Undergraduate Lecture Series (Math Monday): Helpful ways to Visualize Spaces

Lecture | February 27 | 5-6 p.m. | 740 Evans Hall

 Jeff Hicks, UC Berkeley

 Department of Mathematics

A lot of my intuition for mathematics comes from drawing pictures of the problem I want to solve. As a topologist, this means trying to come up with clean visual representations of various topological spaces. A good drawing for a space should ideally be

- Mathematically Motivated: the diagram has an explanation coming from some underlying structure on the space

- Intuitive: one should be able to understand how to manipulate the space from manipulating the diagram

- Informative: One should be able to read of mathematical facts about the space from looking at the diagram

- Forgiving: It shouldn’t be too hard to draw!

In this talk, we’ll start with techniques for visualizing surfaces, and gradually increase the dimension—time permitting, we’ll be able to visualize some 6-dimensional manifolds by the end of the talk. Bring something to draw with!