Matthew B. Young
Contact Information
State University of New York at Stony Brook
Stony Brook NY, 11794-3651, USA
Office: Math Tower, 4-116
E-mail: myoung@deletethis.math.sunysb.edu
Office Hours: Tuesday 11:30 -12:30
MLC Hours: Monday, Wednesday 1-2pm
Research Interests
Differential geometry, algebraic topology, quantum gravity, quantum field theory and gauge theories.Ciriculum Vitae: .pdf
Papers and Notes
R.B. Mann and M.B. Young. "Perturbative quantum gravity coupled to particles in (1 + 1) dimensions." Class. Quant. Grav. 24, 951-964.Abstract: We consider the problem of (1 + 1)-dimensional quantum gravity coupled to particles. Working with the canonically reduced Hamiltonian, we obtain its post-Newtonian expansion for two identical particles. We quantize the (1 + 1)-dimensional Newtonian system first, after which explicit energy corrections to second order in c-1 are obtained. We compute the perturbed wavefunctions and show that the particles are bound less tightly together than in the Newtonian case.
R.B. Mann and M.B. Young. "Aspects and Generalizations of BCEA and \Sigma \Phi EA Theories." In progress.
I. Fuentes Schuller, R.B. Mann and M.B. Young. "A Perturbative Approach to Inelastic Collisions in Bose-Einstein Condensates." In progress.
M.B. Young. "An Investigation of a Potential Spin Liquid State in a Frustrated Triangular Lattice." Honours Thesis, Queen's University at Kingston, April, 2007.
Abstract: We consider the Heisenberg model applied to a frustrated triangular lattice with nearest and next-nearest neighbour antiferromagnetic interactions. We find that the system may have spin liquid ground states for suffciently strong next-nearest neighbour coupling. Before obtaining these results a brief review of the necessary background in quantum magnetism is presented and the theory of spin waves is developed. Completed under the helpful supervision of Dr. R. J. Gooding.
M.B. Young. "Bernstein's Theorem." MATH 413 Commutative Algebra Term Project, Dec., 2006.
Abstract: We investigate some topics in the theory of polytopes in $\mathbb{R}^n$, which leads naturally to the introduction of Newton polytopes. These ideas are then used to prove Bernstein's Theorem, which gives an upper bound to the number of common solutions in $\left( \mathbb{C}^* \right)^n$ to a system of $n$ Laurent polynomials in $n$ variables. Moreover, in the case that the coefficients of the polynomials are generic, the bound in fact gives teh exact number of common solutions. A short discussion is included about the extensions of these results to common solutions in $\mathbb{C}^n$.
M.B. Young. "An Introduction to Quantization." Differential-geometric methods in mathematical physics, Seminar at Queen's University, March, 2007.
Abstract: A breif introduction to geometric and algebraic quantization and the WKB approximation.
M.B. Young. "An Introduction to Topological Quantum Field Theory." Waterloo Symposium in Undergratudate Mathematics, University of Waterloo, June 9, 2007.
Abstract: We introduce some notions from topological quantum field theory and provide motivation from both mathematics and physics.
M.B. Young. "Geometric Mechanics and Partical Differential Equations." Canadian Undergraduate Mathematics Conference, McGill University, July 5-9, 2006.
Abstract:In the recent past, the use of techniques from differential geometry has become very common in the fields of partial differential equations and mathematical physics. This has lead to the geometric formulation of many problems that were classically treated using the Fourier transform or functional (path) integrals. I will explain how differential geometry lends itself nicely to these fields and provides many new insights. Examples will be taken from classical and quantum mechanics as well as more modern theories. A geometric interpretation of some differential operators will also be discussed.
Teaching
Spring 2008: MAT 126 Calculus B Home PageFall 2007: MAT 171 Accelerated Single Variable Calculus Home Page
Photos
About
I am a first year Ph.D. student in the mathematics department and am currently a Renaissance Fellow. During the 2008-09 academic year I will be a NSERC doctoral fellow. I completed my B.Sc. in mathematical physics from Queen's University in Kingston, Ontario, in April, 2007. I am from Waterloo, Ontario, Canada, which has lots of fun math and physics opportunities, including the Mathematics and Physics departments at the Univeristy of Waterloo, the Perimeter Institute for Theoretical Physics and the Institute for Quantum Computing.When not doing math, I enjoy playing fastball; last year I played for the Breslau Black Sox Fastball Club. I am also an avid music fan and enjoy playing guitar when I have the time.