Continuum description of profile scaling in nanostructure decay

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This Spring the Math Department offers the
graduate course
MATH 648M Advanced Analytic Methods with
Applications
TuTh 930-1045am, Rm Math 0411
Website www.math.umd.edu/dio/courses/648M
Instructor Prof. Dio Margetis
(dio_at_math.umd.edu, x 5-5455)
FOCUS Mathematical concepts and analytical
tools used in classical mechanics as well as
quantum mechanics and quantum field theories.
Applications from fluid mechanics, elasticity,
electromagnetism, atomic and particle physics.
TOPICS PART I Greens functions and boundary
value problems in classical mechanics. Integral
equations Fredholm eqns the Wiener-Hopf
technique. Lagrangian formulation action
principle symmetries. Perturbation theory
Born-Neumann series and extensions.
FIG. 1 Temperature around a plate (red hot, to
blue cold). This can be derived by solving a
singular integral eqn.
PART II Mathematical elements of quantum
mechanics. Quantum fields Basic notions
canonical quantization invariance properties and
gauge transformations Yang-Mills gauge field
theories. Calculus of Feynman diagrams The
S-matrix divergencies analytical properties
high-energy asymptotics. .
e-
e-
e-
e-
FIG. 2 Electron-electron elastic scattering in
quantum electrodynamics What is the total
scattering cross section in the limit of high
energy?
UMCP Department of Mathematics