Degrees and Accolades:

Ph.D. (Massachusetts Institute of Technology)

Research Profile:

Number Theory: Artin's conjecture, Elliptic curves, Modular Forms, Automorphic forms, Langlands Program, Selberg's conjectures, Sieve Methods, Cryptography

• More research description can be found at CICMA
• Here is list of recent mathematical and philosophical publications
• This is the link for Mathematical Reviews of my papers.
• Here is the link to my mathematical genealogy.

Research Areas:

Project 1: Classical number theory focuses on arithmetical functions of a single variable. Current number theory now realizes the importance of the study of arithmetical functions of several variables and their associated Dirichlet series of several complex variables. One of my projects is to extend the classical theory of a single variable to the multi-variable context. Some of my recent papers represent a modest beginning in this direction.

Project 2: Graph theory is a powerful tool to analyze many problems confronting the human race. It is a profound method to represent complicated processes which allows for the introduction of mathematical tools to be applied to “real world” problems. This is evident in what is now called “network theory”. Spectral graph theory exhibits analogies with the theory of zeta functions in number theory. Thus, this analogy can be used to discover new theorems in graph theory. A viable research project is to re-visit classical graph theory in the light of modern problems arising from technologies, environments and other biological processes with a view to understand and solve them.

Project 3: Probability theory is often studied as a branch of mathematics divorced from number theory. In the last century, a new branch of mathematics called probabilistic number theory has taken shape. This theory needs to be expanded into the algebraic realm of the adele ring of global fields and in particular, the Prüfer ring Z. Thus, a third research project can be classified as “adelic probability theory”. At present there are only a few papers that have given serious attention to this perspective. Clearly these papers represent a humble beginning of a larger theory yet to be discovered.

Current Post-Doctoral Fellows:

Sunil Naik.

Current Doctoral Students:

Nicolo Fellini, Becca Carter.

Recent Thesis Supervised:

• Siddhi Pathak, The Chowla problem and its generalizations, (M.Sc., Queen's, 2015)
• Kannappan Sampath , The saddle point method and its applications to number theory(M.Sc., Queen's, 2015)
• Akshaa Vatwani, Higher rank sieves and applications(Ph.D., Queen's, 2016).
• Arpita Kar, Representation of numbers by quaternary quadratic forms, (M.Sc. Queen's, 2016).
• Peng-Jie Wong, Character theory and Artin L-functions (Ph.D., Queen's, 2017).
• Francois Seguin, The two-variable Artin conjecture and elliptic analogues (Ph.D., Queen's, 2018)
• Siddhi Pathak, Special values of L-series, periodic coefficients, and related themes (Ph.D., Queen's, 2019).
• Christopher Zajner, An Encounter between East and West: The notion of truth in William James and Swami Vivekananda (M.A. Philosophy, Queen's, 2020).
• Paul Wilson, Lattices, codes and sphere packing problems (M.Sc., Queen's, 2020).
• Arpita Kar, Normal order of certain arithmetic functions and new analogues of the Erdos-Kac theorem (Ph.D., Queen's, 2020).
• Benoit Urvari, Cicero's Search for Yoga, (M.A. Philosophy, Queen's, 2022).
• Stephen Berry, Panpsychism, Vivekananda and the Hard Problem of Consciousness, (M.A. Philosophy, Queen's, 2024).