AFS-I - 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), One-parameter 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, Paley-Wiener 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, Sub-basis 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, Stone-Cech 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 Stone-Weierstrass 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

(3.35-3.55)

Tutorial 2

4.00 – 5.00

Snacks

5.05-5.30

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the tutor)

 

(Name of the tutor)

 

Mon

04-05-2019

VKB

 

TS

 

Topology

 

Topology

 

Tues

05-05-2019

VKB

 

NKT

 

Complex

 

Complex

 

Wed

06-05-2019

NKT

 

VKB

 

Algebra

 

Algebra

 

Thu

07-05-2019

VKB

 

TS

 

Topology

 

Topology

 

Fri

08-05-2019

TS

 

NKT

 

Complex

 

Complex

 

Sat

09-05-2019

NKT

 

TS

 

Algebra

 

Algebra

 

 SUNDAY : HOLIDAY

Mon

11-05-2019

RT

 

OP

 

Complex

 

Complex

 

Tue

12-05-2019

OP

 

TS

 

Algebra

 

Algebra

 

Wed

13-05-2019

TS

 

RT

 

Topology

 

Topology

 

Thu

14-05-2019

RT

 

OP

 

Complex

 

Complex

 

Fri

15-05-2019

OP

 

TS

 

Algebra

 

Algebra

 

Sat

16-05-2019

TS

 

RT

 

Topology

 

Topology

 

 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)

 

 

(name of the speaker

 

(name of the speaker

 

(name of the tutor

 

(Name of the tutor)

 

Mon

18-05-2019

RS

 

AP

 

Complex

 

Complex

 

Tue

19-05-2019

AP

 

HM

 

Algebra

 

Algebra

 

Wed

20-05-2019

HM

 

RS

 

Topology

 

Topology

 

Thu

21-05-2019

RS

 

AP

 

Complex

 

Complex

 

Fri

22-05-2019

AP

 

HM

 

Algebra

 

Algebra

 

Sat

23-05-2019

HM

 

RS

 

Topology

 

Topology

 

SUNDAY : HOLIDAY

Mon

25-05-2019

AKS

 

AP

 

Algebra

 

Algebra

 

Tue

26-05-2019

AP

 

AKU

 

Topology

 

Topology

 

Wed

27-05-2019

AKU

 

AKS

 

Complex

 

Complex

 

Thu

28-05-2019

AKS

 

AP

 

Algebra

 

Algebra

 

Fri

29-05-2019

AP

 

AKU

 

Topology

 

Topology

 

Sat

30-05-2019

AKU

 

AKS

 

Complex

 

Complex

 

 

 

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