# What is...? Seminar Previous Talks

The seminar's main goal is to expose culturally ambitious participants to some mathematical notions not taught in standard courses.  These topics form an important part of mathematical folklore, and may prove useful for doing research and enhancing teaching. Lectures will be given mostly by graduate and undergraduate student participants.

The current years talks can be found at What is ...? Seminar talks.

## Previous What is ...? talks

### 2010

• Thursday, June 24:  Charles Baker,What is a Turing Machine[pdf]
• Monday, June 28:  Donald RobertsonWhat is Desargue's theorem? [pdf]
• Thursday, July 1: Andy Nicol,What is a Cayley graph? [pdf]
• Thursday, July 8: Jeff Lindquist, What is a Ford Circle?
Ford Circles provide a method of embedding the rational numbers into the Euclidean plane R^2.  We will describe this embedding and use it to prove some facts related to Farey Series and Diophantine Approximation, most notably Hurwitz's theorem.
• Monday, July 12: Rob Bradford,  What is Zariski Topology?
In algebraic geometry, the Zariski topology defines the basic structure of varieties and schemes.  We will define this topology, discuss some of its basic properties, and give examples of its applications in algebraic geometry.
• Thursday, July 15: Brittany Albrinck: What is Phyllotaxis? [pdf]
Math surrounds us in our everyday lives, even in nature.  When a normal human being looks at a sunflower they see beauty.  But why is it so beautiful?  One could argue it is because Fibonacci numbers are hidden within its seeds and create an aesthetically pleasing pattern. Math can be found in the arrangement of most plants and phyllotaxis is the study of these mathematical arrangements. Further information appears in Scott Hotton's thesis? [pdf]
• Monday, July 19: Daniel Shapiro, What is the 1, 2, 4, 8, Theorem?
In 1898, Hurwitz proved that a bilinear n-square identity exists only when  n  is 1, 2, 4, or 8.  Consequently:  If a real finite-dimensional algebra  A  has a multiplicative "norm" then  dim A = 1, 2, 4 or 8.  We will outline a proof and mention some generalizations.
• Thursday, July 22; Jack Cheng,  What is the Cook-Levin Theorem?
• Monday, July 26:  Vitaly Bergelson,  What is the Hindman's theorem (via ultrafilters)?
• Thursday, July 29: Daniel Poole, What is the Cauchy principal value?
• Monday, August 2: Theodore Dokos, What is squaring the square?
• Monday, August 9: Younghwan Son,What is the Duffin Schaeffer conjecture? [pdf]
• Thursday, August 12: Drew Meyer, What is Pick's theorem?
• Monday, August 16: Neal Edgren,  What is Bieberbach's conjecture?
• Thursday, August 19: Ross Askanazi,  What is the Perron-Frobenius theorem?