Research

Current research interests include number theory, arithmetic geometry, elliptic curves, and Galois representations. My thesis, with advisor Álvaro Lozano-Robledo, focuses on classifying torsion subgroups of elliptic curves over function fields of genus zero and one. Recently, I have become interested in torsion subgroups of elliptic curves over function fields of hyperelliptic curves, and with this, bounding the gonality of certain families of modular curves.

Thesis

PhD Thesis: Torsion Subgroups of Ellitpic Curves over Function Fields

Research Articles

  1. Torsion Subgroups of Elliptic Curves over Function Fields of Genus 0 , in JNT
  2. Torsion Subgroups of Elliptic Curves over Function Fields of Genus 1 (current rough draft)

Talks Given

Seminar Talks

  • Undergraduate Math Club Talk, University of Connecticut March 11, 2020
  • Number Theory Seminar, Wesleyan University November 22, 2019
  • Five College Number Theory Seminar, University of Connecticut March 5, 2019
  • Algebra Seminar, University of Connecticut November 28, 2018
  • Number Theory Seminar, Boston University December 11, 2017
  • SIGMA Seminar, University of Connecticut April 1, 2017
  • Undergraduate Math Club Talk, University of Connecticut Spring 2017

Conference Talks

  • AMS Sectional Meeting April 14, 2019
  • 2019 Joint Math Meetings January 19, 2019
  • 2018 Automorphic Forms Workshop, Tufts University March 20, 2018
  • Maine-Québec Number Theory Conference, University of Maine October 14, 2017

Conferences Attended

  • Connecticut Summer School in Number Theory - Research Conference June 2020 online, University of Connecticut, Storrs, CT
  • Cross Atlantic Representation Theory and Other topics ONline (CARTOON) May 2020 online
  • 1148th AMS Sectional Meeting April 2019 University of Connecticut Hartford, Hartford, CT
  • Northeast Consortium for Quantitative Literacy XXII Meeting March 2019 Bay Path University, Longmeadow, MA
  • 2019 Joint Math Meetings January 2019 Baltimore, MD
  • Connecticut Summer School in Number Theory (CTNT) May 2018 University of Connecticut, Storrs, CT
  • Automorphic Forms Workshop March 2018 Tufts University, Boston, MA
  • Arizona Winter School: Iwasawa Theory March 2018 University of Arizona, Tucson, AZ
  • Maine-Québec Number Theory October 2017 University of Maine, Orono, ME
  • MSRI Summer School: Automorphic Forms and Langlands Program July/August 2017 MSRI, Berkeley, CA
  • Seventh Upstate New York Number Theory Conference May 2017 Binghamton University, Binghamton, NY
  • Arizona Winter School: Perfectoid Spaces March 2017 University of Arizona, Tucson, AZ
  • Connecticut Summer School in Number Theory August 2016 University of Connecticut, Storrs, CT
  • Arizona Winter School: Arithmetic Geometry March 2016 University of Arizona, Tucson, AZ
  • BU/Keio University Workshop 2015 September 2015 Boston University, Boston, MA
  • Elliptic Curves @ UConn May 2014 University of Connecticut, Storrs, CT
  • Advanced Technological Education (ATE) 2013 Conference Fall 2013 American Association of Community Colleges, Washington DC

Teaching

Shaped by my past instruction, I recognize the responsibility to provide students with a positive mathematical experience. This is especially important in service courses, which are often terminal courses, where students may have developed a negative attitude toward mathematics. I remember the teachers who were successful in fostering my interest in the material they taught. I incorporate my favorite memories into my own teaching. In my experience, successful teachers made learning enjoyable by doing special examples and applications that were relevant and stimulating. They told stories about their own experiences with mathematics. They showed a genuine love for the craft. In the same spirit, I try to impart a love for mathematics in my students by sharing my joy for teaching, the way my favorite teachers did for me.

Teaching Experience

Yale University

Lecturer

  • Introduction to Functions and Calculus I (coordinator) Fall 2020
  • Approximation and Prediction 1 Summer 2020
  • Introduction to Functions of Several Variables Spring 2020
  • Introduction to Functions and Calculus II Spring 2020
  • Calculus of Functions of One Variable IIFall 2019
  • Calculus of Functions of Several VariablesFall 2019
University of Connecticut

Instructor of Record

  • Applied Linear AlgebraFall 2018
  • Calculus for Business and EconomicsSpring 2016, Fall 2016, Fall 2017, Spring 2018
  • BRIDGE CalculusSummer 2015

Teaching Assistant

  • CTNT Graduate AssistantSummer 2018
  • Calculus IISpring 2017
  • Calculus for Business and EconomicsSummer 2016
  • CTNT Graduate AssistantSummer 2016
  • Calculus IIFall 2015
  • Calculus ISpring 2015
  • Calculus IIFall 2013, Spring 2014, Fall 2014
Eastern Connecticut State University

Internship in College Teaching

  • Geometry Fall 2012

Curriculum Vitae

Coordinates and Contact Information

Department of Mathematics
Yale University
10 Hillhouse Ave
New Haven, CT 06511

Office: 418 DL
Email: robert.j.mcdonald@yale.edu
Phone: 860 - four eight four - three six one nine

Family and Home

Me and the fam. Currently, I live in Middletown, CT, with my wife, Kayla, and our newborn son, Andrew, born June 2019. We are absolutely in love with him. We also have a cat, Lemma, who's been with us since I started graduate school. Kayla and I love to travel, and have taken a trip every year since we met. Most notable was our two-month cross country trip in 2016. We took a very awkward route to California which saw us in Nashville, St. Louis, New Mexico, the Grand Canyon, and Vegas. Our route back was more direct. We loved seeing the Grand Canyon, the redwoods, Yosemite, Yellowstone, and so much more.

Experiences in Education

I've been living in Connecticut since I was six years old. I grew up in a small town called Scotland, about 45 minutes east of Hartford, CT. Scotland is a very small town, with a population of about 1700 people. There were 20 students in my class at primary school, and with two other towns, Chaplin and Hampton (with a total population of around 4000 between all three), I had a high school graduating class of 30 students. Honestly, I loved the experience of a small school and a small community, which is why I ended up going to a small local community college and Eastern Connecticut State University, a small liberal arts college in Willimantic, CT, to complete my bachelor's in mathematics. ECSU was by far the best choice for me; they had 5000 undergraduates, and my class sizes were rarely over 10-15 students. The liberal arts philosophy fostered great relationships between me, my class, and my professors, and I left feeling more well-rounded than I would have with a more pre-professional education at a larger university.

While finishing up at Eastern, I spent some time working as a metal cutting engineer at Spirol International in Danielson, CT. Tere, I designed side and end-work cutting tools for multispindle lathes. It was very fun, but ultimately, I decided my true passion was for math research and teaching. That's when I decided to go to the University of Connecticut (a not so small school) to pursue my PhD in mathematics, which I received in May of 2019!

Some Hobbies

Tough mudder.

I love to hike, bike, and run, though I'm trying to get back into the latter. I'm really into table top RPGs, and may have dabbled a little bit in LARP (don't tell anyone). I'm equally interested in video games, and fill a lot of my "free time" playing new and retro games. Finally, I love to sing and play music. I'm in the Vernon Chorale, a small choral ensemble in Vernon, and I'm getting ready to play the saxophone in the Middletown Symphonic Band. I don't think I'm particularly good at either, but it's an amazing outlet. I've run a few half marathons, and one full marathon (where "run" is an operative term). I've also done a rugged maniac, but my all time favorite was the Tough Mudder!