Arthur Huang

Shaosai (Arthur) Huang

Mathematics Department
University of Wisconsin
480 Lincoln Drive
Madison, Wisconsin 53706

Office: Room 520 Van Vleck Hall
Phone: (608)262-3601
Email: huang@math.wisc.edu

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.

Research Interests

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
Seiberg-Witten
spin geoemtry
index theory
irrational rotation algebras
K-theory
sheaf cohomology
maximal functions (averaging over hyper-surfaces )

Some Notes

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.

Teaching

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.

Conference Talks

August 2012, I talked about "Germ-Implicit Function Theorom and Regularizing Sections" at the 2012 MIT-RTG Geometry Workshop.

Seminar Talks

June 2012, I talked about "Harmonic functions on manifolds" at the 2012 USTC Geometry Summer School.
October 2010, I talked about "Refinement of the Strichartz's inequality for non-elliptic Fourier restriction" at the dispersive PDE seminar.
August 2010, I talked about "Profile decomposition of solutions to the free Schrodinger equation" in the summer PDE course.
July 2010, I talked about "L^2-mass concentration for NLS in 2+1 dimension" in the summer PDE course.
Feburary 2010, I talked about "Sheaf Cohomology, Derived and Triangulated Categories" at the Topology of Algebraic Varieties Learning Seminar.
January 2010, I talked about "Irrational Rotation Algebras and Their Canonical Extensions" at the Operator Algebras Seminar.

Conferences Attended

October 2012, Stony Brook NY, International Conference on Cycles, Calibrations and Nonlinear Partial Differential Equations, Celebrating Blaine Lawson's 70th Birthday
August 2012, Wastonville CA, 2012 MIT-RTG Geometry Workshop, with Professor Helmut Hofer
May 2010, Waterloo ON: Connections in Geometry and Physics.

Some Links