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Jesse Franklin's website

Graduate student

Dept. of Mathematics and Statistics

University of Vermont

Tel: ask me in person

Email: first.last@uvm.edu

Office: Innovation Hall E324

Areas of interest: Algebraic Geometry, Number Theory (more details below)

Background

CV.

I am a graduate student in the Department of Mathematics and Statistics at the University of Vermont pursuing a PhD in math. In May 2019 I recieved a Bachelors of Arts in Mathematics from the University of Colorado at Boulder with Latin honors. I spent my first year of undergrad at the Georgia Institute of Technology and then transfered to CU Boulder for my other two years.

My teaching background includes gymnastics coaching for the City of Boulder, tutoring with National Honors Society in high school, yoga instruction for CorePower Yoga during college and finally my TA work at UVM, where I have been instructor of record for my courses for four years. During this time I worked as a teaching assistant at the Park City Mathematics Institute during summer 2022, a program of the Institute for Advanced Study.

My research projects right now are about stacks in the Drinfeld setting.

Research

Subjects:

  1. Number Theory.
  2. Algebraic Geometry.
  3. Arithmetic Geometry.

Specific Interests:

  1. Explicit Computations with Stacks.
  2. Canonical Rings of Stacks.
  3. Drinfeld setting - modular forms, modular curves, Bruhat-Tits tree.
  4. Rigid Analytic Geometry.
  5. Shtukas.
  6. Differential Algebra.

A Recent Research Statement.

UVM Number Theory Seminar

I organized unQVNTS, the UVM Number Theory and Algebra Seminar, for the 2022-2023 Academic Year.

Talks:

  1. Poster for AGNES @UPenn October 2023 -- The Geometry of Drinfeld Modular Forms.
  2. lightning talk slides Geometry of Drinfeld Modular Forms @ the first ever Dartmouth-UVM Math Day 2/10/2024.
  3. slides Geometry of Drinfeld Modular Forms @ Workshop on Number Theory in Function Fields at Penn State 3/12/2024.

Some documents I wrote:

  1. (Preprint) -- The Geometry of Drinfeld Modular Forms.
  2. (Preliminary Version) -- Section Rings of Q-divisors on Genus-1 curves --- joint with Michael Cerchia and Evan O'Dorney.
  3. Notes on Rigid Analytic Stacks and Rigid Stacky GAGA.
  4. Thesis proposal about Petri's theorem.
  5. Notes for the previous document about Petri's theorem with open problems and other information which does not appear in the final version.
  6. Translation Notes by A. Beauville in a Szpiro seminar about Pencils of Curves of Genus at least 2, called The Minimal Number of Singular Fibers of a Stable Curve over P^1.

Scholarship

Since my CV includes my most notable scholarships, honors and publications in detail, this website will include only supplementary information to the CV. I want to ackowledge the Keller Family and the Ryan Keller Memorial Scholarship and my first algebra instructor Dr. Richard Green, both of which parties were crucial for my academic career.

References

Advisors: Christelle Vincent and Taylor Dupuy. UVM.

Former (BA) Advisor: Nat Thiem. CU Boulder.

Teaching

A Recent Teaching Statement

My Syllabi are:

  1. Math 17 Sp 21.
  2. Math 19 F 19.
  3. Math 19 F 20.
  4. Math 19 Sp 20.
  5. Math 17 F 21.
  6. Math 10 S 22.
  7. Math 19 F 22.
  8. Math 19 S 23.
  9. Math 1034 F 23.
  10. Math 1034 B 24.

Recent teaching review: "I am sure that Newton, Leibniz, and many of their colleagues would not have objected to it. Lots of activity, especially for a class so early in the morning. He spoke and wrote clearly, had everything well organized, and he had good rapport with the students. As a Math 19 class, I cannot fault it."

About

I study numbers for a living, climb rocks, ski uphill both ways, read, and play games. Here is a link to some climbing videos, and maybe some day some math ones.

Here is a link to a super interesting paper about academic practice. I won't go so far as to say I completely agree with this thing in a blanket way, but it sure is thought provoking.