Gandalf seminar 2011-2012
With the start of the new term it seems high time to bring back Wednesday afternoon Biscuits, and the reason for the Biscuits, namely the GandAlF* seminar!
*Geometry and ALgebra Forum, name due to H. Gangl.
GandAlF is run by and for Pure postgraduates, but welcomes anyone who is interested in coming along. The topics presented have ranged from classical (Greek) geometry, through elliptic functions, Lie theory, projective geometry, and number theory, to a whole host of other things that spark the imagination.
Gandalf seminar archive: 2010-2011, 2011-2012, 2012-2013, 2013-2014, 2014-2015, 2015-2016, 2017-2018, 2018-2019, 2019-2020.
Epiphany 2012 Talks
Organised by John Mcleod
Hook-arrow trees
John Rhodes
Wednesday 21 March 2012, at 16:15, in CM107
Abstract: We outline how to extract the symbol of a multiple polylogarithm from a hook-arrow tree and then prove a simple result. It is the the end of term so talk will be 'easy' and include many tikz pictures. Disclaimer: previous exposure to this material from the speaker not needed.
Lehmer's conjecture and hyperbolic geometry
Scott Thomson
Wednesday 7 March 2012, at 16:15, in CM107
Abstract: Given a monic integral polynomial \( p \), one may define its Mahler measure as the product of all its roots with absolute value at least 1. The smallest known Mahler measure is for a polynomial of degree 10, and Lehmer's problem is to find a smaller Mahler measure; the conjecture is that one cannot. The truth of the conjecture would imply another conjecture, known as the Short Geodesic Conjecture, in hyperbolic geometry. I will explain some of these ideas and how they relate to some of my own work (joint with M. Belolipetsky).
The \( p \)-adic Riemann Zeta Function
Jonathan Crawford
Wednesday 29 February 2012, at 16:15, in CM107
Abstract: I will be discussing some introductory \( p \)-adic analysis and the \( p \)-adic weight space with the aim (time permitting) of defining a \( p \)-adic Riemann Zeta function.
Riemann Existence Theorem III: The Profinite Riemann Existence Theorem
John Mcleod
Wednesday 22 February 2012, at 16:15, in CM107
Profinite Completions
Scott Thomson
Wednesday 15 February 2012, at 16:15, in CM107
Abstract: Continuing last week's discussions, I will begin with a quick review of the analytic construction of the \( p \)-adic numbers, showing its link to the algebraic construction via inverse limits. I will then introduce the notion of "profinite completion" and show how the profinite completion of the integers relates to the \( p \)-adic integers.
Riemann Existence Theorem II: Profinite Groups
John Mcleod
Wednesday 8 February 2012, at 16:15, in CM107
Abstract: An important part of the proof of the Riemann Existence Theorem involves the theory of Profinite Groups which are exactly those groups which arise from an inverse limit. We will delve a little deeper into the theory of inverse limits, starting from Category Theory and working up to the derivation of the \( p \)-adic numbers via an inverse limit.
Quasi-reflective Bianchi Groups
John Mcleod
Wednesday 1 February 2012, at 16:15, in CM107
Riemann Existence Theorem I: Fundamental groups of the punctured Riemann sphere
John Mcleod
Wednesday 25 January 2012, at 16:15, in CM107
Abstract: We open this term with a couple of seminars on the Riemann Existence Theorem, which states the connection between the punctured Riemann sphere and Fuchsian groups. Along the way we will touch on a bit of Topology, a dash of algebraic geometry, and a smidgeon of group theory. The RET is an important ingredient in an approach to the Inverse Galois problem. By the end of the second seminar, we hope to have proven a lesser result, the Profinite Riemann Existence Theorem.