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 the 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.
Tuesday, January 29th, 2019
TBA
Tuesday, January 29th, 2019
TBA
Tuesday, February 5th, 2019
Gabriel Paternain, Cambridge University
Nonlinear detection of Hermitian connections in Minkowski space
I will describe how to recover a Hermitian connection form the source-to-solution map of a cubic non-linear wave equation in Minkowski space; the equation is naturally motivated by the Yang-Mills-Higgs equations. The recovery is reduced to a geometric problem of independent interest and not considered before: recovering a connection from its broken non-abelian X-ray transform along light rays. This is joint work with Chen, Lassas and Oksanen.
Tuesday, February 12th, 2019
Ralph Abraham, University of California Santa Cruz
Santa Cruz and Chaos: The place of UCSC in the History of Chaos Theory.
In this sequel my colloquium talk of May 30, 2017,I will give a concise history of the early development of chaos theory, followed by an outline of contributions from the math and physics departments of UCSC.
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
Metric collapsing of hyperkahler K3 surfaces
A K3 surface is a simply connected compact complex surface with trivial canonical bundle. Moduli space of K3 surfaces has been extensively studied in algebraic geometry and it can be characterized in terms of the period map by the Torelli theorem. The differential geometric significance is that every K3 surface admits a hyperkahler metric (a metric whose holonomy group is SU(2)), which is in particular Ricci-flat. The understanding of limiting behavior of a sequence of hyperkahler K3 surfaces gives prototype for more general questions concerning Ricci curvature in Riemannian geometry. In this talk I will survey what is known on this, and talk about a new glueing construction that shows a multi-scale collapsing phenomenon and further questions in this area.
