Research

My research interests are in number theory. More specifically my work involves Diophantine equations, p-adic and algebraic number theory. I am also interested in the theory of Quadratic forms.

Currently, I am a Professor of Mathematics at the Oregon Institute of Technology. Before coming here, I was a Visiting Assistant Professor in the Department of Mathematics at the University of Toledo, OH from 2010 to 2013. I completed my Ph.D. in Mathematics from the University of Kentucky in August 2010, under the supervision of Prof. David Leep. My research interests are in Number Theory and Quadratic Forms. My Ph.D. thesis was titled Diagonal Forms and Rationality of the Poincaré Series, which, loosely speaking, is the study of the number of solutions of a polynomial modulo powers of prime and the power series that it generates.

I did my undergraduate education – B.S. (Hons.) in Mathematics from the Chennai Mathematical Institute, India in 2004.

CV (.pdf)

Publications

  1. The 21 card trick and its generalization, arXiv.org:1809.04072
  2. On the Diophantine equation \(p^x + p^y = z^{2n}\), arXiv.org:1709.01814
  3. (with David Leep) The Poincare series of a diagonal polynomial
  4. (with David Leep) Powers in complete discrete valuation rings
  5. Diagonal forms and the rationality of the Poincare series, Ph.D. thesis, University of Kentucky, 2010.

OIT Mathematics Colloquium

I have been organizing the OIT Mathematics Colloquium since Fall 2018. I’m always looking for speakers. If you are interested in giving a talk, then please contact me. Here are the list of former speakers.

List of Speakers

Fall 2018

  • Dibyajyoti Deb, Dept. of Mathematics - The 21 Card Trick and Its Generalization, October 18, 2018.
  • David Hammond, Dept. of Mathematics - Fractal Geometry of Julia Sets, November 8, 2018.
  • Jesse Kinder, Dept. of Natural Sciences - Hartree-Fock Theory, November 29, 2018.

Winter 2019

  • Peter Overholser Dept. of Mathematics - Artificial Neural Networks and Applications, January 24, 2019.
  • Pat Schaeffer, Dept. of Management - Factorial Designed Experiments Using Minitab Statistical Software for Laser Weld Process Robustness, February 11, 2019.
  • Rosanna Overholser, Dept. of Mathematics - Causation, not just correlation, February 14, 2019.
  • Yuehai Yang, Dept. of Natural Sciences - How “Squishy” is a Roll of Graphene, a.k.a., a Single-Walled Carbon Nanotube?, February 25, 2019.
  • Randall Paul, Dept. of Mathematics - Mathematical Perspectives and Projective Geometry, March 14, 2019.

Spring 2019

  • Peter Overholser Dept. of Mathematics - Curves, blocks, chains, and coins, April 18, 2019.
  • Matthew Sleep, Dept. of Civil Engineering - The use of probability and statistics in geotechnical engineering - A case study on the Whittier Narrows Dam, May 9, 2019.
  • Reid Anderson, Math Major - Mathematical Ears!, May 23, 2019.
  • David Brookes, Dept. of Physics, Cal State, Chico - Dabbling in the “dark arts”: A physicist does education statistics, June 6, 2019.

Fall 2019

  • Gregg Waterman, Dept. of Mathematics - The Laplacian of a Graph: Is the Name Justified?, October 19, 2019.
  • Jim Fischer, Dept. of Mathematics - Introduction to Singularity Functions and How to Bend Beams with Your Mind, November 7, 2019.
  • Eve Klopf, Dept. of EERE - Application of Numerical Methods for Solving Problems in Electromagnetics, November 21, 2019.

Winter 2020

  • Jesse Kinder, Dept. of Natural Sciences - Hypercubes and Hyperspheres: Geometry in More Than Three Dimensions, January 23, 2020.
  • Gregg Waterman, Dept. of Mathematics - Vectors to Function Spaces, February 13, 2020.
  • Gregg Waterman, Dept. of Mathematics - A Basic Introduction to Wavelets, February 20, 2020.
  • Peter Overholser, Dept. of Mathematics - Information on information and why you can never come out ahead, no matter how hard you try, March 12, 2020.

Spring 2019

  • Talks cancelled due to COVID-19 pandemic.

Fall 2020

  • Alexis Harris, Math Major - Observing the Sensitivity of Step Sizes in a Neural Network, November 10, 2020.
  • Curtis Michaels, Math Major - The Regularizing Effects of the Heat Equation, November 24, 2020.

