Joseph Albert Helfer
I am a postdoc in mathematics at the Simons Center for Geometry and Physics.
I study symplectic and algebraic geometry, and categorical logic.
Previously, I did a postdoc at the University of Southern California.
I completed my PhD at Stanford University under the supervision of
Yasha Eliashberg in
Symplectic Geometry.
Before that, I completed my Master's degree at McGill University under the supervision of
Dani Wise in
Geometric Group Theory.
Teaching
Spring 2025, MAT 308 (Differential equations with linear algebra)
In previous semesters, I've taught MAT 200 (Logic, Language, and Proof) and (at USC) Math 635 (Algebraic Geometry), Math 435 (Differential Geometry), Math 440 (Point-Set Topology), Math 540 (Algebraic Topology), and Math 471 (Linear Algebra).
Things I've written
Publications
Exotic tight contact structures on R4m+1 (with François-Simon Fauteux-Chapleau). 2021. (Preprint)
First-order homotopical logic. 2019. (Preprint)Homotopies in Grothendieck fibrations. 2019. (Preprint)
A Note on Maxima in Random Walks (with Dani Wise). 2016.
Counting cycles in labeled graphs: The nonpositive immersion property for one-relator groups (with Dani Wise). 2015. (Preprint)
Preprints
Y is a least fixed point combinator. 2025. 
Internal 1-topoi in 2-topoi. 2024.
Severi curves of rational elliptic surfaces (with François Greer and John Sheridan). 2023.
Notes
The ugly truth about simplicial sets.
The first talk of the Fall 2017 HTTCLHIE seminar.
Schoolwork
My CEGEP independent study project. It describes the implementation of a Unix shell.
My Bachelor's thesis, about computing the space of Delaunay triangulations of a punctured Riemann surface. Here is the accompanying code.
My Master's thesis, which is an expanded version of the paper with Dani Wise (above) about counting cycles in labeled graphs.
My PhD thesis on contact homology for open manifolds.
Writing LaTeX in emacs
Here is a great emacs package for writing LaTeX in emacs (in addition to the indispensable Auctex package).
It automatically adds “newcommand” and “usepackage” statments to your file, based on a global file you maintain with command definitions.