Quinn La Fond

Email: clafond AT bu DOT edu

About Me

I am a PhD student in pure mathematics at Boston University. I am interested in how derived geometry and higher category theory interact with theoretical physics, particularly in formalizations of quantum field theory.

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.

Here is my CV.