Chris Spencer's Homepage

...alas - still work in progress...

About Me

I am a postgraduate research student in the School of Mathematics at the University of Edinburgh, having joined in 2008. Currently I am in the fourth year of my PhD and my supervisors are Prof. Iain Gordon and Prof. Tom Lenagan .
Before coming to Edinburgh I was an undergraduate at King's College in Cambridge . I also did Part III (aka CASM) there.

Research Interests

My research interests are in Algebra and Representation Theory. My particular interests vary regularly, but some things I have consistently enjoyed are:

Lie Theory, in particular 'category O' and Harish-Chandra bimodules
D-Modules
Cherednik Algebras and in particular their Harish-Chandra bimodules
Homological Algebra and Morita Theory
Algebraic Geometry and its links with Representation Theory

I am currently preparing a preprint on the category of Harish-Chandra bimodules for rational Cherednik algebras at regular parameter values.

Conferences and Workshops

26th June-2nd July 2011: A workshop on New developments in noncommutative algebra and its applications
From January-April 2011 I took part in the HIM Trimester Program "On the Interaction of Representation Theory with Geometry and Combinatorics" in Bonn.
23rd-29th may 2010: A joint workshop and conference on Sheaves in Representation Theory on the Isle of Skye, funded by the "Representation Theory across the Channel" network
6th-9th April 2010: The British Mathematics/British Applied Mathematics Colloquium was held here in Edinburgh.
5th April 2010: A CALF meeting in Glasgow. Thanks to Tarig for organizing everything.
14th-18th September 2009: Yet another week-long workshop, this time in Luminy (France) on the topic of Quiver Varieties, Donaldson-Thomas invariants and instantons.
7th-11th September 2009: A one week LMS/EPSRC short course on Derived Categories and Applications held at City University, London.
22nd-26th June 2009: A one week workshop on Representation Theory and Lie Theory again in Cambridge at the Isaac Newton Institute
20th-22nd April 2009: Sir Michael Atiyah's birthday conference (his 80th birthday!), appropriately named Geometry and Physics: Atiyah80 organised by the ICMS here in Edinburgh.
13th-18th April 2009: A 6-day workshop in Glasgow on Categorification and Geometrisation from Representation Theory organised by the ICMS as part of the programme on Algebraic Lie Theory of the Isaac Newton Institute for Mathematical Sciences
23rd-27th March 2009: A one week workshop on Algebraic Lie Structures with Origins in Physics
12th-23rd January 2009: Two week Instructional Workshop as part of the programme on Algebraic Lie Theory, held at the Isaac Newton Institute for Mathematical Sciences in Cambridge
10th-13th December: A workshop on Infinite Group Theory held here in Edinburgh
27th-29th November 2008: Jacques Alev's 60th Birthday conference at the Unversity of Reims
15th-19th September 2008: A one week LMS/EPSRC funded course on Algebraic groups and related topics held at the University of Birmingham
Various ARTIN meetings (the 18th in Aberdeen, 19th in Manchester, 20th in Glasgow and the 21st in Edinburgh so far).

Teaching

In the first semester of 2010, I was a tutor for Master's students taking the algebra lectures in Edinburgh.

In the academic year 2009-2010 I tutored the course "Foundations of Calculus/Several Variable Calculus" in semester 1 and a course on "Discrete Mathematics" in semester 2.
FC/SVC combines both an introduction to rigorous analysis, for example sequences, convergence and continuity ( think epsilon-delta proofs) with vector calculus, e.g. partial differentiation, gradients and line and surface integrals. Discrete Mathematics is an introsduction to combinatorics and graph theory, dealing with topics such as sets and functions, binomial and multinomial coefficients, counting principles like inclusion-exclusion or the generalized pigeonhole principle, isomorphism of graphs, the handshaking lemma, Euler tours and Hamiltonian cycles amongst others.

In the academic year 2008-2009, I was tutoring Prof. Lenagan's course "Jewels of Algebra", a fourth year course on group theory and Galois theory.
The syllabus included in a revision of basic group theory, the isomorphism theorems, group actions, symmetric and alternating groups, Sylow theorems, composition series, finite Abelian groups, soluble and nilpotent groups and in semester 2 a review of rings and fields, polynomial rings, Euclidean algorithm and factorization, field extensions, simple extensions, degree, classical ruler and compass constructions, normality and separability, Galois correspondence and solubility by radicals.

Contact

The easiest way to contact me is via email: C [dot] C [dot] Spencer [at] sms [dot] ed [dot] ac [dot] uk
(If you don't understand what this means, you can find my email address on the department website here or the graduate school website here).

Normal mail can be sent to:

C.C.Spencer
School of Mathematics
University of Edinburgh
5404 James Clerk Maxwell Building
King's Buildings
Mayfield Road
Edinburgh, EH9 3JZ
UK