Joseph Albert Helfer
I am a postdoc in mathematics at the University of Southern California.
I study symplectic and algebraic geometry, and categorical logic.
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
Fall 2023, Math 540 (Algebraic Topology)
In previous semesters, I've taught Math 435 (Curves and Surfaces) Math 440 (Point-Set Topology) Math 540 (Algebraic Topology) and Math 471 (Linear Algebra).
Things I've written
Publications
First-order homotopical logic. 2019. (Preprint)
Homotopies in Grothendieck fibrations. 2019. (Preprint)
Counting cycles in labeled graphs: The nonpositive immersion property for one-relator groups (with Dani Wise). 2015. (Preprint)
A Note on Maxima in Random Walks (with Dani Wise). 2016.
Preprints
Severi curves of rational elliptic surfaces (with François Greer and John Sheridan). 2023. 
Exotic tight contact structures on R4m+1 (with François-Simon Fauteux-Chapleau). 2021.
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.
Amusements
After all, what's the point if you don't have a little fun?
To me, fun primarily
means generating
various
lists.
Also this.
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.