Name: Ziwei Tan
Class Year: 2025
Major: Mathematics
Hometown: Beijing, China
Internship Organization: Williams College
Internship Title: Student Researcher, SMALL Undergraduate Research Program
Location: Williamstown, MA
What's happening at your internship? We would love to hear what kind of work you are doing!
I am working as a student researcher at Williams College under the guidance of Professor Adams. In the past few weeks, we have studied concepts from several papers on hyperbolic knots and considered some specific open problems. The research problem I am working on is to prove that a compact, orientable three-manifold (without spherical boundary) contains hyperbolic handlebodies of arbitrary genus. As a corollary, we can remove a finite, disjoint set of handlebodies of any chosen genera from the manifold, ensuring that the closure of the resulting manifold is tg-hyperbolic.
Why did you apply for this internship?
· Professor Adams' research on knot theory aligns perfectly with my current interests.
· I wanted to see if I liked math enough to consider going to graduate school.
· I’m happy to do some math during such a long break.
What is something you have learned from your internship that you didn't expect?
I learned algebraic topology by myself since my team members are really into calculating fundamental groups…
Can you give us three adjectives and three nouns that describe your internship experience?
Three adjectives:
1. Hyperbolic
2. Essential
3. Incompressible
Three nouns:
1. Beads
2. Bracelets
3. Bongles
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