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Yat-Sen Wong
Department of Mathematics
Email:
wong65 AT illinois DOT edu |
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About Me:
I am a third year Ph.D. student in the department of Mathematics at the University of Illinois at Urbana-Champaign.Research Interests:
My research interest is symplectic geometry and I am currently working on problems about symplectic embeddings and J-holomorphic curves.Publications and Preprints:
Education:
Teaching:
I am currently teaching one discussion section (ED3) of MATH 231 EL1, Calculus II.| Here is a list of my past teaching duties: |
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| University of Illinois at Urbana-Champaign (UIUC): | |
| Fall 2011 | MATH 241 Calculus III discussion section |
| Spring 2011, Fall 2010, Spring 2010 | Math 231 Calculus II discussion section |
| Fall 2009 | Grading jobs |
The Chinese University of Hong Kong: |
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| Spring 2009 | Tutorial classes (similar to discussion sections in UIUC) for MAT4210 Financial Mathematics |
| Fall 2008 | Tutorial classes for MAT2310 Linear Algebra & Applications |
| Summer 2008 | Tutorial classes for MAT3280 Introductory Probability | Spring 2008 | Tutorial classes for MAT4210 Financial Mathematics |
| Fall 2007 | Tutorial classes for MAT2310 Linear Algebra & Applications |
I am in the "list of teachers ranked as
excellent by their students" for Spring 2011
Besides those teaching experiences listed above, I also served as a head TA in Enrichment Programme for Young Mathematics Talents during summer 2010.
Interesting Mathematics: Turning a sphere "inside-out"
Let $f:S^2\rightarrow\mathbb{R}^3$ be the standard embedding of a 2-sphere into the 3-dimensional Euclidean space, Stephen Smale (1958) proved that $f$ and $-f$ are regularly homotopic. (This means if we view $f$ and $-f$ as immersions from $S^2$ into $\mathbb{R}^3$, then they are homotopic through immersions and the homotopy extends continuously to a homotopy of the tangent bundles.) Smale prove the theorem by considering the homotopy group of the Stiefel manifold and showing that the homotopic group of immersions from 2-sphere to Euclidean 3-space vanishes, hence $f$ and $-f$ are regularly homotopic.
People notice that Smale's proof did not produce any explicit regular homotopy that turns the sphere inside out, therefore the question remains is to give such an explicit regular homotopy. This problem is solved after many years by several models like "half-way models" and "minimax eversions". Aside from the real models, there are many digital videos clearly explain how to turn the sphere inside out, for example:
"Sphere Inside out Part-I"
"Sphere Inside out Part-II"
"The Optiverse"