Annual Foundation School - I (2019) HRI, Prayagraj

Names of the tutors and their affiliation :

Sl. No.	Tutors	Affiliation
1	Amit Kumar Singh	IIT Madras
2	Satyanarayana Reddy	SNU, Delhi
3	Jaitra Chattopadhyay	HRI, Prayagraj
4	Mithun Das	HRI, Prayagraj
5	Bidisha Roy	HRI, Prayagraj
6	Pradeep Das	HRI, Prayagraj
7	Anoop Singh	HRI, Prayagraj
8	Veekesh Kumar	HRI, Prayagraj
9	Debasis Karmakar	HRI, Prayagraj
10	Subha Sarkar	HRI, Prayagraj
11	S. Manikandan	HRI, Prayagraj

 Syllabus: 

 Actual syllabus covered by each speaker with his/her affiliation

Sl. No.	Speaker	Actual syllabus covered by each speaker
1	Umesh K.V. Dubey (HRI, Prayagraj)	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.
2	Gyan Prakash (HRI, Prayagraj)	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.
3	Kalyan Chakraborty (HRI, Prayagraj)	Bilinear forms, Symmetric forms, orthogonality, orthogonal projection, Hermitian Forms, Spectral theorem for Hermitian and Normal operators, Conics and Quadric.
4	R. Thangadurai (HRI, Prayagraj)	Morera’s Theorem, Sequences of holomorphic functions, Schwarz reflection principle, Runge’s approximation theorem, Zeros and Poles, Residue Formula.
5	Punita Batra (HRI, Prayagraj)	Group Action, Cayley’s Theorem, Class Equation, Simple Group, Examples, Icosahedral group, Sylow Theorems and its applications, Free group, Generators and Relation.
6	N. Raghavendra (HRI, Prayagraj)	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.
7	B. Ramakrishnan (HRI, Prayagraj)	Singularities and Meromorphic functions, The argument principle, Rouche’s theorem, Open mapping theorem, Maximum modulus principle, The complex logarithm, Fourier Series and Harmonic Functions.
8	D. Surya Ramana (HRI, Prayagraj)	The Classical Linear Groups, Special Unitary Group SU(2) and its orthogonal representation.SL(2,R), One-parameter subgroups, Lie Algebra, Simple Group.
9	S.D. Adhikari (RKMVERI, Belur)	Urysohn Imbedding Theorem, Stone-Cech Compactification, Connected Spaces, Components of a space, totally disconnected spaces, Locally connected Spaces, Weierstrass Approximation Theorem, Stone-Weierstrass Theorem.
10	B. Sahu (NISER, Bhubaneswar)	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 orthogonality relations, Representations of the Group SU(2).
11	Satya Deo Tripathi (HRI, Prayagraj)	Locally Compact Hausdorff Spaces, Extended Stone-Weierstrass Theorem, Constructing Mobius Strips, Torus and higher genus surfaces, Cone construction, Gluing lemma, Quotient space, Topological Group, Orbit Space.
12	P.K. Ratnakumar (HRI, Prayagraj)	Fourier Transform, Class of Holomorphic functions on strip with moderate decay, Paley-Wiener Theorem.

 Time Table

List of actual Participants

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