Hello! I am a mathematician with research interests in the realm of Function Field Arithmetic. Born in Apple Valley, California on June 3rd, 1985, I received my Bachelor’s degree in 2009 from the University of California, San Diego, where I was awarded the Department of Physical Sciences’ Dean’s Undergraduate Award for Excellence in 2008. I obtained my Ph.D. in December 2013 from The Ohio State University under the supervision of D. Goss, where I was named a Presidential Fellow for the year of 2013. For the year of 2014, I held a postdoc position at the Universite Jean Monnet, St. Etienne, under the supervision of Prof. F. Pellarin, with an office at the Institut Camille Jordan, Lyon. From mid-January 2015 to mid-Sept. 2015, I was a postdoctoral fellow at the Mathematics Center Heidelberg (MATCH), and up until July 2017, I held a postdoctoral fellowship from the Alexander von Humboldt foundation and worked at the University of Heidelberg under in the group of Prof. Dr. G. Boeckle. I’ve also held an AMS-Simons Travel Grant for the period of July 2014 to June 2017.
Presently, I am an adjunct faculty in the Mathematics Department at Cuyamaca College in the beautiful desert of East San Diego, where I am teaching Mathematics for Elementary School Teachers and Statistics with Support. Cuyamaca College is on the cutting edge of instruction where open enrollment is available allowing all students to take transfer level courses in mathematics and several other subjects during their first semester in college, and I am excited to be a part of a team of dedicated teachers who are passionate about making the world of higher education available to all. On the weekends you can find me at the Art of Problem Solving Academy, where I teach mathematics enrichment courses in Middle School Contest Math (including Number Theory, Geometry, Algebra, and Counting and Probability), Classical Geometry, and Precalculus. At both Cuyamaca College and AoPS Academy, I practice a student centered instructional style full of questions and discussion so that the students are actively engaging with the material while in the classroom.
At the moment, my research has taken a back-seat to my teaching, but I am staying as active as possible, and my interests continue to include modular forms and special values of L-functions in positive characteristic. Currently, F. Pellarin and I are jointly expanding on his theory of deformations of vectorial modular forms; we have a new preprint here. I also have interest in L. Taelman’s unit and class modules and his class number formula (possible further topics include Taelman’s Herbrand-Ribet Theorem and Anderson’s log-algebraicity), and their generalizations by Angles, Pellarin and Tavares Ribeiro. There are still many interesting questions for Taelman’s class and unit modules arising from analogies with class and unit groups of number fields which beg to be investigated. I hope to eventually secure a professorship at a liberal arts college.
If you would like to contact me, please write to: rudolph (dot) perkins (at) gmail (dot) com