Syllabus:
Name of the Speakers with their affiliation. 
No. of Lectures/Hrs 
Detailed Syllabus 
Speakers 2) Ganesh Kadu (S. P. Pune Univ., Pune) 3) Vijay Patankar (JNU, New Delhi) 4) ParvatiShastri (Mumbai Univ.) Associate Teachers: 1) Dilpreet Kaur (IISER, Pune) 
6 Hrs 
Algebra I (Linear Algebra and Group Theory)
Topics: (i) Operations of a group on itself, the class equation of the icosahedral group, operations on subsets, the Sylow theorems, the groups of order 12, computations on the symmetric group, the free group, generators and relations, the ToddCoxeter Algorithm. (ii) Bilinear forms, symmetric forms: orthogonality, the geometry associated to a positive form, Hermitian forms, the spectral theorem, conics and quadrics, the spectral theorem for normal operators, skewsymmetric forms, summary of results in matrix notation. (iii) Linear groups, the classical linear groups, the special unitary group SU2, the orthogonal representation of SU2, the special linear group SL2(R), oneparameter subgroups, the Lie algebra, translations in a group, simple groups. (iv) Group representations, Ginvariant forms and unitary representations, compact groups, Ginvariant subspaces and irreducible representations, compact groups, Ginvariant subspaces and irreducible representations, characters, permutation representations and the regular representation, the representations of the icosahedral group, onedimensional representations, Shur’s Lemma, and proof of the orthogonality relations. 
Speakers 2) Rohit Holkar 3) Shantanu Dey 4) A. R. Shastri (IIT, Mumbai) Associate Teachers: 1) Krishna Masalkar (Garware College, Pune) 
6 Hrs each 
Analysis I (Complex Analysis) [Stein and Shakarchi] Chapters 2,3,4.
Topics: Cauchy’s Theorem and Its Applications, Meromorphic Functions and the Logarithm, The Fourier Transform 
Speaker 1) Sandeep Singh (IITB, Mumbai) 2) Amit Kuber (IITK, Kanpur) 3) Priyavrat Deshpande (CMI) 4) Dheeraj Kulkarni (IISER, Bhopal) 
6 Hrs each 
Topology I (Point Set Topology): [Simmons] Chapters 17 and Quotient spaces: [Armstrong] Chapter 4 ‘Identification Spaces’.
Topics: Sets and functions, metric spaces, topological spaces, quotient spaces, compactness, separation, connectedness, approximation, Weierstrass approximation theorem, StoneWeierstrass theorem. 
Special Talks:
 Dinesh Thakur (Univ. of Rochester),
 A. R. Shastri (IITB, Mumbai)
Note: Faculty Members may pick and choose, or even introduce extra topics, so as to make the program more relevant to the students who have come to participate in AFS I.
Time Table:
Day 
Lecture 1 (9.30–11.00) 
Tea (11.00–11.30) 
Lecturer 2 (11.30–1.00) 
Lunch (1.00–2.30) 
Tutorial 1 (2.30–3.30) 
Tea (3.304.00) 
Tutorial 2 (4.005.00) 
Snacks 5.00 
Mon 
AlgebraL1 

AnalysisL1 

AlgebraT1 

AlgebraT2 

Tues 
TopologyL1 

AlgebraL2 

AnalysisT1 

AnalysisT2 

Wed 
AnalysisL2 

TopologyL2 

TopologyT1 

TopologyT2 

Thu 
AlgebraL3 

AnalysisL3 

AlgebraT3 

AlgebraT4 

Fri 
TopologyL3 

AlgebraL4 

AnalysisT3 

AnalysisT4 

Sat 
AnalysisL4 

TopologyL4 

TopologyT4 

TopologyT4 
