AFS-I - Annual Foundation School - I (UOHHYD 2019)

Speakers and Syllabus


Name of the Speakers with their affiliation. No. of Lectures Detailed Syllabus
Dr. Mohan Chintamani
(MC) UoH, Hyderbad/
Dr. T K S Moothathu
UoH Hyderabad
6 [Artin, Ch 6] ]Group Actions, Cayley’s Theorem, Class Equation, Simple Group & Examples, Icosahedral group, Sylow Theorems and its applications, Free group, Generators and Relations
Prof. R Thangadurai (RT)
HRI, Prayagraj
(Allahabad)
6 [Artin, Ch 7] Bilinear forms, Symmetric forms : Orthogonality, Orthogonal projection, Hermitian Forms, Spectral Theorem, Conics and Quadric
Prof. Shanta Laishram
(SL) ISI Delhi
6 Artin, Ch 8] Classical Linear Groups, Special Unitary Group SU(2) and its Orthogonal Representation SL(2,R), One-parameter subgroups, Lie Algebra & Simple Groups
Prof. S. Ilangovan (SI)
UoH, Hyderabad
6 [Artin, Ch 9] 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. Archana Morye (AM)
UoH, Hyderabad
6 [SS] 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
Prof. Sanoli Gun (SG)
IMSc, Chennai
6 [SS] Morera’s Theorem,, Sequences of holomorphic functions, Schwarz reflection principle, Runge’s approximation theorem, Zeros and Poles, Residue Formula
Prof. Sameer Chavan (SC)
IIT Kanpur
6 [SS] 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. Prasanna Kumar N
(PK), BITS Goa
6 [SS] Fourier Transform, Class of Holomorphic functions, Paley-Wiener Theorem
Dr. Biswajyoti Saha
(BS) UoH, Hyderabad
6 [Simmons] 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
Prof. Purusottam Rath
(PR) CMI, Chennai
6 [Simmons] 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. Prabal Paul
(PP) BITS Goa
6 [Simmons]  Urysohn  Imbedding  Theorem,  Stone-Cech Compactification, Connected Spaces, Components of a space, totally disconnected spaces, Locally connected Spaces, Weierstrass Approximation Theorem, Stone Weierstrass Theorem
Prof. M S Datt (MS)
UoH, Hyderabad
6 [Simmons, Armstrong] 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  [Artin]
2. Complex Analysis, Stein E.M and Rami Shakarchi  [SS]
3. Introduction to Topology and Modern Analysis, G.F.Simmons [Simmons]
4. Basic Topology, M.A. Armstrong [Armstrong]

Names of the tutors / course associate with their affiliation :

1. Laba Sa [LS] (UoH)
2. Mansoor Ali [MA] (UoH)
3. Rubayya [Rb] (UoH)
4. Arijit [Ar](UoH)
5. Pabitra Mandal [PM] (UoH)
6. Bijay Sahoo [BSa](BITS Goa)
7. Vandana Pandey[VP] (BITS Goa)
8. Shayantan G [ShG](BITS Goa)
9. Pramod Ghatage[PG] (SSMM, Pune)
10. Biman Roy [BR](ISI, Delhi)
11. Manabendra Giri[MG] (ISI Delhi)
12. One/Two Tutors to be Announced/Decided Later.


Time Table

Day Date Lecture 1
(9.30– 11.00)
Tea
(11.05– 11.25)
Lecture 2
(11.30– 1.00)
Lunch
(1.05– 2.25)
Tutorial 1
(2.30 – 3.30)
Tea
(3.35- 3.55)
Tutorial 2
(4.00 – 5.00)
Snacks
(5.05- 5.30)
    Speaker Speaker Tutor Tutor

Mon 06-05- 2019 AM BS Topology (PM/Ar) Topology (PM/Ar)
Tues 07-05- 2019 MC AM Analysis (MA/Rb) Analysis (MA/Rb)
Wed 08-05- 2019 BS MC Algebra (LS/PG) Algebra (LS/PG)
Thu 09-05- 2019 AM BS Topology (PM/Ar) Topology (PM/Ar)
Fri 10-05- 2019 MC AM Analysis (MA/Rb) Analysis (MA/Rb)
Sat 11-05- 2019 BS MC Algebra (LS/PG) Algebra (LS/PG)
SUNDAY : HOLIDAY
Mon 13-05- 2019 SG

PR

Topology (BR/MG)

Topology (BR/MG)
Tue 14-05- 2019 RT SG Analysis (LS/PG Analysis (LS/PG)
Wed 15-05- 2019 PR RT Algebra (PM/Ar) Algebra (PM/Ar)
Thu 16-05- 2019 SG PR Topology (BR/MG) Topology (BR/MG)
Fri 17-05- 2019 RT SG Analysis (BSa/PG) Analysis (BSa/PG)
Sat 18-05- 2019 PR RT Algebra (PM/Ar) Algebra (PM/Ar)
SUNDAY : HOLIDAY
Day Date Lecture 1
(9.30– 11.00)
Tea
(11.05– 11.25)
Lecture 2
(11.30– 1.00)
Lunch
(1.05– 2.25)
Tutorial 1
(2.30 – 3.30)
Tea
(3.35- 3.55)
Tutorial 2
(4.00 – 5.00)
Snacks
(5.05- 5.30)
    Speaker Speaker Tutor Tutor

Mon 20-05- 2019 PP SC Topology (ShG/VP) Topology (ShG/VP)
Tue 21-05- 2019 SL PP Analysis (LS/BSa) Analysis (LS/BSa)
Wed 22-05- 2019 SC SL Algebra (MA/Rb) Algebra (MA/Rb)
Thu 23-05- 2019 PP SC Topology (ShG/VP) Topology (ShG/VP)
Fri 24-05- 2019 SL PP Analysis (BR/BSa) Analysis (BR/BSa)
Sat 25-05- 2019 SC SL Algebra (MA/Rb) Algebra (MA/Rb)
SUNDAY : HOLIDAY
Mon 27-05- 2019 MS

IG

Topology (PM/Ar)

Topology (PM/Ar)
Tue 28-05- 2019 PK MS Analysis (ShG/VP) Analysis (ShG/VP)
Wed 29-05- 2019 IG PK Algebra (BR/MG) Algebra (BR/MG)
Thu 30-05- 2019 MS IG Topology (BSa/VP) Topology (BSa/VP)
Fri 31-05- 2019 PK MS Analysis (LS/PG) Analysis (LS/PG)
Sat 01-06- 2019 IG PK Algebra (BR/MG) Algebra (BR/MG)

 

 

 

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