Talk Notes

Some notes for talks I have given are hosted here. A word of warning - I often write these notes with a certain flow in mind. These notes are intended for me to have somewhere to keep myself organized ​during the talk, and they are not intended to be read as a written introduction to the content. There may also be some mistakes.

  1. Non-Abelian Hodge Theory. We introduce the ideas of Non-Abelian Hodge theory and we discuss how to study complex variations of Hodge structure on a space by studying its non-abelian cohomology theories. This talk was loosely based on the ideas in Carlos Simpson's amazing paper "Higgs bundles and Local Systems".
  2. Six Functor Formalisms. This talk introduces Grothendieck's six operations. This talk is based on these notes by Martin Gallauer ​and was part of a series of talks for an Étale cohomology learning seminar hosted at the University of Toronto in the summer of 2024. 
  3. Étale Fundamental Groups. This talk introduces Étale fundamental groups and computes some basic examples and examples of related objects, such as the prime-to-p part of the Étale fundamental group for curves over fields of characteristic p. This talk is based on this book by James Milne, and was part of a series of talks for an Étale cohomology learning seminar hosted at the University of Toronto in the summer of 2024.
  4. Why an Engineer Can Draw Better Than You. We introduce mechanical linkages and then we draw all (bounded components of) algebraic curves with them. This talk was based on this paper by Michael Kapovich and John J. Millson, and the talk is intended for an audience of graduate students.
  5. Counting Curves and Gromov-Witten Invariants. We discuss how to count curves by Gromov-Witten invariants, and then we discuss the Gromov-Witten theory of the projective plane. This talk was based on these notes by Simon Rose.
  6. Character Varieties . We review the notion of a character variety, and then we compute the tangent space of a smooth point in terms of group cohomology. This talk was based on  this paper by Adam Sikora and was given as a part of a series of talks for a learning seminar on rigid local systems.
  7. Symplectic Toric Manifolds. We review the notion of a symplectic toric manifold, and then we use morse theory to compute the homology of these manifolds. This talk was based on these notes by Ana Cannas da Silva.