Hello! Welcome to my webspace. I am a mathematician and an engineer. I am currently with the Department of Mathematics, State University of New York, at Plattsburgh. You can find my faculty profile here.

As my education and scholarship can attest, I have broad interests and tend to be transdisciplinary in my problem solving approach. My research interests in pure mathematics are primarily on questions in number theory. I am motivated by problems with an analytical flavor that have a rich algebraic and topological structure, and these usually tend to come from number theory. I also work on problems in linear algebra and matrix theory, and applied problems in computer science and engineering. I am interested in collaborating with people from academia, government and industry.

I am also interested in mathematics education, history, and pedagogy of mathematics. One of my current projects is on the history of compactness in advanced calculus, and its use in pedagogical design of an advanced calculus class.

I have an overarching interest is in philosophy. Particularly, in the philosophy of mathematics, mathematical philosophy (click here for the difference between the two!), Buddhist and eastern philosophy, and the interrelations between these.

I love doing math outreach projects for kids in K12 and the general public. See my outreach page for more information.

Below you will find some of my published and unpublished work, and presentations. Although I am quite introverted, I love collaborating with people! So, if you are interested in collaborating on any of the areas mentioned above please email me.

Education:

Ph.D. Mathematics

Oregon State University, 2019.

Specialization: Analytic number theory.

Ph.D. Electrical and Computer Engineering

University of California, Santa Barbara, 2010.

Specialization: Scientific computing, Numerical linear algebra, Signal Processing.

B.S. Electrical and Computer Engineering

California State University, Chico, 2003.

Specialization: Embedded Systems, Signal Processing.

Publications:

5. Understanding Compactness Through Primary Sources: Early Work, Uniform Continuity to the Heine-Borel Theorem. Book chapter to appear in Teaching Undergraduate Mathematics with Primary Historical Sources: Projects for Real Analysis, Topology, and Complex Variables. Editors Janet Heine Barnett, Nicholas A. Scoville and David K. Ruch, AMS/MAA Classroom Resource Materials Series.

Available online as part of TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS), Summer 2022, digitalcommons.ursinus.edu/triumphs_analysis/16/ .

4. Non-Archimedean Koksma inequalities, variation, and Fourier analysis (with Clayton Petsche). Uniform Distribution Theory, Vol.17, No. 22, 2022, 21- 50. (Journal, Open access).

3. A Leveque-type inequality on the ring of p-adic integers. International Journal of Number Theory, Vol. 18, No. 3, (2022), 655-671. (Journal). (An Arxiv version is available here).

2. On the infinitesimal limits of the Schur complements of tridiagonal matrices (with S. Chandrasekaran). Linear Algebra and its Applications, Volume 436 (3), 2012, Pg. 659-681. (Journal)

1. On the numerical ranks of the off-diagonal blocks of the Schur complements of discretized elliptic PDEs (with S. Chandrasekaran, P. Dewilde, M. Gu). SIAM J. Matrix Anal. Appl., 31(5), 2010, 2261–2290. (Journal)

Selected Talks:

8. Fourier Analysis, Discrepancy, and Koksma Inequalities on the p-adic integers. Conference on Equidistribution and Arithmetic Dynamics, Oklahoma State University, Stillwater, OK, June 22, 2022.

7. An introduction to p-adic numbers. 2022 Teacher to Teacher conference, NYS Master Teacher Program, April 9, 2022, SUNY, Plattsburgh.

6. p-adic numbers and Harmonic Analysis. Math Club, Department of Mathematics, California State University, Chico, April 16, 2021 .

5. The ABC pedagogy for teaching mathematics. Department of Mathematics, Washington State University, Vancouver, September 2018.

4. Equidistribution of sequences on the p-adic unit ball. Analysis seminar, Portland State University, Portland, Oregon, May, 2018.

3. Equidistribution of sequences on the p-adic unit ball. Joint Mathematics Meetings, Special Session on Analytic Number Theory, January, 2019.

2. Harmonic analysis on the p-adic unit ball. Great Lakes Mathematical Physics Meeting, Institute for Mathematical and Theoretical Physics, Michigan State University, East Lansing, Michigan, June 2018.

1. A LeVeque type inequality for the distribution of sequences on the p-adic unit ball. Upstate New York Number Theory Conference, SUNY, Buffalo, New York, April, 2018.