Research interests

My research interest is in composition laws of binary forms and other homogeneous forms and their applications to arithmetic. In my PhD thesis, I worked on explicit composition identities for the higher composition laws in the quadratic case discovered by Manjul Bhargava. This is a generalization of Gauss composition of binary quadratic forms to the space of 2x2x2 cubes and other spaces obtained from cubes by certain natural operations. 

Currently, I am working on composition identities of binary quartic forms and its connections with elliptic curves.

In the past, I have also worked on projects in the area of automorphic forms and representation theory. 

 Publications

1.  Explicit composition identities for higher composition laws, Gautam Chinta and Ajith Nair, submitted (arxiv)

2. Hilbert modular forms and Galois representations, Ajith Nair and Ajmain Yamin, accepted for publication in AMS Contemporary Mathematics series (arxiv)

1.  PhD thesis - Explicit composition identities for higher composition laws in quadratic case (pdf)

2. Masters' thesis - Harmonic analysis on locally symmetric spaces associated to discrete cocompact subgroups of SL(2,R) (pdf)

1.  Towards a higher composition law of binary quartic forms  - Postdoc seminar, ASU.

2.  Explicit composition identities for higher composition laws - GANIT seminar, IIT-Gandhinagar.

3. Presented poster on Explicit composition identities for higher composition laws - Automorphic forms and Bloch-Kato conjecture, ICTS Bengaluru (2025).

4. Presented poster on Explicit composition identities for higher composition laws - Texas-Oklahoma Representations and Automorphic forms XIV conference (2025).

5.  Explicit composition identities for higher composition laws - Postdoc seminar, ASU.

6.  Explicit composition identities for higher composition laws - Algebra and Number theory seminar, ASU.

7.  Composition identities for higher composition laws - Southern Regional Number theory conference, Louisiana State University, USA (2024).

8.  The density of discriminants of quartic rings and fields - Student Study Seminar on the work of Manjul Bhargava, Columbia University, USA.

9.  Lie algebra of an algebraic group - Algebraic groups seminar, Fordham University, New York.

10.  Gauss Composition and Higher Composition Laws  - Conference on Arithmetic Statistics, Centre International de Rencontres Mathematiques (CIRM) France (2023).

11.  Higher Composition Laws and Gauss Composition - Eleventh Annual Upstate NY Number theory Conference, University of Rochester, USA (2023).

12.  Higher Composition Laws and Gauss Composition - Southern Regional Number theory conference, Louisiana State University, USA (2023).

13.  Higher Composition Laws and Gauss Composition - Binghamton University Graduate Conference on Combinatorics, Algebra and Topology (2022).