### Fall 2016

The Fall 2016 SASMS will be held on Thursday, November 24 at 5:00 in MC 5479. If you would like to give a talk, you may do so by clicking "Sign Up" above.

### Talks

Time
Speaker
Talk Title
5:00
Taras Kolomatski
Invariant subspaces of the unilateral shift
5:30
Nam-Hwui Kim
On the existence of mathematical rigour in statistics.
6:00
Pizza Math Club
Dinner
6:30
Ilia Chtcherbakov
The arithmetical derivative
7:00
David Benjamin Urbanik
A Brief Survey of Quantum Physics
7:30
Felix Bauckholt
The Jordan Curve Theorem
8:00
Bryan Coutts
something something optimization
8:30
Wenyi Zheng
A proof of the existance of Haar Measure

### Abstracts

#### Invariant subspaces of the unilateral shift

The space $l^2(\mathbb{N})$ is the space of square sumable sequences. There is an operator on this space that appends a zero entry in front of a sequence - a shift. The question is: what are the closed invariant subspaces of this simple operator? The answer is surprising and involves cute Fourier theory and complex analysis.

#### On the existence of mathematical rigour in statistics.

Statistics? Rigourous? Gasp, how could it be? Well, it turns out that statistics is also an area in mathematics. In this talk, I will attempt to expose the audience to some interesting areas in statistics in a non-STAT231 manner (aka. things will make a bit more sense). Tentative list of topics include: Mixture modelling; Bayesian statistics; Information geometry. The number and the depth of topics covered will be time-dependent.

#### Dinner

We will prove by example the formula for the area of a sector of a circle.

#### The arithmetical derivative

This is a talk that nobody remembers and that I didn't do proper justice to at the time. The setup went something like this... "All your friends, function spaces like $\mathbb C[t]$ and $C^\infty(\mathbb R)$, have really cool derivatives like $\frac{d}{dt}$, but you ($\mathbb Q$) can only afford a cheap knockoff $({-})'$ that isn't even additive! How could this ever be useful or interesting?"

#### A Brief Survey of Quantum Physics

In which I attempt to cover the entirety of a subject I know little about.

#### The Jordan Curve Theorem

I will (hopefully) be able to prove it.