AIS - Analysis and Partial Differential Equations (2025)

Speakers and Syllabus

Detailed syllabus

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Prof. E K Narayanan (EKN)	6	Definition and examples of topological vector spaces (TVS), locally convex spaces, Continuity of linear functionals on (LCS), Frechet spaces and examples, The Hahn-Banach theorems and Applications.
Prof. G S Raju K (GSR)	6	Review of Lp spaces and basic properties, dual of Lp spaces, weak and weak* convergence in Lp spaces, Convolution and Fourier transforms.
Prof. Mnamohan Vashisth (MV)	6	Definition and examples of distributions, calculus with distributions, convolution and Fourier transform of distribution, Paley-Wiener theorems, Notion of Fundamental solutions to PDEs.
Prof. Venky P Krishnan (VPK)	6	Sobolov spaces-Properties, Embedding theorem, Poincare inequality, Trace theory.
Prof. K Sandeep (KS)	6	Lax-Milgram's theorem, Existence and uniqueness of weak solutions of Poisson's equation.
Prof. Bidhan Chandra Sardar (BCS)	6	Time-dependent Sobolev spaces, Second-order parabolic equations, Existence and uniqueness of weak solution (Galerkin's method), Maximum principles.

References:

Partial Differential Equations by Lawrence C. Evans.
Partial Differential Equations in Action by Sandro Salsa.
Introduction to PDEs by Gerald B. Folland.
Functional analysis by W. Rudin.
Measure theory and fine properties of functions by Lawrence C. Evans and Ronald F. Gariepy.
Topics in functional analysis by S. Kesavan
Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis.

Time Table

Day	Date	Lecture 1 9.30 to 11.00	Tea 11.05 to 11.25	Lecture 2 11.30 to 1.00	Lunch 1.05 to 2.25	Tutorial 2.30 to 3.30	Tea 3.35 to 3.55	Tutorial 4.00 to 5.00	Snack 5.05 to 5.30
		(name of the speaker)		(name of the speaker		(name of the speaker + tutors)		(name of the speaker + tutors)
Mon	26 May	EKN		GSR		EKN+MAB+KL		GSR+PS+AD
Tues	27 May	EKN		GSR		EKN+MAB+KL		GSR+PS+AD
Wed	28 May	EKN		GSR		EKN+MAB+KL		GSR+PS+AD
Thu	29 May	EKN		GSR		EKN+MAB+KL		GSR+PS+AD
Fri	30 May	EKN		GSR		EKN+MAB+KL		GSR+PS+AD
Sat	31 May	EKN		GSR		EKN+MAB+KL		GSR+PS+AD
SUNDAY: OFF
Mon	2 June	MV		VPK		MV+RB+PK		VPK+VR+MK
Tues	3 June	MV		VPK		MV+RB+PK		VPK+VR+MK
Wed	4 June	MV		VPK		MV+RB+PK		VPK+VR+MK
Thu	5 June	MV		VPK		MV+RB+PK		VPK+VR+MK
Fri	6 June	MV		VPK		MV+RB+PK		VPK+VR+MK
Sat	7 June	MV		VPK		MV+RB+PK		VPK+VR+MK
SUNDAY: OFF
Mon	9 June	KS		BCS		KS+RT+SG		BCS+RR+SA
Tues	10 June	KS		BCS		KS+RT+SG		BCS+RR+SA
Wed	11 June	KS		BCS		KS+RT+SG		BCS+RR+SA
Thu	12 June	KS		BCS		KS+RT+SG		BCS+RR+SA
Fri	13 June	KS		BCS		KS+RT+SG		BCS+RR+SA
Sat	14 June	KS		BCS		KS+RT+SG		BCS+RR+SA

Full forms for the abbreviations of speakers and tutors:

Tutorial Assistants:

S. No.	Abbreviations of speakers	Name of the speaker	Affiliation
1	EKN	Prof. E. K. Narayanan	IISc Bangalore
2	VK	Prof. Venkateswan Krishnan	TIFR CAM Bangalore
3	SK	Prof. K. Sandeep	TIFR CAM Bangalore
4.	GSR	Dr. G Sankara Raju Kosuru	IIT Ropar
5.	MV	Dr. Manmohan Vashisth	IIT Ropar
6.	BCS	Dr. Bidhan C Sardar	IIT Ropar

Tutorial Assistants:

S. No.	Name	Affiliation
1	Vinay Rana (VR)	PhD student, Department of Mathematics, IIT Ropar
2	Mandeep Kumar (MK)	PhD student, department of Mathematics, IIT Ropar
3	Parveen Kuamr (PK)	PhD student, department of Mathematics, IIT Ropar
4.	Rahul Bhardwaj (RB)	PhD student, Department of Mathematics, IIT Ropar
5.	Mohd. Ashraf Bhat (MAB)	PhD student, Department of Mathematics, IIT Ropar
6.	Krishna Kumar Lal (KL)	PhD student, Department of Mathematics, IIT Ropar
7.	Priti Saha (PS)	PhD student, Department of Mathematics, IIT Ropar
8.	Dr. Abhik Digar (AD)	Post Doctoral Fellow, Department of Mathematics, IIT Kanpur
9.	Ritu Raj (RR)	PhD student, Department of Mathematics, IIT Ropar
10.	Dr. Ranjith T (RT)	Post Doctoral Fellow, ISI Bangalore
11.	Sahil (SA)	PhD student, Department of Mathematics, IIT Ropar
12.	Dr. Swati Garg (SG)	Central University of Punjab (University in Bathinda), Punjab

File Attachments: