Gandalf seminar 2012-2013

Gandalf is the postgrad-student-run pure maths seminar. Gandalf stands for the Geometry AND ALgebra Forum, name due to Herbert Gangl

Gandalf seminar archive: 2010-2011, 2011-2012, 2012-2013, 2013-2014, 2014-2015, 2015-2016, 2017-2018, 2018-2019, 2019-2020.

Epiphany 2013 Talks

Organised by Jonathan Crawford

Flatland!

John Mcleold

Wednesday 13 March 2013, at 16:00, in CM103

Abstract: This week due to it being the end of term and John leaving by the end of March as well to start his new job, we will be having a extra special viewing of the amazing "Flatland", followed by pub and even a curry as well! Amazing!

Compactness-like covering properties

Petra Staynova (Visiting)

Wednesday 6 March 2013, at 16:00, in CM221

Michaelmas 2012 Talks

Organised by Luke Stanbra

Khovanov Homology and the Universal Tangle Category

Jonathan Grant

Wednesday 5 December 2012, at 16:00, in CM221

Abstract: Khovanov homology is an invariant of knots that 'categorifies' the Jones polynomial. In this talk, I will give a basic introduction to Khovanov homology for knots, and then show that by staying in the topological world of cobordisms we can obtain a chain complex that serves as an invariant of tangles, and specialises to Khovanov homology in the case of knots and links.

Primes of the Form \( x^2 + ny^2 \)

Steven Charlton

Wednesday 28 November 2012, at 16:00, in CM221

Slides of Talk
Notes of Talk
Maple worksheets implementing some of the criteria discussed for: \( x^2 + y^2 \), \( x^2 + 2y^2 \), \( x^2 + 3y^2 \), \( x^2 + 5y^2 \), \( x^2 + 17y^2 \), \( x^2 - 2y^2 \), \( x^2 - 142y^2 \)
Maple worksheet implementing the criteria for the cubic form \( a^3 + 11b^3 + 121c^3 - 33abc \)
Maple worksheet to count the number of solutions to \( N = x^2 + 5y^2 \) and \( N = 2x^2 + 2xy + 3y^2 \)

Abstract: Fermat's observation about which primes can be written as the sum of two squares motivates the question: which primes does a given quadratic form represent? After relating quadratic forms with ideals in quadratic fields, we show how Class Field Theory can be applied to construct general criteria describing these primes.

A Theta Lift in \( \operatorname{SL}(1,2) \)

Jonathan Crawford

Wednesday 21 November 2012, at 16:00, in CM221

Abstract: We will first define half weight vector valued forms and then construct a twisted theta lift of weak harmonic Maass forms of weight 1/2 to automorphic forms on the upper half plane, as well as the relationship with the Shimura lift.

Quasi-reflective groups in hyperbolic space

John Mcleod

Wednesday 14 November 2012, at 16:00, in CM221

Abstract: We will discuss the structure of a quasi-reflective group (sometimes known as a parabolic-reflection group), and give some examples from among the Bianchi groups. There are only finitely many of these groups in each dimension, and we present a classification of quasi-reflective Bianchi groups.

Computing the Cohomology of Chain Spaces

Dan Jones

Wednesday 7 November 2012, at 16:00, in CM221

Slides of talk

Abstract: At a recent talk in St. Mary's College, I introduced a way of generalising chain spaces to an arbitrary vector space \( V \), with an action of an arbitrary Lie group \( G \). A lot is known for these chain spaces when \( V \) is real \( d \)-space and \( G = \operatorname{SO}(d) \). In this talk, I will state some results in the real case and suggest a method of calculating cohomologies in the more general case. This method involves the Leray-Serre spectral sequence, and we will hopefully see a few particular examples. (If you haven't seen/heard of spectral sequences before, don't worry as I will explain what they are and why they are useful).

The Congruent Number problem

Luke Stanbra

Wednesday 31 October 2012, at 16:00, in CM221

Abstract: The congruent number problem is that of determining whether an given integer is the area of a right angled triangle with rational sides. This deceptively simple to state problem has a solution which leads us through some of the most intriguing theorems of modern number theory, including the Birch and Swinnerton-Dyer conjecture, one of the Clay Mathematical Institute's Millennium problems.

Induction Half-Day of Talks

Thursday 4 October 2012, at 13:30-17:00, in CM221

Organised by John Mcleod

As a companion to the thrilling and stimulating offerings from the Graduate School about joining the postgraduate community here, I would like to invite you to a half day of talks from existing PhD students, who will be speaking about their research and the methods they have used during their work here.

The idea is to advertise those areas of expertise which the graduate community has, which may save you a month of struggling to learn a tool that is badly documented, or six months following the paper trail to discover some particular result, or many other examples. Mathematics is highly connected, and so it may be that some Pure student has the tools to integrate a particular Feynman diagrams (and may not realise it), or a Statistician has detailed knowledge of infinite-dimensional functional analysis. These are two examples which I am aware of in this department that surprised me!

It will not be possible to get very far in half a day, but I hope that a bit of "interdisciplinary mixing" will carry forward and bear fruit.

Mathematical Physics: The Centre for Particle Theory

James Allen