# Mathematics Colloquium Winter 2019

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 a****rt 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 seen****before. In the picture below, the tile has sides (2,3,4), and N = 48.**

**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**