One Parameter Semigroups
Matt Mahoney
I will be talking about something near and dear to my heart: one parameter semigroups of operators on a Hilbert space. In particular, I will discuss Stone's theorem which classifies these semigroups as the exponentials of (possibly unbounded) operators on a Hilbert space. The talk will hopefully also include some applications to physical problems, e.g. the heat operator, which is the solution operator of the heat equation, and the momentum operator in quantum mechanics. Only time and effort will tell if this is too ambitious for a fifty minute talk. This talk will be accessible to anyone who already understands the ins, outs, and what-have-yous of Stone's theorem. All others may simply have to hold on for the wild ride. But as the old adage goes, "Free pizza eaters can't be choosers".
|
|
On Galaxy Consuming Cosmic Horrors (that reside between Centaurus and Vela)
Geoff Goehle
"Scientific study and reflection had taught us that the known universe of three dimensions embraces the merest fraction of the whole cosmos of substance and energy. In this case an overwhelming preponderance of evidence from numerous authentic sources points to the tenacious existence of certain forces of great power and, so far as the human point of view is concerned, exceptional malignancy." — H.P. Lovecraft
|
|
The complexity of the integral
Jared Corduan
The existence of the Riemann integral on a closed
interval (given a continuous function) is a well behaved
limit, at least from a computability or proof theoretic
point of view. I will explain what it means to be well
behaved and why the integral is such.
|
|
Firefighting on the Infinite Hexagonal Grid
Amir Barghi
I will introduce firefighting in graph theory and particularly talk about firefighting on an infinite hexagonal grid.
|
|
Be Careful What You Vote For.
Jonathan Brown
Do elections reflect the will of the people? Can how we count votes effect the result? Voting is a way to decide the preferences of a society based on individual preferences. When the votes are tallied is the winner always the one that makes us happiest as a society? Most democratic elections are held using some varriety of a plurality vote, what are some other ways we can hold elections? Are any of these other methods better than plurality voting and can mathematics give us any incite into the best way to hold an election? In my talk we will discuss these questions and maybe some others in an attempt to find the best way to vote.
|
|
Weak vs. Strong Refocussing
Paul Kinlaw
I'll talk about refocussing of light rays in spacetime, and my current
research project which is to determine whether or not two notions, weak and
strong refocussing, are equivalent. I'll also discuss some different
definitions of the weaker notion of refocussing and try to show that they're
equivalent. We'll discuss examples and applications to Lorentzian geometry.
|
|
Generalized Cone and Killing Lengths
Nick Scoville
We'll look at some concepts and use some tools in
higher homotopy to eventually define several metrics on the
collection of CW-complexes. Categorical language will be
held to a minimum. Diagrams galore!
|
|
The Factorization of Polynomials $\bmod \, p$
Ben Linowitz
Given an irreducible polynomial $f(x)$ with integer coefficients, one can ask for the probability that $f(x)$ will factor a given way modulo an arbitrary prime $p$ (i.e. remain irreducible, split into linear factors, ...). I'll show how one can answer this question with basic Galois theory, and will then explain how the answer is related to one of the most fundamental topics in algebraic number theory: the splitting of primes in extensions of $\mathbb{Q}$.
|
|
Bayesian Networks
Giulio Genovese
I will explain what a Bayesian network is together with the concept of independence, inference, and $d$-separation. I will talk about algorithms to make inferences within Bayesian network with concrete examples of where Bayesian networks are and can be used. A clear understanding of basic probability and Bayes rules is required to follow the arguments.
|
|