[California poppies]

George Melvin

Mathematics Department
University of California, Berkeley, CA, U.S.A.
[my email]

[picture of me]

About Me

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 north-east 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 August 25, 2015.


Research

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.1052-1079

• Soergel Bimodules and the Shape of Bruhat Intervals (with W. Slofstra) In preparation


Undergraduate Research & Mentoring

Summer Undergraduate Research Program: During the summer of 2015, I helped co-organise 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.


Teaching

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: (Fall 2015)
Math 110 Linear Algebra, Prof. Holtz
Math 250A Groups, Rings and Fields, Prof. Ribet

Previous Semesters:
Math 110 Linear Algebra, Fall 2014 (Course GSI; UC Berkeley, Prof. Givental)
Math 113 Abstract Algebra, Summer 2014(Course Instructor; UC Berkeley)
Math 110 Linear Algebra, Spring 2014 (Course GSI; UC Berkeley, Prof. Ribet)
Math 110 Linear Algebra, Fall 2013 (Course GSI; UC Berkeley, Prof. Nadler)
Math 54 Linear Algebra and Differential Equations, Fall 2012 (Course GSI; UC Berkeley, Prof. Voiculescu)
Math 110 Linear Algebra, Summer 2012 (Course Instructor; UC Berkeley)
Math 110 Linear Algebra, Fall 2012 (Course GSI; UC Berkeley, Prof. Gu)
Math 54 Linear Algebra and Differential Equations, Summer 2011 (Course Instructor; UC Berkeley)
Math 53 Multivariable Calculus, Fall 2010 (Course GSI; UC Berkeley, Prof. Auroux)
Math 54 Linear Algebra and Differential Equations, Summer 2010 (Course Instructor; UC Berkeley)
Math 54 Linear Algebra and Differential Equations, Spring 2010 (Course GSI; UC Berkeley, Prof. Lott)
Math 1B Calculus, Fall 2009 (Course GSI; UC Berkeley, Prof. Persson)

[find it]

♦ In addition to the above teaching responsibilities, I have been a course grader for the following courses:

Math 142 Elementary Algebraic Topology, Spring 2014 (UC Berkeley, Prof. Agol)
Math 141 Elementary Differential Topology, Fall 2013 (UC Berkeley, Prof. Teleman)
Math 142 Elementary Algebraic Topology, Spring 2013 (UC Berkeley, Prof. Poirier)
Math 143 Elementary Algebraic Geometry, Fall 2012 (UC Berkeley, Prof. Lott)
Math 116 Introduction to Cryptography, Spring 2009 (UC Berkeley, Prof. Ribet)

♦ 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.


Activities

Past Seminars:

Fall 2013, UC Berkeley:
Student Algebraic Geometry Seminar (UC Berkeley; co-organised by Katrina Honigs and Piotr Achinger)
  • Notes from a talk on the Cayley-Bacharach Theorem given by Adam Boocher on September 6, 2013. (All errors, inaccuracies, inconsistencies are due to me.)
Koszul Duality Seminar (co-organised by Constantin Teleman and myself)
FLAGS Seminar (mostly organised by myself)

Spring 2013, UC Berkeley:
Macdonald Polynomials (co-organised by Maria Monks and Steven Sam)
  • q-Kostka Polynomials and Garnir Translates; notes for a talk I gave on March 8, 2013.
  • The n! and (n+1)^{n-1} 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 Halpern-Leistner)

Past Conferences:
(September 2-5, 2014) Introductory Workshop: Geometric Representation Theory; MSRI, Berkeley.
(August 5-9, 2013) Quantum/Affine Schubert Calculus; University of Oregon, Eugene.
(June 17-21, 2013) Hilbert Schemes, Sheaves and Representations; SISSA, Trieste, Italy.
(April 24-28, 2013) Algebra, Combinatorics and Representation Theory: Zelevinsky's 60th Birthday Conference; Northeastern University, Boston.
(April 8-12, 2013) Interactions between Noncommutative Alebra, Representation Theory and Algebraic Geometry; MSRI, Berkeley.
(March 18-22, 2013) Masterclass on Soergel bimodules and Kazhdan-Luszstig conjectures, by Geordie Williamson and Ben Elias; Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark.