Mathematics Colloquium Winter 2019

Tuesdays - 4:00 p.m.
McHenry Library Room 4130
Refreshments served at 3:30 in the Tea Room (4161)
For further information please call the Mathematics Department at 459-2969

Tuesday, January 15th, 2019

Vinicius Ramos, Instituto de Matemática Pura e Aplicada (IMPA)

TBA


Tuesday, January 22nd, 2019

Michael Beeson, Professor Emeritus of Mathematics and Computer Science, San José State University

Triangle Tiling

Triangle tiling is t
he art and science of cutting a triangle ABC into N smaller congruent triangles, the "tiles". The tiles do not have to be the same shape as ABC. If this can be done, we say that ABC has been N-tiled by the tile. The talk will explain the tools used, which are "elementary" in nature, and I will prove a theorem: No triangle can be cut into seven congruent triangles. The general aim of the subject is to answer all the questions about which triples (ABC, tile, N)

correspond to tilings. There are many answered questions, and many unanswered questions. New families of tilings have been discovered. I will show pictures of some tilings that you have never seenbefore. In the picture below, the tile has sides (2,3,4), and N = 48.

 tiling.png

 


Tuesday, January 29th, 2019

TBA


Tuesday, January 29th, 2019

TBA


Tuesday, February 5th, 2019

Gabriel Paternain, Cambridge University

TBD


Tuesday, February 12th, 2019

TBA


Tuesday, February 19th, 2019

Theo Johnson-Freyd, Perimeter Institute

Bott periodicity from quantum Hamiltonian reduction

The "quantization dictionary" posits that constructions in noncommutative algebra often parallel constructions in symplectic geometry. I will explain an example of this dictionary: I will produce the 8-fold periodicity of Clifford algebras as an example of quantum Hamiltonian reduction of a free fermion quantum mechanical system. No knowledge of the words "quantization", "Clifford algebra", "free fermion", or "Hamiltonian reduction" will be assumed. The exceptional Lie group $G_2$ will make a cameo appearance.


Tuesday, February 26th, 2019

TBA


Tuesday, March 5th, 2019

Song Sun, University of California Berkeley