TIMC-FC Regional Programme on Real and Functional Analysis.

Coordinators:

• Dr. V. V. Acharya

Speakers:

• Dr. Chandrasheel Bhagwat, IISER Pune
• Dr. Rohit Holkar, IISER Pune

Supported by:

• TIMC, Fergusson College

Participants:

• About 30 B.Sc. (Mathematics) 3rd Year/ M.Sc. (Mathematics) 1st Year students and a few undergraduate teachers.

Theme:

• To discuss some of the interesting topics in real analysis and functional analysis which are typically not covered in detail in the regular mathematics curriculum at undergraduate level.

Topics:

• Function spaces: Space of continuous functions on a compact metric space, Metric given by uniform convergence, Banach *-algebra structure, Introduction to Banach spaces and linear operators, Spectrum of an element of Banach *-algebra, Computations in some special and simple cases
• Arzela-Ascoli Theorem and its applications in Functional analysis and other areas of Mathematics
• Introduction to measure theory and integration via Lebesgue measure on [0,1] and analysis on spaces like L^1  [0,1], L^2 [0,1] etc., Introduction to Fourier analysis

Programme:

• Six lectures of 90 minutes each (2 per day, 3 days)
• Problem solving sessions of 2 hours every day for 3 days.