Gandalf seminar 2014-2015
Gandalf is the postgrad-student-run pure maths seminar. Talks normally take place on Thursday at 15:00 in CM107, or whatever room happens to be free at the time. Biscuits are always supplied!
Gandalf stands for the Geometry AND ALgebra Forum, name due to Herbert Gangl. Occasionally it becomes the Radagast seminar, Research And Development in Algebra, Geometry And Sometimes Topology, if the Topologists are feeling particularly left out.
Gandalf seminar archive: 2010-2011, 2011-2012, 2012-2013, 2013-2014, 2014-2015, 2015-2016, 2017-2018, 2018-2019, 2019-2020.
Michaelmas 2014 Talks
Organised by Steven Charlton. If you have any suggestions for speakers, or want to volunteer to give a talk yourself, please feel free to email me.
A theorem in topology with a view towards quantum entanglement
Henry Maxfield
Thursday 4 December 2014, at 15:00, in CM107
Abstract: A central property of quantum mechanical systems is entanglement: knowledge of the parts does not constitute knowledge of the whole. It turns out that in some circumstances, quantifying entanglement is equivalent to a classical problem, of finding minimal surfaces. I'll wave my arms a bit to motivate where this comes from, and then do some proper maths to prove a theorem in algebraic topology, which tells us which topological class of minimal surfaces to consider in the problem.
Quivers, Clusters and Simplices
John Lawson
Thursday 30 October 2014, at 15:00, in CM107
Abstract: A quick introduction to cluster algebras from combinatorial and geometric view points.
The Alexander polynomial as a Reshetikhin-Turaev invariant
Jonathan Grant
Wednesday 22 October 2014, at 15:00, in CM221
Abstract: The Alexander polynomial is a classical invariant of knots introduced in the 1920's with clear connections to the topology of knots and surfaces. The Reshetikhin-Turaev invariants are much more recent, and are in general much more poorly understood. These often arise from the representation theory of quantum groups. I will show how the Alexander polynomial can be interpreted as a Reshetikhin-Turaev invariant using representations of \( U_q(\mathfrak{gl}(1|1)) \), and show how this can be used to understand a category of representations of \( U_q(\mathfrak{gl}(1|1)) \). Finally, I will give some suggestions about how this should tie into categorifications of knot invariants, and particularly the connection between HOMFLY homology and Heegaard Floer knot homology.
Surreal Numbers
Steven Charlton
Thursday 16 October 2014, at 15:00, in CM107
Abstract: Surreal numbers were invented by Conway, and used in his study of game theory. While the definition of a surreal number is surprisingly simple, it rapidly leads to a rich and deep structure encompassing not only the usual real numbers, but infinities, infinitesimals and more. In this talk I'll give an introduction to how surreal numbers work and an overview of the some of the weirdness that ensues.