HOW TO FILL A BIG SPACE WITH LITTLE THINGS

Wake Forest University
Department of Mathematics & Statistics

Colloquium

HOW TO FILL A BIG SPACE WITH LITTLE THINGS
Dr. Herman Gluck, University of Pennsylvania

Thursday, September 23, 11 :00AM
In Person Event: 121 Manchester Hall
or Join Zoom Meeting

There is a repeated pictorial theme in mathematics, in which a big space is filled up with non-intersecting copies of a smaller space, such as when the plane is filled up with parallel lines. Buzz words describing such situations are “fibrations” or “foliations” or “contact structures”.  These occur, for example, in algebraic geometry, differential geometry, geometric topology, algebraic topology, fluid dynamics and plasma physics. In any single situation, the most natural question is: in how many different ways can we do this? For example, there’s just a “circle’s worth” of ways to fill up the plane with parallel lines. In this talk, we’ll give some more substantial examples, try to understand the different ways to do this, and quickly find ourselves dealing with infinite-dimensional spaces. We won’t give any proofs, but we’ll comment on the variety of tools that we use, and tell you how to learn more. This talk is aimed at advanced undergraduate math majors, master’s students, and faculty from all areas.

In person host: John Gemmer (gemmerj@wfu.edu) Zoom host: Leandro Lichtenfelz (lichtel@wfu.edu)

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