Xingyu Cheng

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Some miscellaneous notes

Here are various notes that I've typed up over time, either for class presentations, various talks I've given at UNC, or for personal use. These are listed in no strict order, though maybe the top ones are more recent (and perhaps better). All mistakes are my own.

• Just enough complex geometry to be dangerous. These are notes that I've written for a JGMRT talk introducing some of the basic ideas of complex geometry and how it should relate to algebraic geometry.
• Notes on quantum cohomology. Some notes I've written up while I was learning about quantum cohomology of Grassmannians. I believe I learned much of this material from Buch's papers on the subject. These documents contain some worked out examples of multiplying Schubert classes in 'small' Grassmannians.
• What's in a scheme? A set of notes for a talk I gave at jGMRT, a weekly student ran seminar about topics in geometric representation theory.
• Zariski's Main Theorem. This is a set of notes I wrote for a class presentation on Zariski's Main Theorem.
• Module of Differentials. This is a set of notes for a class presentation on module of differentials.
• Semigroup Theory. This is a set of notes for a final class project on semigroup theory in PDEs.
• Dynkin Diagrams. A set of notes for a final project about Dynkin Diagrams and root systems.