Pure Postgraduate Seminars

The Pure Postgraduate Seminar Series provides an informal environment for pure maths postgrads to present mathematical ideas. During this time, the University of Manchester were still split as UMIST and The Victoria University of Manchester. The seminar organisation was split over the two semesters. The Spring semester was organised by Matthew Craven, and the Autumn semester was organised by Sara Santos.

In the Spring semester, the seminars were held in the MSS building, Q5, Thursdays at 4pm. In the Autumn semester, the seminars were held fortnightly in the now non-existant Maths Tower, Room 2.11, Fridays at 4pm. Postgraduates and Postdocs from both universities were invited.

Spring Semester 2003

6 Mar
2003
Algebraic Aspects of Braid Groups
Matt Craven (UMIST)
13 Mar
2003
Grigorchuk Groups
George Petrides (UMIST)
20 Mar
2003
Fractals, Self Similar Sets and a Conjecture of Furstenburg
Thomas Jordan (VUM)
27 Mar
2003
Fun With Sturmian Words
Robin Houston (VUM)
3 Apr
2003
The Green Algebra and Adams Operations in Characteristic p
Colin D E Rose (UMIST)
8 May
2003
Monstrous Moonshine
Chris Bates (UMIST)
15 May
2003
Why Fractals (and a Little Bit More)?
Carlos Semedo (VUM)
22 May
2003
Sieves, Zeta Functions and Gaussian Primes
Andrew Swallow (UMIST)
28 May
2003
All Triangles are Isosceles, and Other Mathematical Truths
Sarah Perkins (UMIST)
5 Jun
2003
Period Three Implies Chaos
Sara Isabel Santos (VUM)

Abstract (click to view)

Given a continuous function f from the real line to the real line, the existence of a point of period three implies existence of points of any period. This theorem is a particular case of a theorem by Sharkovsky. Such a striking result has a simple explanation: is just a game with the Intermediate Value Theorem.
12 Jun
2003
Neighbourhoods of Randomness and the Information Geometry of the McKay Bivariate Gamma 3-Manifold
Khadiga Alrawini (UMIST)

Autumn Semester 2003

10 Oct
2003
60 minutes of Bernoulli Convolutions
Thomas Jordan (VUM)

Abstract (click to view)

We define self-similar measures and in particular the specific case of symmetric and asymmetric Bernoulli convolutions. We then look at various properties of Bernoulli convolutions, including whether thay are singular or absolutely continuous, their local dimension and their Fourier transforms (definitions of these will be given and are not that complicated). The talk gives a very brief overview of some of the research done on Bernoulli convolutions starting with Erdos and friends in the 1930's and going on up to the present day.
24 Oct
2003
An Introduction to Constructive Mathematics
Christopher Fox (VUM)

Abstract (click to view)

Constructive mathematics differs from classical mathematics in two ways: firstly the principle of excluded middle (which says that every statement is either true or false) is not valid constructively, and secondly impredicative (or "circular") definitions such as the powerset axiom are not allowed. In this talk I will cover some of the history of constructivism, and then describe Constructive Set Theory (CZF), giving some examples from topology to illustrate what can and cannot be proved construction.
7 Nov
2003
K-Theory for C*-algebras: a quick review
Jamila Jawdat (VUM)

Abstract (click to view)

In the recent years, K-theory for C*-algebras has become one of the vital subjects in researches that involves several fields of mathematics. It plays a great role in topology, geometry, operator algebra and operator theory. K-theory for a C*-algebra A, deals with certain operators (projections and unitaries) on some matrix algebra M_n(A) and so it is sometimes called "Operator K-theory", since one can consider the elements of a C*-algebra as operators. In brief, it associates to each C*-algebra A a pair of Abelian groups K₀(A) and K₁(A). The former is related to the projections in M_n(A), and the latter concerns the unitary operators.

K-theory for C*-algebras, is a replacement of Atiyah's topological K-theory for the non-commutative case. Whereas topological K-theory is a cohomology theory of locally compact topological spaces, operator K-theory works as a homology theory for the category of C*-algebras.

In the seminar, we will give a quick overview of how the above abelian groups are constructed, relating that to topological K-groups, and illustrating how K-theory enters the non-commutative world. Finally, if time permits, we give a brief account of the relation between K-theory and the index theory of a Fredholm operator.
21 Nov
2003
An introduction to the basic properties of Julia sets (of polynomials)
Matthew Horsham (VUM)

Abstract (click to view)

We will first introduce the concept of the Riemann sphere and iteration of polynomials thereon. We will define the Julia set of such a polynomial and show, via an example, the range of complex dynamics exhibited by such sets. We will then prove a series of small results exposing some of the properties of Julia sets finishing with the Julia/ Fatou dichotomy and connectedness conditions mentioning briefly (if time allows) the Mandelbrot set.
12 Dec
2003
Involutions of Lie Algebras
Paul Levy (VUM)

For the current seminar timetable, please click here.

Previous Seminars

List of 2008/2009 seminars (Ali Everett)
List of 2007/2008 seminars (Jacob George)
List of 2006/2007 seminars (Stephen Clegg)
List of 2005/2006 seminars (Marianne Johnson)
List of 2004/2005 seminars (Matt Horsham)
List of 2003 seminars (Matthew Craven/Sara Santos)
List of 2002 seminars (Sarah Perkins/Sara Santos)