For a positive integer $n$, we compute the shape of a totally real multiquadratic extension of degree $2^n$ in which the prime $2$ does not ramify. From this calculation, we see that the shape of such a number field is parametrized by the generators of its $2^n-1$ quadratic subfields. Restricting to the case $n=3$, we use this parametrization to count the number of triquadratic extensions of bounded discriminant and bounded shape parameters. We then show that, as the discriminant goes to infinity, these shapes become equidistributed in a regularized sense in the subset of the space of shapes of rank $7$ lattices that contains them.

Taylor Markham of the University of Calgary

Title: Integer Factorization

Abstract: The security of many modern day cryptosystems are impacted by the fact that it is computationally difficult to factor large numbers. This talk will give an introduction to the general number field sieve, which is currently the most efficient algorithm for factoring large integers.

I will present on the paper “Largest initial segments pointwise fixed by automorphisms of models of set theory” by Enayat, Kaufmann, and McKenzie.

https://arxiv.org/abs/1606.04002

Keller Hall 301

I will present on the paper “Largest initial segments pointwise fixed by automorphisms of models of set theory” by Enayat, Kaufmann, and McKenzie.

https://arxiv.org/abs/1606.04002

Keller Hall 301

Speaker: Stuart White (U. of Oxford)

Title: Amenable Operator Algebras

Abstract: Operator algebras arise as suitably closed subalgebras of the bounded operators on a Hilbert space. They come in two distinct types: von Neumann algebras which have the flavour of measure theory, and C*-algebras which have the flavour of topology. In the 1970’s Alain Connes obtained a deep structural theorem for amenable von Neumann algebras, leading to a complete classification of these objects. For the last 25 years the Elliott classification programme has been seeking a corresponding result for simple amenable C*-algebras, and now, though the efforts of numerous researchers worldwide, we have a definitive classification theorem. In this talk, I’ll explain what this theorem says, and the analogies it makes to Connes work, using examples from groups and dynamics as motivation. I won’t assume any prior exposure to operator algebras or functional analysis.

Speaker: Asaf Hadari (UHM)

Title: In search of a representation theory of mapping class groups.

Abstract:

Mapping class groups are nearly ubiquitous in low dimensional topology. They’ve been studied for over a century. Various results discovered during the past few decades it has become quite clear that there is much to gain by studying them via their linear representations.

Somewhat surprisingly, many such representations are known. Unfortunately, until recently there was almost no representation theory, that is – no underlying structure that allows you to say anything about the class of representations as a whole. It is precisely such an understanding that is necessary for studying mapping class groups.

In this talk I’ll talk about the major source of representations of mapping class groups, and talk about new results in their emerging representation theory.

“Iterated ultrapowers for the masses”, part 2