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".

*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).

(*in reverse chronological order)

- (upcoming)
*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 8-11, 2025. - (upcoming)
*Strong u-invariant and Period-Index Bounds*, Zoom talk at OSU Number Theory Seminar, The Ohio State University, December 02, 2024. - (upcoming)
*Strong u-invariant and Period-Index Bounds*, Talk at unQVNTS (Vermont) seminar, University of Vermont, October 24, 2024. *Strong u-invariant and Period-Index Bounds*, Talk at Algebra and Number Theory Seminar, Emory University, October 01, 2024.*The Brauer Dimension of a Field*, Special Talk, at ALGAR Summer School, University of Antwerp, Belgium, August 22-30, 2024.*Twisted Number Field Counting*, MAA Invited Paper Session on Rethinking Number Theory, at MAA MathFest, Indianapolis, IN, August 7-10, 2024.

(*in reverse chronological order)

- (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 (Fall 2024) on October 5, 2024. - (cancelled due to hurricane Helene)
*Twisted Number Field Counting*, Contributed Paper Session I, at Georgia Southern University for AMS Southeastern Sectional Meeting (Fall 2024) on October 5, 2024. *A Twisted Variant of Malle's Conjecture*, Contributed Paper Session at Palmetto Number Theory Series (PANTS) XXXVIII, Wake Forest University, September 22, 2024.*Twisted Number Field Counting*, Graduate Student Conference in Algebra, Geometry, and Topology called GTA: Philadelphia 2024, at Temple University in Philadelphia from May 31 to June 2, 2024.*Local-Global Principles Over The Years*, Pre-talk for Igor Rapinchuk’s talk at Algebra and Number Theory Seminar, at Emory University on October 3, 2023.

(*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.

(*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.

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