A brief Description of the school : In recent years, fractional order partial differential equations have moved at the forefront of mathematics research and interest in the subject is growing by the day.

The most important aspect of these equations is that they are nonlocal and are often viewed as integrodifferential operators. Such equations have its origin in the study stochastic control/game problems  where the state processes are driven by Levy processes. There are other application areas such as dislocation dynamics. The study of such problems requires looking beyond traditional available methods for PDEs and development of new techniques. It is  essential to have an in depth knowledge on fractional order Sobolev spaces and elements of Fourier analysis. The study of nonlinear problems requires re­interpretation of the notion of viscosity solution  theory.

This workshop aims at introducing this subject to interested students, postdocs and young researchers from institutes/universities across India. We plan to cover aspects of fractional order Sobolev spaces, methods involving Fourier analysis, basic solvability issues, and the notion of viscosity solution for fully nonlinear problems.  We also intend to motivate the study by drawing the connection of these equations with  relevant control/game problems.

List of Speakers:

1­ Prof. Adimurthi , TIFR­CAM, Bangalore. ( AM)

2­ Dr. Imran Biswas, TIFR­CAM, Bangalore. ( IB)

3­ Prof. KT Joseph, TIFR­CAM, Bangalore. (KTJ)

4­ Prof. K. Sandeep, TIFR­CAM, Bangalore. (KS)

5­ Dr. Saugata Bandyopadhyay, IISER Kolkata. (SB)

6­ Dr. Venky Krishnan, TIFR­CAM, Bangalore. (VK)

Course Associates :

1­ Arka Malik, TIFR­CAM, Bangalore. (AM)

2­ Debabrata Karmakar, TIFR­CAM, Bangalore. (DK)

3­Indranil Chowdury, TIFR­CAM, Bangalore. (IC)

Syllabus :

Note: Each lecture/tutorial is for 1 1⁄2 hours

Time­Table  (Fill in initials of speakers and course associates)