Courses for Sep-Dec 2021

  1. Topology & Geometry - Core

    Course no.: MTH 122.5

    Instructor: Prof. Rukmini Dey

    Venue: Online

    Class timings: Tuesdays and Thursdays from 11:00 AM to 12:30 AM (1 hr tutorial once a week, tutorial timings to be announced later)

    First meeting: 10th August 

    Course description:

    Topology: Homotopy, retraction and deformation, fundamental group, Van Kampen theorem, covering spaces and their relations with the fundamental group, universal coverings, automorphisms of a covering, regular covering. 

    Geometry: Differential geometry of curves and surfaces, mean curvature, Gaussian curvature, differentiable manifolds, tangent and cotangent spaces, vector fields and their flows, Frobenius theorem, differential forms, de Rham cohomology.   

    Grading policy:

    20% assignments,  40% midterm,  40% final.


  2. Topics in Nonlinear Partial Differential Equations - Topical

    Course no.: MTH 247.5

    Instructor: Prof. Vishal Vasan

    Venue: Online

    Class timings:  Monday and Wednesday 2:00-3:30 (Additional tutorial TBD).

    First meeting: 30th August 2021, last lecture in the second week of December.

    Course description:

    This course is aimed at students and researchers working in the field of nonlinear PDEs. We will focus on semilinear evolution equations (mostly scalar-valued) with the emphasis on (a) the mathematical theory behind such equations, (b) how this theory informs the development of numerical methods. Selected topics include: transform techniques for linear equations; spectral methods for evolution PDEs; wellposedness theory for nonlinear PDEs. Additional topics as per the interest of the instructor and students.

    Prerequisites: Interested individuals should have prior experience with nonlinear PDEs and numerical methods (through coursework or research). A course in real and complex analysis will be useful but not essential. Students should consult the instructor before registering.

    Course structure: 50% Homework + 20% Report + 30% Final viva exam.

    References:

    T Tao Nonlinear Dispersive Equations: local and global analysis

    R Temam Infinite dimensional dynamical systems in mechanics and physics

    C Doering Applied analysis of Navier-Stokes

    selected papers to be distributed in class