Pure Mathematics Postgraduate Seminar 2010-2011
- Thursday 27 January 2011 - 4pm, MALL
Mayra Montalvo - "Martin's Axiom"
- Thursday 3 February 2011 - 4pm, MALL
Robert Barham - "The higher dimension Platonic solids"
Abstract: This talk will describe what sort of Platonic objects can exist in higher dimensions, and will try to give a variety of methods that allow us to draw representations of them.
- Thursday 17 February 2011 - 4pm, MALL
Phil Ellison - "Quantum computing?!"
- Thursday 24 February 2011 - 4pm, MALL
Naz Miheisi - "Physics in 2 minutes (via C*-algebras)"
Andrew Reeves - "Catalan numbers"
- Thursday 10 March 2011 - 4pm, MALL
- Thursday 24 March 2011 - 4pm, MALL
- Thursday 28 October 2010 - 4pm, MALL
Stijn Vermeeren - "The Banach-Tarski paradox"
Abstract: I will show how you can cut an apple into a finite number of pieces, and rearrange these pieces to make TWO apples, of the same size as the original one. But beware: you will need to do some axiom-of-choice cutting of non-measurable apple pieces.
- Thursday 11 November 2010 - 4pm, MALL
Benedict Durrant - "The Complexity of the Real Line, as a Fractal"
Abstract: This talk covers the basic notions from computability of descriptive and normalised complexity. It also briefly covers the ideas of Hausdorff
and Topological dimension. With this machinery out of the way we are able to consider the relation between a string and its complexity, specifically the set got by taking the Cartesian product of a string with it's normalised complexity - which it turns out (for any subset of the reals) is fractal. The talk will not be overly technical, but aims to give an explanation of the results from "On Hausdorff and Topological Dimensions of the Kolmogorov Complexity of the Real Line" [Cai and Hatmanis, 1994] in an accessible way.
- Thursday 18 November 2010 - 4pm, MALL
Ahmet Cevik - " Intuitive Motivation for Higher Axioms of Infinity"
Abstract: This talk covers a gentle introduction to relative consistency and some basics of large cardinal assumptions in ZFC. Godel's Incompleteness Theorems will be given first. Then the notion of relative consistency will be discussed. It will be observed that some axioms of infinity are powerful enough to imply the consistency of ZFC. A result on the limits of large cardinal assumptions, Kunen's Inconsistency Theorem, will be reviewed. Finally, an open problem will be given due to the joint work of D.Friedman, P.Welch, H.Woodin related to the consistency strength of a large cardinal assumption. The talk will not be technical. The aim is just to give a general idea on higher axioms.
- Thursday 25 November 2010 - 4pm, MALL
Alexandra Omar-Aziz - "Infinite Galois theory and profinite groups"
Abstract: In this talk, I shall first introduce profinite groups, and then introduce the Krull topology on the Galois group of an (infinite) Galois extension. With this topology, the Galois group becomes a profinite group. I shall then show how every profinite group can be realised as the Galois group of a Galois extension.
- Thursday 9 December 2010 - 3pm, location to be confirmed
Thomas Wieber - "How a geometer proves the fundamental theorem of algebra"