MATH 697 - Topics in Mathematical Physics and String Theory

Institution:

University of Pennsylvania

Subject:

Description:

Staff. Prerequisite(s): Math 696 or permission of the instructor. Continuation of Math 696. Topics may include the family index theorem, equivariant cohomology and loop spaces, the homological algebra of BRST invariance and the Wess-Zumino consistency condition, the descent equations, and worldsheet anomalies in string theory. Topics in Algebra. (M) Staff. Topics from the literature. The specific subjects will vary from year to year. Topics in Algebra. (M) Staff. Topics from the literature. The specific subjects will vary from year to year. Advanced Number Theory. (M) Staff. Prerequisite(s): Math 620/621. Ramification theory, adeles and ideles, Tate's thesis, group cohomology and Galois cohomology, class field theory in terms of ideles and cohomology, Lubin-Tate formal groups, Artin and Swan conductors, central simple algebras over local and global fields, general Hasse principles. Other topics may include the following: zero-dimensional Arakelov theory, Tate duality, introduction to arithmetic of elliptic curves, local and global epsilon factors in functional equations, p-adic L-functions and Iwasawa theory, modular forms and functions and modular curves. Advanced Number Theory. (M) Staff. Prerequisite(s): Math 720 or with the permission of the instructor. Continuation of Math 720. (MATH694) Topics in Algebraic Geometry. (M) Staff. Prerequisite(s): Either Math 622/623 or Math 624/625. Topics from the literature. The specific subjects will vary from year to year. Topics in Algebraic Geometry. (M) Staff. Prerequisite(s): Either Math 622/623 or Math 624/625. Topics from the literature. The specific subject will vary from year to year. (MATH540) Topics in Algebraic and Differential Topology. (M) Staff. Prerequisite(s): Math 618/619. Topics from the literature. The specific subjects will vary from year to year. Topics in Algebraic and Differential Topology. (M) Staff. Prerequisite(s): Math 618/619. Topics from the literature. The specific subjects will vary from year to year. Topics in Classical Analysis. (M) Staff. Prerequisite(s): Math 608 and Math 609 and permission from the instructor. Harmonic analysis in Euclidean space, Riemann surfaces, Discontinuous groups and harmonic analysis in hyperbolic space, Pseudodifferential operators and index theorems, Variational methods in non-linear PDE, Hyperbolic equations and conservation laws, Probability and stochastic processes, Geometric measure theory, Applications of analysis to problems in differential geometry. The specific subjects will vary from year to year. Topics in Classical Analysis. (M) Staff. Prerequisite(s): Math 748 or with the permission of the instructor. Continuation of Math 748. Topics in Functional Analysis. (M) Staff. Topics from the literature. The specific subjects will vary from year to year. Topics in Functional Analysis. (M) Staff. Topics from the literature. The specific subjects will vary from year to year. Topics in Operator theory. (M) Staff. Topics from the literature. The specific subjects will vary from year to year. Topics in Operator Theory. (M) Staff. Topics from the literature. The specific subjects will vary from year to year. Topics in Differential Geometry. (M) Staff. Prerequisite(s): Math 660/661. Topics from the literature. The specific subjects will vary from year to year. Topics in Differential Geometry. (M) Staff. Prerequisite(s): Math 660/661. Topics from the literature. The specific subjects will vary from year to year.

Credits:

3.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.upenn.edu

Phone Number:

(215) 898-5000

Regional Accreditation:

Middle States Association of Colleges and Schools

Calendar System:

Semester

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