IST - Analysis and PDE

Speakers and Syllabus


Analysis and Partial differential equations (PDEs) are now the integral part of the curriculum in any postgraduate course in Mathematics. Advanced analysis like Measure Theory and Functional Analysis are playing a vital role in many mathematical disciplines including PDEs. PDEs naturally arise often in many mathematical modeling of physical phenomenon and engineering applications. Measure Theory and Functional analysis are the backbones for setting up the study of PDEs in the modern sense. Functional Analysis studies linear spaces provided with suitable topological structures and continuous linear transformations between such spaces. It has far-reaching applications in several disciplines. An introduction to the theory of measure and integration is helpful since the richest examples in functional analysis come from function spaces whose study demands such a knowledge. The topics in the school are designed in such a way that the participants get exposure to topics in Linear Algebra, Measure Theory, Functional analysis and Partial Differential Equations.

 Name of the Speaker with affiliation

 No. of Lectures

 Detailed Syllabus

 R. Venkatesh

Dept. Math.IISc, Bangalore

 

 6

 Finite dimensional spectral theory. Inner product spaces, Orthonormal sets. Spectral theorem for the Hermitian and normal operators on finite dimensional inner product spaces.

 ManjunathKrishnapur

Dept. Math.IISc, Bangalore

 6

 Lebesgue measure and integration. Construction of Lebesgue measure, Measurable functions, Lebesgue integration, convergence theorems and Lp-spaces.

 Tirthankar Bhattacharyya

Dept. Math. IISc, Bangalore

 

6

 Spectral theory for compact self-adjoint operators.Hilbert spaces, Bounded and compact operators on a Hilbert space. Spectrum of a compact operators and the spectral theorem for compact self-adjoint operators.

 A. K. Nandakumaran

Dept. Math.IISc, Bangalore

 

6

 Partial Differential Equations. First order PDE-Method of characteristics-Elliptic PDE, in particular Laplacian, fundamental solution, Green’s functions, Mean value theorem, maximum principle, regularity.

References:

  1. Hoffman, K. and Kunze, R., Linear Algebra (2nd Ed.) ,Prentice-Hall of India, 1992.
  2. Artin, M., Algebra, Prentice-Hall of India, 1994.
  3. Terence Tao. An Introduction to Measure Theory.American Mathematical Society. Graduate Studies in Mathematics Vol. 126; 2011.
  4. Elias M Stein and Rami Shakarchi. Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press (2005).
  5. Conway, J. B., A course in functional analysis, GTM 96, Springer.
  6. Rudin, Walter., Functional Anaysis (2nd Ed.) ,McGraw-Hill, 2006.
  7. Garabedian, P. R., Partial Differential Equations, John Wiley and Sons, 1964.
  8. Renardy, M. and Rogers, R. C., An Introduction to Partial Differential Equations, Springer-Verlag, 1992.

 

 Tutors:

S. No.

Name

Affiliation

1

R. Venkatesh

Mathematics, IISc Bangalore

2

ManjunathKrishnapur

Mathematics, IISc Bangalore

3

Tirthankar Bhattacharya

Mathematics, IISc Bangalore

4

A. K. Nandakumaran

Mathematics, IISc Bangalore

5

G.V.K. Teja

Mathematics, IISc Bangalore

6

SubhajitGhosh

Mathematics, IISc Bangalore

7

Lakshmi Priya M.E.

Mathematics, IISc Bangalore

8

Rahul Biswas/Ramesh ChSau

Mathematics, IISc Bangalore

9

Poornendu Kumar

Mathematics, IISc Bangalore

10

ShubhamRastogi

Mathematics, IISc Bangalore

11

Abu Sufian

Mathematics, IISc Bangalore

12

S. Aiyyappan

Mathematics, IISc Bangalore

 

 

 


Time Table

 

Day

Date

Lecture 1

(9.30
to
11.00)

Tea

(11.00 to
11.30)

Lecturer 2

(11.30
to
1.00)

Lunch

(1.00 to
2.30)

Tutorial 1

(2.30
to
3.30)

Tea

(3.30 to
4.00)

Tutorial 2

(4.00
to
5.00)

Snacks

5.00-5.30

 

 

(name of the speaker

 

(name of the speaker

 

(name of the speaker/tutor

 

(name of the speaker/tutor

 

Mon

06/05/ 2019

RV

Tea

MK

Lunch

RV/T12

Tea

MK/T34

Snacks

Tues

07/05/ 2019

RV

Tea

MK

Lunch

RV/T12

Tea

MK/T34

Snacks

Wed

08/05/ 2019

RV

Tea

MK

Lunch

RV/T12

Tea

MK/T34

Snacks

Thu

09/05/ 2019

RV

Tea

MK

Lunch

RV/T12

Tea

MK/T34

Snacks

Fri

10/05/ 2019

RV

Tea

MK

Lunch

RV/T12

Tea

MK/T34

Snacks

Sat

11/05/ 2019

RV

Tea

MK

Lunch

RV/T12

Tea

MK/T34

Snacks

 SUNDAY

Mon

13/05/ 2019

TB

Tea

AN

Lunch

TB/T56

Tea

AN/T78

Snacks

Tues

14/05/ 2019

TB

Tea

AN

Lunch

TB/T56

Tea

AN/T78

Snacks

Wed

15/05/ 2019

TB

Tea

AN

Lunch

TB/T56

Tea

AN/T78

Snacks

Thu

16/05/ 2019

TB

Tea

AN

Lunch

TB/T56

Tea

AN/T78

Snacks

Fri

17/05/ 2019

TB

Tea

AN

Lunch

TB/T56

Tea

AN/T78

Snacks

Sat

18/05/ 2019

TB

Tea

AN

Lunch

TB/T56

Tea

AN/T78

Snacks

 RV: R. Venkatesh, MK: ManjunathKrishnapur, TB: Tirthankar Bhattacharyya, AN: A.K. Nandakumaran.
T12: G.V.K. Teja&SubhajitGhosh, T34: Lakshmi Priya M.E. & Rahul/Ramesh
T56: Poornendu Kumar &ShubhamRastogi, T78: Abu Sufian& S. Aiyyappan.

 

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