Winter 2021

  • Joseph Reid, Dept. of Mathematics - An Introduction to Modeling Outbreak Investigations, January 27, 2021.
  • Yan Jiao, Univ. of Adelaide, Australia - Design Electrocatalysts for Clean Energy Conversions – A Theoretical Point of View, February 10, 2021.
  • Jesse Kinder, Dept. of Natural Sciences - Monte Carlo simulation of epidemics on complex networks, February 24, 2021.

Spring 2021

  • Robyn Wilde, Dept. of Natural Sciences - Positronium collisions with atoms and molecules, April 21, 2021.
  • Austin Moyer, Math Major - The 2014 Ebola Outbreak, May 19, 2021.
  • Randall Paul, Dept. of Mathematics - Conics Like You’ve Never Seen Them, June 2, 2021.

Fall 2021

  • Randall Paul, Dept. of Mathematics - Harmonic Sets in Music and Art, October 21, 2021.
  • David Hammond, Dept. of Mathematics - The discrete Laplacian deconvolution method for differential interference contrast microscopy, November 4, 2021.
  • Dibyajyoti Deb, Dept. of Mathematics - The Geometry of Numbers, December 2, 2021.

Winter 2022

  • Rosanna Overholser, Dept. of Mathematics - A Tale of Three Frameworks for Estimating Uncertainty, January 20, 2022.
  • Peter Overholser, Dept. of Mathematics - Views From a Train, February 10, 2022.
  • David Johnston, Dept. of Natural Sciences - Fusion Energy, Ray Tracing, and the Normal Form, March 3, 2022.

Spring 2022

  • Randall Paul, Dept. of Mathematics - Dots and Boxes and Donuts, April 28, 2022.
  • Jesse Kinder (Dept. of Natural Sciences), Kim Kinder (M.D.) - The Most Beautiful Instrument, May 19, 2022.
  • Lukasz Zbroszczyk & Peter Bigica, Math Major, Western Connecticut State University - Using Machine Learning to Forecast Outcomes of Baseball At-Bats, June 2, 2022.

Fall 2022

  • Jesse Kinder, Dept. of Natural Sciences - Quantum Math, October 19, 2022.
  • Jason Smith, Dept. of Mathematics - Iteratively Counting Edges to Sum Squares and Cubes, November 9, 2022.
  • Su Jin Lee, Dept. of Geomatics - Introduction to GIS, December 7, 2022.

Winter 2023

  • Kenneth Davis, Dept. of Mathematics - Fair Division and the Problem of Redistricting, February 8, 2023.
  • Jesse Kinder, Dept. of Natural Sciences - What is a Quantum Computer?, February 22, 2023.
  • Tiernan Fogarty, Dept. of Mathematics - Modeling the hanging beam in a first term differential equations course, March 15, 2023.

Spring 2023

  • Terri Torres, Dept. of Mathematics - Honey Bee Research with Students at Oregon Tech, April 26, 2023.
  • Joseph Reid, Dept. of Mathematics - Minimize Your Writing Stress: Tools for Efficient and Reproducible Research, May 10, 2023.
  • Ashton Greer, Dept. of Civil Engineering - Rainfall Roulette: Climate Change and the Shifting Rainfall Patterns in Stormwater Infrastructure Design, May 31, 2023.

Fall 2023

  • Doug Gardner, Dept. of Mathematics, Rogue Community College - The Ubiquitous Truss: a marvel of engineering, October 17, 2023.
  • Jim Fischer, Dept. of Mathematics - Optimal Control and The Linear Quadratic Regulator, November 8, 2023.
  • Pake Melland, Dept. of Mathematics - Adventures in bistable perception: a low-dimensional perspective to a high(?) dimensional problem, November 29, 2023.

Winter 2024

  • Gregg Waterman, Dept. of Mathematics - A History of Photography and Cameras, January 31, 2024.
  • Joseph Reid, Dept. of Mathematics - What I learned from the Mouse – A perspective from working as a Mathematician in Industry, February 21, 2024.
  • Cristina Negoita, Dept. of Mathematics - A Mathematician Goes to Washington: My Year at the National Science Foundation, March 6, 2024.

Spring 2024

  • Cameron Castillo, Student - The Optimal Path: Low Thrust Orbital Transfers for CubeSats, April 24, 2024.
  • Tiernan Fogarty (Dept. of Mathematics), Graeme Wiltrout (Math Major) - Exploring Discrete Data Through Taylor Series, May 15, 2024.
  • Alissa Whiteley, Dept. of Mathematics - Modeling Greening Using Agent-Based and Ordinary Differential Equation Models, June 5, 2024.