Fall 2023: Characteristic classes & K-theory
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Anibal Aravena Lopez - Comparison of sheaf cohomology with Cech and singular cohomology
Robin Huang - Riemann-Roch theorem for curves
Skyler Hudson - Hopf’s Theorem
Kerem Inal - First and Second Stiefel-Whitney classes as Obstructions
Sophia Marx - Introduction to Obstruction Theory and Eilenberg-MacLane Spaces
Bela Nelson - An Introduction to Spectral Sequences
Dalton Pettway - Hopf algebras motivated from algebraic topology
Isaac Pliskin - Introduction to spin structures
Takuto Sato - Chern-Weil homomorphism
Chunlin Shao - Equivariant K-theory of flag varieties
Leo Xu - Gauss-Bonnet theorem & characteristic classes
Ethan (Yang) Zhou - Holomorphic Vector Bundles on Riemann Surfaces
Fall 2021: Introduction to Homological Algebra
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Frank Cole - On examples of categorification in mathematics
Jacob Cordeiro - Cohomology and homology of commutative rings
William Dugan - An introduction to Hochschild cohomology and Hopf algebras
Josiah Foster - Derived categories and the canonical bundle
Seong Eun Jung - Tate cohomology
Pranav Kalkunte - DGAs and Kadeishvili's theorem
Benny Levine - Weak Mordell-Weil by way of Selmer groups
Brody Lynch - An introductory survey of Galois cohomology and elliptic curves
Porter Morgan - Joyal's model category for quasicategories
Baz Pratt and Noah Solomon - Combinatorial species
Chunlin Shao - Lie algebra cohomology
Arthur Wang - Homological algebra techniques in link homology
Yuxuan Yang - Vanishing theorem for high degree of sheaf cohomology
Chujiao Zhang - Grothendieck Galois Theory
Ethan (Yang) Zhou - Equivalence Derived Categories of Coherent Sheaves on an Abelian Variety and Its Dual
Spring 2021: Moduli Spaces in Representation Theory (co-taught with Chris Elliott)
The papers below take a few moments to load from Google Drive, so be patient after you click the link.
Al Baraa Abd Aldaim - An Introduction to Topos Theory
Mihail Arabadji - Survey on the invariants, operations on 4-manifolds and their effect on Seiberg-Witten invariants
Jacob Cordeiro - Applying symplectic geometry to GIT through the Kempf-Ness theorem
Filip Dul - Quotient Stacks and Physics
Muldrow Etheredge - Calabi-Yau manifolds and string theory
Josiah Foster - GIT and the Moduli Space of Genus g Curves
Andreas Hayash - Zastava spaces for SL_2
Weiyang Li - A reading journal of quantum group
Bela Indurkhya Nelson - Classification of holomorphic vector bundles over CP^1
Audrey Rosevear - An Introduction to the Hitchin Moduli Space as an Integrable System
Jesse Selover - The dot action on the cohomology of Hessenberg varieties
Arthur Wang - Hilbert scheme of points on a surface
Chujiao Zhang - Foundations of stacks and orbifolds