Speaker: Bakhadyr Khoussainov (University of Auckland)
Title: A quest for algorithmically random algebraic structures

Speaker: Alexei Miasnikov (Stevens Institute of Technology)

Title: Elementary classification questions for groups and algebras II: Associative and Lie algebras.

Abstract:
We consider some fundamental model-theoretic questions that can be asked about a given algebraic structure (a group, a ring, etc.), or a class of structures, to understand its principal algebraic and logical properties. These Tarski type questions include: elementary classification and decidability of the first-order theory.

In the case of free groups we proved that two non-abelian free groups of different ranks are elementarily equivalent, classified finitely generated groups elementarily equivalent to a finitely generated free group (also done by Sela) and proved decidability of the first-order theory.

We describe partial solutions to Tarski’s problems in the class of free associative and Lie algebras of finite rank and some open problems. In particular, we will show that unlike free groups, two free associative algebras of finite rank over the same field are elementarily equivalent if and only if they are isomorphic. Two free associative algebras of finite rank over different infinite fields are elementarily equivalent if and only if the fields are equivalent in the weak second order logic, and the ranks are the same. We will also show that for an infinite field the theory of a free associative algebra is undecidable.

These are joint results with O. Kharlampovich.

Speaker: Paul Kim Long V. Nguyen (UH Leeward Community College)
Title: $&#;92;Sigma^0_3$-completeness of subdirect irreducibility of lattices

Speaker: Anna Barry (UBC)

Title: Vortex Crystals and the (1+N)-Vortex Problem.

Title: Regular and Super Regular Tessellations of E^3 and H^3

Abstract: We shall define the tessellations of the talk and introduce the Klein and Poincare disk and ball models for H^2 and H^3. We shall introduce the concept of a universal group and state our main theorem, which is that a universal group exists that preserves a “wall set” associated to a super regular tessellation of H^3.

Title: Introduction to Topological Data Analysis.

Speaker: Chris Moseley (Calvin College)

Title: Rotations and the Fourth Dimension

Abstract: we are familiar with the idea of a fourth dimension, as in Einstein’s Special Theory of Relativity. However, the first thorough mathematical exploration of the fourth dimension predates Einstein by 60 years! In this colloquium we will see how the mathematician William Hamilton “jumped… into a fourth dimension” (his words) as he discovered quaternions, 4-dimensional numbers that are used today in the control of spacecraft and the programming behind 3D graphics in computer games.