Syllabus to be covered in terms of modules of 6 lectures each :
|
Name of the Speaker with affiliation, who will cover each module of 6 lectures |
No. of Lectures |
Detailed Syllabus |
|
Dr. Parvati Shastri (PS) (Mumbai University) |
6 |
Group Action, Cayley’s Theorem, Class Equation, Simple Group, Examples : Icosahedral group, Sylow Theorems and its applications, Free group, Generators and Relation |
|
Dr Santosha K Pattanayak (IIT Kanpur) (SP) |
6 |
Bilinear forms, Symmetric forms : orthogonality, , orthogonal projection, Hermitian Forms, Spectral theorem for Hermitian and Normal operators, Conics and Quadric |
|
Dr Sachin Sharma (IIT Kanpur) (SS) |
6 |
The Classical Linear Groups, Special Unitary Group SU(2) and its orthogaonal representation.SL(2,R), One-parameter subgroups, Lie Algebra, Simple Group |
|
Dr Preena Samuel (IIT Kanpur) (PRS) |
6 |
Group Representations, Group Invariant forms and Unitary Representations, Compact groups, Invariant Subspaces and Irreducible representations, Characters, Permutation Representations and regular representation, Schur’s Lemma and Proof of orthogonalty relations, Representations of the Group SU(2) |
|
Dr Sameer Chavan (IIT Kanpur) (SC) |
6 |
Goursat’S Theorem, Local existence of primitives, Cauchy’s Theorem on Disc, Cauchy’s integral formulas, Liouville’s theorem, Fundamental Theorem of Algebra, Identity Theorem |
|
Dr Parasar Mohanty (IIT Kanpur) (PM) |
6 |
Morera’s Theorem,, Sequences of holomorphic functions, Schwarz reflection principle, Runge’s approximation theorem, Zeros and Poles, Residue Formula |
|
Dr Saurabh Shrivastava (IISER Bhopal) (SKS) |
6 |
Singularities and Meroporhic functions,The argument principle, Rouche’s theorem, Open mapping theorem, Maximum modulus principle, The complex logarithm, Fourier Series and Harmonic Functions. |
|
Dr Rama Rawat (IIT Kanpur) (RR)
|
6 |
Fourier Transform, Class of Holomorphic functions on strip with moderate decay, Paley-Wiener Theorem |
|
Dr Anant Shastri (IIT Bombay) (AS) |
6 |
Metric Spaces, Open and Closed sets, Convergence, Completeness, Baire’s Theorem, Lebesgue Lemma, Continuous mappings, Space of Continuous Functions, Topological Spaces, Basis of a topology, Sub-basis of a topology, Weak Topologies |
|
Dr Ashish Mandal (IIT Kanpur) (AM) |
6 |
Compact Spaces, Product of Spaces, Tychonoff's theorem, locally compact spaces, Compactness for Metric Spaces, Ascoli's theorem, Hausdorff Spaces, Completely Regular Spaces and Normal Spaces, Urysohn's Lemma, Tietze Extension theorem |
|
Dr Abhijit Pal (IIT Kanpur) (AP) |
6 |
Urysohn Imbedding Theorem, Stone-Cech Compactification, Connected Spaces, Components of a space, totally disconnected spaces, Locally connected Spaces, Weierstrass Approximation Theorem, Stone Weierstrass Theorem |
|
Dr Ajay Singh Thakur (IIT Kanpur) (AT) |
6 |
Locally Compact Hausdorff Spaces, Extended Stone-Weierstrass Theorem, Constructing Mobius Strips, Torus and higher genus surfaces, Cone construction, Glueing lemma, Quotient space, Topological Group, Orbit Space. |
References:
1. Algebra, Michael Artin
2. Complex Analysis, Stein E.M and Rami Shakarchi
3. Introduction to Topology and Modern Analysis, G.F.Simmons
4. Basic Topology, M.A. Armstrong
Names of the tutors / course associate with their affiliation and status:
1. Rajeev Gupta (Post Doc IIT Kanpur)
2. Sailesh Trivedi (Post Doc, IIT Kanpur)
3. Few more postdocs from outside Kanpur
Tentative time-table:
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.00 |
Lecture 2 (11.30–1.00) |
Lunch (1.00–2.00) |
Tutorial 1 (2.30–3.30) |
Tea (3.30-4.00) |
Tutorial 2 (4.00-5.00) |
Tea 5.00 |
|
|
|
speaker |
|
speaker |
|
speaker / |
|
speaker/ |
|
|
Mon |
7.05.18 |
AS |
SC |
Topology |
Topology |
||||
|
Tues |
08.05.18 |
SC |
PS |
Complex |
Complex |
||||
|
Wed |
09.05.18 |
PS |
AS |
Algebra |
Algebra |
||||
|
Thu |
10.05.18 |
AS |
SC |
Topology |
Topology |
||||
|
Fri |
11.05.18 |
SC |
PS |
Complex |
Complex |
||||
|
Sat |
12.05.18 |
PS |
AS |
Algebra |
Algebra |
||||
|
Sunday : Off |
|||||||||
|
Mon |
14.05.18 |
PM |
|
SP |
|
Complex |
|
Complex |
|
|
Tue |
15.05.18 |
SP |
AM |
Algebra |
Algebra |
||||
|
Wed |
16.05.18 |
AM |
PM |
Topology |
Topology |
||||
|
Thu |
17.05.18 |
PM |
SP |
Complex |
Complex |
||||
|
Fri |
18.05.18 |
SP |
AM |
Algebra |
Algebra |
||||
|
Sat |
19.05.18 |
AM |
PM |
Topology |
Topology |
||||
|
Sunday : Off |
|||||||||
|
Mon |
21.05.18 |
SKS |
|
SS |
|
Complex |
|
Complex |
|
|
Tue |
22.05.18 |
SS |
AP |
Algebra |
Algebra |
||||
|
Wed |
23.05.18 |
AP |
SKS |
Topology |
Topology |
||||
|
Thu |
24.05.18 |
SKS |
SS |
Complex |
Complex |
||||
|
Fri |
25.05.18 |
SS |
AP |
Algebra |
Algebra |
||||
|
Sat |
26.05.18 |
AP |
SKS |
Topology |
Topology |
||||
|
Sunday : Off |
|||||||||
|
Mon |
28.05.18 |
PRS |
|
AT |
|
Algebra |
|
Algebra |
|
|
Tue |
29.05.18 |
AT |
RR |
Topology |
Topology |
||||
|
Wed |
30.05.18 |
RR |
PRS |
Complex |
Complex |
||||
|
Thu |
31.05.18 |
PRS |
AT |
Algebra |
Algebra |
||||
|
Fri |
01.06.18 |
AT |
RR |
Topology |
Topology |
||||
|
Sat |
02.06.18 |
RR |
PRS |
Complex |
Complex |
||||