Contact Information

address

Department of Physics Sharif University of Technology P. O. Box: 11155-9161 Tehran, Iran

e-mail:

vahid AT sharif.ir

Office Tel:

+98 21 66164524

Cell Phone:

+98 912 2972504

Description of the course

    This is a one-semester course on advanced mathematical physics (Winter-Spring semester of 1398-99) taught be me in Sharif University of Technology. It is open to all Phd students from departments of physics and mathematics. (MS and BS students are supposed to consult me before they enroll for this class.) At the end of the course, the student is supposed to be able to master the essentials of modern mathematics used in various fields of research in physics, including high energy physics, condensed matter theory, mathematical physics and quantum information theory. I should stress that while these concepts and techniques are becoming widespread in some fields of theoretical physics, you may or may not need this level and kind of mathematical methods depending on your specific subject of research.

Prerequisites

    Knowledge of essential mathematics, linear algebra, and group theory and some geometry is useful but not necessary. Students are required to stuy a great deal on their own.

Textbook

    example graphic
    Geometry, Topology and Physics, by Mikio Nakahara, Institute of Physics Publishin (IOP), Bristol and Philadelphia.


    Due to the Covid-19 Virus crisis, there will be no classes in the university until futher notice. Instead I teach the course via the virtual class at the following address https://vclass.ecourse.sharif.edu/ch/vahid.karimipour several times a week. For your reminder, I post the handwritten lecture notes here after each leccture and each week I post exercises that you are supposed to solve by reading the textbook. The final exam will be from these exercies. You are weclome to ask for guidance and by sending me emails.

Contents:

  • Basic notions of topology, homotopy groups, homology groups, differential geometry and manifolds, Riemmanian geometry, differential forms, cohomology groups, complex manifolds, fibre bundles....

    Exams: There will be a final exam.

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