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

Speakers and Syllabus


Name of the Speakers with their affiliation. No. of Lectures Detailed Syllabus
ALGEBRA
Dr. Archana Morye (AM)
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. Sameer Chavan (SC)
IIT Kanpur
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
Dr. Mohan Chintamani
(MC) 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)
ANALYSIS
Prof. R Thangadurai (RT)
HRI, Prayagraj
(Allahabad)
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. Purusottam Rath
(PR) CMI, Chennai
6 [SS] Morera’s Theorem,, Sequences of holomorphic functions, Schwarz reflection principle, Runge’s approximation theorem, Zeros and Poles, Residue Formula
Prof. S. Ilangovan (SI)
UoH, Hyderabad
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.
Prof. S. Sivananthan (SS)
IIT Delhi
6 [SS] Fourier Transform, Class of Holomorphic functions, Paley-Wiener Theorem
TOPOLOGY
Dr. TKS Moothathu (TM)
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. Sanoli Gun (SG)
IMSc, 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 Tea Lecture 2 Lunch Tutorial 1 Tea Tutorial 2 Snacks
(9.30– 11.00) (11.05– 11.25) (11.30– 1.00) (1.05– 2.25) 2.30 – 3.30) (3.35- 3.55) 4.00 – 5.00 5.05-5.30
Speaker   Speaker   Tutor   Tutor  
Mon 06-05- 2019 TM   RT   Topology (PM/Rb)   Topology (PM/Rb)  
Tues 07-05- 2019 AM   TM   Analysis (MA/ShG)   Analysis (MA/ShG)  
Wed 08-05- 2019 RT   AM   Algebra (LS/Ar)   Algebra (LS/Ar)  
Thu 09-05- 2019 TM   RT   Topology (PM/Rb)   Topology (PM/Rb)  
Fri 10-05- 2019 AM   TM   Analysis (MA/ShG)   Analysis (MA/ShG)  
Sat 11-05- 2019 RT   AM   Algebra (LS/Ar)   Algebra (LS/Ar)  
SUNDAY: HOLIDAY
Mon 13-05- 2019 PR   SG   Topology (BR/MG)   Topology (BR/MG)  
Tue 14-05- 2019 SC   PR   Analysis (LS/Ar)   Analysis (LS/Ar)  
Wed 15-05- 2019 SG   SC   Algebra (PM/PG)   Algebra (PM/PG)  
Thu 16-05- 2019 PR   SG   Topology (BR/MG)   Topology (BR/MG)  
Fri 17-05-2019 SC   PR   Analysis   Analysis  
Sat 18-05-2019 SG   SC   (ShG/Ar) Algebra (PM/PG)   (ShG/Ar) Algebra (PM/PG)  
SUNDAY: HOLIDAY
Day   Date   Lecture 1 Tea Lecture 2 Lunch Tutorial 1 Tea Tutorial 2 Snacks
(9.30-11.00) (11.05– 11.25) (11.30– 1.00) (1.05– 2.25) 2.30 – 3.30) (3.35- 3.55) 4.00 – 5.00 5.05-5.30
Speaker   Speaker   Tutor   Tutor  
Mon 20-05- 2019 SI   PP   Analysis (BSa/Rb)   Analysis (BSa/Rb)  
Tue 21-05- 2019 SL   SI   Topology (BP/BSa)   Topology (BP/BSa)  
Wed 22-05- 2019 SI   PP   Algebra (BR/MG)   Algebra (BR/MG)  
Thu 23-05- 2019 SL   SI   Analysis (PG/Rb)   Analysis (PG/Rb)  
Fri 24-05- 2019 PP   SL   Topology (ShG/BP)   Topology (ShG/BP)  
Sat 25-05- 2019 PP   SL   Algebra (BR/MG)   Algebra (MG/BR)  
SUNDAY: HOLIDAY
Mon 27-05- 2019 SS   MC   Topology (MA/Rb)   Topology (MA/Rb)  
Tue 28-05- 2019 MD   SS   Analysis (BSa/BP)   Analysis (BSa/BP)  
Wed 29-05- 2019 MC   MD   Algebra (LS/BR)   Algebra (LS/BR)  
Thu 30-05- 2019 SS   MC   Topology (MA/BP)   Topology (MA/BP)  
Fri 31-05- 2019 MD   SS   Analysis (BSa/PG)   Analysis (BSa/PG)  
Sat 01-06- 2019 MC   MD   Algebra (LS/MG)   Algebra (LS/MG)  

 

 

 

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