Shaosai (Arthur) Huang
480 Lincoln Drive
Office: Room 520 Van Vleck Hall
I am a second-year PhD student in mathematics at the Univeristy of Wisconsin-Madison. Prior coming to Madison, I finished my master and undergraduate study in mathematics at the University of Toronto.
For more information please look at my CV.
I am currently studying the limit behavior of Riemannian manifolds with certain curvature bounds, especially the theory of Cheeger-Colding, and its various applications.
I'm also interested in the following side topics:
- holomorphic curves and their bubbling phenomena
- spin geoemtry
- index theory
- irrational rotation algebras
- sheaf cohomology
- maximal functions (averaging over hyper-surfaces)
- Harmonic functions on manifolds : in this note I learned the amazing geometric argument of Colding and MinicozziII in their 1997 paper.
This is supervised by Professor Nachman in Fall 2010.
- Quantum Mechanics and Topological Invariants: in this note I studied the first and second parts of Witten's paper "Supersymmetry and Morse Theory".
This is supervised by Professor Gualtieri in Spring 2010.
- Matrix Inequalities : in this note I studied several classical results on completely positive linear operators, operator convex functions and operator inequalities.
This is supervised by Professor Choi in Fall 2009.
- H^2(X,Z): in this note I computed the second integral cohomology group for triangulable topological spaces using sheaf cohomology techniques and Snake lemma.
This is supervised by Professor Kamnitzer in Summer 2009.
- A note on dimension: this is a problem in Perrin's book "Algebraic Geometry" that I like a lot.
- A note on the definition of sheaves: I first touched "sheaf" in learning Kirwan's book on intersection cohomology; here I clearified some of my own confusions.
- Fall 2012, Algebra (MATH112), Sections 004 and 009, at UW-Madison.
- Spring 2012, Calculus and Analytic Geometry (MATH222), Discussion Sessions 365 and 366, at UW-Madison.
- Fall 2011, Calculus and Analytic Geometry (MATH221), Discussion Sessions 395 and 398, at UW-Madison.
- Fall 2010 - Spring 2011, Advanced Calculus (MAT237Y1) at UToronto.
- Fall 2010, Linear Algebra I (MAT223H1) at UToronto.
- Fall 2009 - Spring 2010, Calculus I (MAT135Y1) at UToronto.