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 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). 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. Currently, I am an instructor at the Art of Problem Solving Academy in San Diego, where I teach three classes: Jr. High Algebra 1 and two sections of 4th grade math. I enjoy teaching and working with students very much, and I hope to eventually secure a professorship at a liberal arts college.
My research interests 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 arising from analogies with class groups which beg to be answered about these modules.
If you would like to contact me, please write to: rudolph (dot) perkins (at) gmail (dot) com