George Melvin Mathematics Department

I am a graduate student in the maths department at UC Berkeley; my advisor is Constantin Teleman. I grew up on Royal Deeside in the northeast of Bonnie Scotland before going on to complete my undergraduate degree in Mathematics at the University of Edinburgh, and Part III of the Mathematical Tripos at Trinity College, University of Cambridge.
*This page was last updated on January 18, 2016.
My mathematical interests lie in the intersection of representation theory, geometry and combinatorics.
• Representations of quiver Hecke algebras via Lyndon bases (with D. Hill and D. Mondragon) Journal of Pure and Applied Algebra, Vol. 216 5, May 2012, p.10521079
• Soergel Bimodules and the Shape of Bruhat Intervals (with W. Slofstra) Preliminary version
• Quantum cohomology of weight varieties In preparation
• Summer Undergraduate Research Program: During the summer of 2015, I helped coorganise a research program for undergraduates at the University of California, Berkeley and led the 'Schubert varieties and toric degenerations' research group. The program gave exceptional undergraduates from across the US the opportunity to gain research experience in pure mathematics. This program was funded by the UC Berkeley Mathematics Department's 'Geometry & Topology' Research Training Group. More information can be found here.
• Directed Reading Program: I have been a frequent participant in the UC Berkeley Mathematics Department's Directed Reading Program. This program enables undergraduate students to be mentored by a graduate student on a mathematics topic of their choice. In the past I have mentored undergraduates in the following subjects: representation theory of the symmetric group; commutative algebra and algebraic geometry; classification of complex semisimple Lie algebras.
♦ Here is an interesting article highlighting current research into how mathematics courses are taught (with particular emphasis on teaching 'proofs'), focusing on the ways in which teachers and students can differ in their expectations. Current Semester: (Spring 2016)
Previous Semesters:

♦ In Spring 2013 I was awarded an 'Outstanding Graduate Student Instructor Award' at UC Berkeley for 'outstanding work in the teaching of undergraduates'.
♦ I am available for tutoring in all undergraduate (and some graduate) mathematics courses. Feel free to send me an email to find out more about my availability and hourly rates.
Past Seminars:
♦ Fall 2013, UC Berkeley:
◊ Student Algebraic Geometry Seminar (UC Berkeley; coorganised by Katrina Honigs and Piotr Achinger)
• Notes from a talk on the CayleyBacharach Theorem given by Adam Boocher on September 6, 2013. (All errors, inaccuracies, inconsistencies are due to me.)
◊ Koszul Duality Seminar (coorganised by Constantin Teleman and myself)
◊ FLAGS Seminar (mostly organised by myself)
♦ Spring 2013, UC Berkeley:
◊ Macdonald Polynomials (coorganised by Maria Monks and Steven Sam)
• qKostka Polynomials and Garnir Translates; notes for a talk I gave on March 8, 2013.
• The n! and (n+1)^{n1} conjectures; notes for a talk I gave on April 5, 2013. (Caveat lector: there is a minor error in these notes that requires fixing  I shall do so shortly at some point... (9/16))
◊
Moduli Spaces (organised by Daniel HalpernLeistner)
Past Conferences:
(September 25, 2014) Introductory Workshop: Geometric Representation Theory; MSRI, Berkeley.
(August 59, 2013) Quantum/Affine Schubert Calculus; University of Oregon, Eugene.
(June 1721, 2013) Hilbert Schemes, Sheaves and Representations; SISSA, Trieste, Italy.
(April 2428, 2013) Algebra, Combinatorics and Representation Theory: Zelevinsky's 60th Birthday
Conference; Northeastern University, Boston.
(April 812, 2013) Interactions between Noncommutative Alebra, Representation Theory and Algebraic Geometry; MSRI, Berkeley.
(March 1822, 2013) Masterclass on Soergel bimodules and KazhdanLuszstig conjectures, by Geordie Williamson and Ben Elias; Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark.