Twice a year, UW-Madison hosts an seminar dedicated to interactions between mathematics and other academic areas. The only rule is that the speaker must be either a non-mathematician with something to say about mathematics or a mathematician with something to say about non-mathematics. The speakers so far:
Title: "Geometry and Music."
In my talk, I will explain how to translate the basic concepts of music theory into the language of contemporary geometry. I will show that musicians commonly abstract away from five types of musical transformations, the "OPTIC transformations," to form equivalence classes of musical objects. Examples include "chord," "chord type," "chord progression," "voice leading," and "pitch class." These equivalence classes can be represented as points in a family of singular quotient spaces, or orbifolds: for example, two-note chords live on a Mobius strip whose boundary acts like a mirror, while four-note chord-types live on a cone over the real projective plane. Understanding the structure of these spaces can help us to understand general constraints on musical style, as well as specific pieces. The talk will be accessible to non-musicians, and will exploit interactive 3D computer models that allow us to see and hear music simultaneously.
Title: "How to disagree about how to disagree"
When one encounters disagreement about the truth of a factual claim from a trusted advisor who has access to all of one's evidence, should that move one in the direction of the advisor's view? Conciliatory views on disagreement say "yes, at least a little." Such views are extremely natural, but they give bad advice when the issue under dispute is disagreement itself. So conciliatory views stand refuted. But despite first appearances, this makes no trouble for partly conciliatory views: views that recommend giving ground in the face of disagreement about many matters, but not about disagreement itself.
Title: "Grothendieck, Braque, and the formality of relativism"
Abstract: Why do we do mathematics? What place does math have in society? In this talk, I'll discuss some striking common ground shared by the mathematics and art of the first two thirds of the 20th century. I'll talk about how this commonality might have arisen and what I think this says about how we should view the discipline of mathematics.
Back to Jordan Ellenberg's home page