AFSI  Annual Foundation School  I (IIT Patna 2020)
Speakers and Syllabus
Name of the Speakers with their affiliation. 
No. of Lectures 
Detailed Syllabus 
Prof V K Bhat, SMVDU, Jammu (VKB) 
6 
Group Action, Cayley’s Theorem, Class Equation, Simple Group, Examples : Icosahedral group, Sylow Theorems and its applications, Free group, Generators and Relation 
Prof. Om Prakash, IITP (OP) 
6 
Bilinear forms, Symmetric forms : orthogonality, , orthogonal projection, Hermitian Forms, Spectral theorem for Hermitian and Normal operators, Conics and Quadric 
Prof. Ritumoni Sarma, IITD(RS) 
6 
The Classical Linear Groups, Special Unitary Group SU(2) and its orthogaonal representation.SL(2,R), Oneparameter subgroups, Lie Algebra, Simple Group 
Dr. Anupam Kumar Singh, IISER, Pune(AKS)

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 N K Tomar, IITP (NKT) 
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 
Prof. R. Thangadurai, HRI, Prayagraj (RT) 
6 
Morera’s Theorem,, Sequences of holomorphic functions, Schwarz reflection principle, Runge’s approximation theorem, Zeros and Poles, Residue Formula 
Dr Amit Priyadarshi, IITD (AP) 
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 Amit Priyadarshi, IITD (AP) 
6 
Fourier Transform, Class of Holomorphic functions on strip with moderate decay, PaleyWiener Theorem, Mittal Lefflar, Weierstrass theorems, Riemann mapping theorem. 
Dr Tiken Singh, NEHU (TS) 
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, Subbasis of a topology, Weak Topologies 
Dr Tiken Singh, NEHU (TS) 
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 
Prof Himadri Mukherjee, NEHU (HM) 
6 
Urysohn Imbedding Theorem, StoneCech Compactification, Connected Spaces, Components of a space, totally disconnected spaces, Locally connected Spaces, Weierstrass Approximation Theorem, Stone Weierstrass Theorem 
Dr Ashish Kumar Upadhyay, IITP (AKU) 
6 
Locally Compact Hausdorff Spaces, Extended StoneWeierstrass Theorem, Constructing Mobius Strips, Torus and higher genus surfaces, Cone construction, Glueing lemma, Quotient space, Topological Group, Orbit Space. 
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 (3.353.55) 
Tutorial 2 4.00 – 5.00 
Snacks 5.055.30 


(name of the speaker) 

(name of the speaker) 

(name of the tutor) 

(Name of the tutor) 

Mon 
04052019 
VKB 

TS 

Topology 

Topology 

Tues 
05052019 
VKB 

NKT 

Complex 

Complex 

Wed 
06052019 
NKT 

VKB 

Algebra 

Algebra 

Thu 
07052019 
VKB 

TS 

Topology 

Topology 

Fri 
08052019 
TS 

NKT 

Complex 

Complex 

Sat 
09052019 
NKT 

TS 

Algebra 

Algebra 

SUNDAY : HOLIDAY 

Mon 
11052019 
RT 

OP 

Complex 

Complex 

Tue 
12052019 
OP 

TS 

Algebra 

Algebra 

Wed 
13052019 
TS 

RT 

Topology 

Topology 

Thu 
14052019 
RT 

OP 

Complex 

Complex 

Fri 
15052019 
OP 

TS 

Algebra 

Algebra 

Sat 
16052019 
TS 

RT 

Topology 

Topology 

SUNDAY : HOLIDAY 

Day 
Date 
Lecture 1 (9.30–11.00) 
Tea 
Lecture 2 
Lunch 
Tutorial 1 (2.30 – 3.30) 
Tea 
Tutorial 2 
Snacks 


(name of the speaker 

(name of the speaker 

(name of the tutor 

(Name of the tutor) 

Mon 
18052019 
RS 

AP 

Complex 

Complex 

Tue 
19052019 
AP 

HM 

Algebra 

Algebra 

Wed 
20052019 
HM 

RS 

Topology 

Topology 

Thu 
21052019 
RS 

AP 

Complex 

Complex 

Fri 
22052019 
AP 

HM 

Algebra 

Algebra 

Sat 
23052019 
HM 

RS 

Topology 

Topology 

SUNDAY : HOLIDAY 

Mon 
25052019 
AKS 

AP 

Algebra 

Algebra 

Tue 
26052019 
AP 

AKU 

Topology 

Topology 

Wed 
27052019 
AKU 

AKS 

Complex 

Complex 

Thu 
28052019 
AKS 

AP 

Algebra 

Algebra 

Fri 
29052019 
AP 

AKU 

Topology 

Topology 

Sat 
30052019 
AKU 

AKS 

Complex 

Complex 
