Notes

Below is a (semi)complete list of notes I’ve prepared as a speaker or participant in graduate seminars and courses. Please contact me if you have any questions or spot any typos¹.

Seminars

Discrete homotopy and homology of graphs

Seminar talks

• The fundamental group of a graph, December 2, 2020.
• Higher discrete homotopy groups of graphs, February 11, 2021.
• Discrete cubical homology, November 10, 2021.

Seminar notes

• Overview of path homology theory of digraphs by Alexander Grigor’yan, February-March 2022.
  • Talk 1, February 25, 2022.
  • Talk 2, March 4, 2022.
  • Talk 3, March 11, 2022.
  • Talk 4, March 25, 2022.
  • The speaker’s complete notes

Topos theory

Seminar talks

• Sheaves as étale spaces and the inverse image sheaf, November 8, 2021.
• Lattice and Heyting algebra objects in a topos, April 21, 2022.

Homotopical algebra

Seminar talks

• The projective model structure on chain complexes, March 11, 2021.
• Reedy categories and diagrams, April 1, 2021.

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Courses

Mathematical computation (Summer 2021)

Professor Dan Christensen

• Haskell and the power of functional programming presentation slides and recording, June 24, 2021.

Commutative algebra (Winter 2021)

Professor Ajneet Dhillon

• Lecture notes

Convex geometry (Fall 2020)

Professor Graham Denham

• Lecture notes

Field theory (Winter 2020)

Professor Ajneet Dhillon

• Lecture notes

Algebraic geometry (Winter 2020)

Professor Ajneet Dhillon

• Lecture notes

Category theory (Summer 2018)

Professor Chris Kapulkin

Selected exercises from Emily Riehl’s Category Theory in Context:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5

Representation theory (Summer 2018)

Professor Dan Christensen

• Cayley graphs and Fourier analysis on finite groups presentation notes

Algebraic number theory (Winter 2018)

Professor Chris Hall

• Galois theory and quartic polynomials project document

Algebraic topology (Winter 2018)

Professor Dan Christensen

• Long exact sequence of homotopy groups for a fibration presentation notes

Graph theory: Expander graphs (Fall 2017)

Professor Chris Hall

• Cayley graphs and expanders project document

Functional analysis (Fall 2017)

Professor Matthias Franz

• Hilbert spaces: orthonormal bases presentation notes

Rings and modules (Fall 2017)

Professor Nicole Lemire

• Noetherian rings and affine algebraic sets presentation notes