Algebras and Lattices in Hawaii
May 22 – May 24 all-day
Dissertation defense – TJ Combs
Jul 6 @ 2:00 pm – 4:00 pm

Time: Friday, July 6 from 2:00 – 4:00 pm
Location: Keller 401

Draft of dissertation

Abstract: \
We provide some general tools that can be used for polynomials in any degree to show $G_\infty = \text{Aut}(T_\infty)$.  We introduce the idea of Newton irreducibility to help push us closer to a proof to Odoni’s conjecture for monic integer polynomials when $d=4$.  We also show that current techniques used in the literature will not work in proving Odoni’s conjecture for monic quartic polynomials.  Finally, we look at how certain behaviors of the critical points of a polynomial $f(x) \in \mathbb{Q}[x]$ force it to not have full Galois image.

Dissertation defense, John Robertson @ Keller 302
Jul 19 @ 3:00 pm – 4:30 pm

Draft of dissertation:

In this paper we study properties of groupoids by looking at their $C^∗$-algebras. We introduce a notion of rapid decay for transformation groupoids and we show that this is equivalent to the underlying group having the property of rapid decay. We show that our definition is equivalent to a number of other properties which are in direct correspondence to the group case. Additionally, given two bilipschitz equivalent discrete groups we construct an isomorphism of the corresponding transformation groupoids and are able to reformulate the open problem of showing invariance of rapid decay under quasi-isometry.
We then begin to examine various notions of amenability when abstracted to measured ́etale groupoids. In the group case, the following properties are equivalent:
1) $G$ is amenable
2) $C_r^∗(G)=C^∗(G)$
3) The trivial representation decends from ^C^∗(G)$ to $C_r^∗(G)$.
In the groupoid, $G$, case we have 1) ⇒ 2) ⇒ 3), but it was shown by Rufus Willett that $C_r^∗(G) = C^∗(G)$ is not enough in general to give amenability of G. In this paper we study property 3) for groupoids, formulate some equivalent statements and show that 3) ⇒ 2) is also false in general.

MA defense for K. Manguba-Glover @ Keller 301
Aug 2 @ 1:00 pm – Aug 2 @ 3:00 pm
Geuseppe Ayala’s MA defense
Aug 7 @ 1:30 pm – Aug 7 @ 2:30 pm
Sarah Berner: $p$-adic analogs of the Mandelbrot set
Aug 16 @ 2:00 pm – 3:00 pm

To fulfill the specialty exam requirement, Sarah Berner will give a presentation on “p-adic analogs of the Mandelbrot set” in Keller 403. Please join us if you can.

Logic seminar: Sam Birns
Oct 8 @ 2:30 pm – 3:30 pm
Colloquium- Yuriy Mileyko
Oct 12 @ 3:30 pm – 4:30 pm

Speaker: Yuriy Mileyko (UHM)
Title: Another look at recovering local homology from samples of stratified sets.

Recovering homological features of spaces from samples has become one of
the central themes in topological data analysis, which has led to many
successful applications. Most of the results in this area focus on
global homological features, whose recovery predicates on imposing well
understood geometric conditions on the underlying space. Existing work
on recovering local homological information of a space from samples has
been much less abundant, since the required local geometric conditions on
the underlying space may vary from point to point and are not easily
integrated into a global condition, unless the space is a smooth
manifold. In this talk, we show that such global conditions for
recovering local homological information can be obtained for a fairly
large class of stratified sets.