Quinn La Fond
Email:
qlafond AT uoregon DOT edu
About Me
I am a PhD student at the University of Oregon studying pure mathematics.
I am interested in how differential and algebraic geometry interact with theoretical
physics.
Expository Works
The following projects are at various stages of completeness. Please email me with any corrections or questions.
- Algebraic Geometry: Filling in the Gaps
This project originally began as my
study tool for the Part III algebraic geometry and abelian varieties exams, and was an attempt to fill in
the details left as exercises in the lectures. These lectures, by Dhruv Ranganathan and Tony Scholl, were my first introduction to
algebraic geometry, and thus the exposition is from the perspective of someone slowly understanding
the geometric content in scheme theory. Many comparisons are drawn to the theory of smooth
manifolds, as I was at one point much more comfortable with the language of differential geometry
than schemes.
Since Part III, these notes have taken on a bit of a life of their own. They now cover far more than what was
in the original
lecture series while still omitting much content that I plan to include in the future (in fact, the current
draft says nothing of abelian varieties).
Since these began as personal notes, I have done a terrible
job at citing references; hopefully I will fix this one day. At the moment I have drawn mainly
from the aforementioned lectures, EGA, the stacks projects, Vakil's 'Rising Sea', Hartshorne, and 'Liu's Algebraic Geometry
and Arithmetic Curves'. The topics are presented in an order that makes the most sense to me, though I recognize
it may not be the most natural presentation. I am unsure if there
will ever be a point where I will say these notes are finished.
- The Geometry of Gauge Theory
This is my undergraduate honors thesis which I wrote under the supervision of Matt Szczesny in my final year at Boston University.
The goal of the project was to start at the definition of a smooth manifold, and
build up to the construction of the Yang-Mills-Dirac Lagrangian on a pseudo Riemannian manifold. It was heavily inspired
by Mark Hamilton's 'Mathematical Gauge Theory', and Lee's 'Smooth Manifolds'. This project is essentially complete;
one day I would like to add a chapter on general relativity and gauge theory.
Teaching & Office Hours
My office hours this term are 1-3PM Tuesdays and Fridays in University Hall 211.
In the Fall I will be teaching the following courses:
In the past I have taught the following courses:
Here is my CV.