023.
  • Techniques from Group Cohomology-Relation to Subgroups, for a course on Galois Cohomology, Emory University, February 15, 2023.
  • Free Resolutions and Syzygies, for a course on Commutative Algebra, Emory University, April 25, 2022.
  • Additive Number Theory, for a course on Analytic Number Theory, Emory University, May 3, 2022.
  • Unique Factorisation of Ideals, for a course on Algebraic Number Theory, Emory University, February 3, 2021.


Theses

  • (in preparation) Strong u-invariant and Period-Index Bounds, my Ph.D. thesis.
  • Elements of Algebraic Number Theory. (Masters' Thesis; 2020) here.