About
This is an undergraduate student seminar on geometry and topology. This semester, we will be working from Bott and Tu's Differential forms in algebraic topology, with supplementary materials from participants of the Physics Department as well as from Differential cohomology: categories, characteristic classes, and connections edited by Araminta Amabel, Arun Debray, and Peter Haine. We meet on Mondays 8:10–10:00 a.m. in Lecture Hall 1-304.
Here is a course description if you wish to register for credit.
Talks
Sep 11 '21, Yunsheng Li, Introduction; review of differential forms
Sep 13, '21, Yunsheng Li, De Rham theory in Euclidean spaces, notes on De Rham theory
Sep 27, '21, Mingjie Wang, Mayer-Vietoris sequences, notes on Mayer-Vietoris sequences
Oct 11, '21, Ruoyu Xu, Orientation and Integration, notes on orientation and integration
Oct 18, '21, Ruoyu Xu, Poincare Lemmas, notes on Poincare Lemmas
Oct 25, '21, Ruoyu Xu, Degree of Proper Maps, Yunsheng Li, Mayer-Vietoris Argument (Poincaré Duality)
Nov 8, '21, Yunsheng Li, Mayer-Vietoris Argument (Künneth Formula & Poincaré Dual) & Basics About Vector Bundles
Nov 15, '21, Yunsheng Li, Cohomology Theory on Vector Bundles
Nov 22, '21, Yunsheng Li, Cohomology Theory on Vector Bundles (Continue)
Nov 29, '21, Yunsheng Li, Cohomology Theory on Vector Bundles (Fin.), Hao Ouyang, The Generalized Mayer-Vietoris Principle
Dec 6, '21, Hao Ouyang, The Generalized Mayer-Vietoris Principle (Continue), notes
Dec 13, '21, Yunsheng Li, Examples and Applications of the Mayer-Vietoris Principle
Dec 20, '21, Yunsheng Li, Presheaves and Čech Cohomology, Gen Yue, Introduction to Quantum Mechanics, notes on Quantum Mechanics
Dec 27, '21, Gen Yue, Introduction to Quantum Mechanics (continue)
Jan 13, '22, Gen Yue, Introduction to Topological Phase and Application of de Rham Cohomology, notes on Topological Phase