TEW - Symmetries and Calculus

Speakers and Syllabus

 

Name of the Speaker with affiliation

Lecture

Hrs

Detailed Syllabus

Prof. Pralay Chatterjee
IMSc Chennai

 And

Dr. Chandan Maity,
IISER Berhampur

10.5 hrs

Lie Groups via Examples:

Matrices; General linear groups; Special linear groups, Orthogonality in R^n and C^n w.r.to the bilinear and sesquilinear forms. Orthogonal groups; Unitary groups; Topological properties of the matrix groups. Matrix exponentiation.

Differentiable manifolds; Tangent space. Vector fields.

Lie Groups and Their Lie Algebras; Homomorphisms; Lie Subgroups; Simply Connected Lie Groups (intuitive notions); Exponential Maps; Continuous Homomorphisms; Closed Subgroups; The Adjoint Representation.

Prof. Krishnendu Gongopadhyay,
IISER Mohali

 And

Prof. Sudeb Mitra,
CUNY, New York

7.5 hrs

The Möbius group:
Symmetries of the Euclidean plane. Hyperbolic plane. Isometries. Geodesics. Möbius transformation of the complex plane. Cross ratios. Inversions. Classification of isometries. Iwasawa decomposition. Polar decomposition.

 

Dr. Abhishek Mukherjee,
Kalna College

3 hrs

Group action on topological spaces:
Topological manifolds. Group action on topological manifolds. Covering spaces. Fundamental groups.

Dr. Kuntal Banerjee,
Presidency University

3 hrs

Groups acting on the circle:
Locally compact group acting on the circle. Translation number. Rotation number. Dynamics of circle homeomorphisms. Tits alternative.

Dr. Sayani Bera,
IACS Kolkata

3 hrs

Calculus and Metric:
Riemannian metric; Connections; Sectional curvature; Isometries and Curvature.

Target Audience : Our primary target will be the faculty members of colleges and universities and the fellow researchers. Also we may include some masters students and final year undergraduate students of nearby colleges and universities in accordance with the applications. However, the lectures will be comprising of certain important topics which will be useful to both of our targeted audience that is college teachers as well as young graduate students.

 

Time Table

 

 

Day

Date

Lec1

 10:00
to
11:30

11:30–
to
11:45

Lec 2

11:45
to
13:15

 

13:15

Lec 3

14:30
to
16:00

16:00
to
16:15

 16:15
to
17:45

17:45

Mon

05/08

KG-1

Tea

PC-1

Lunch

 

SM-1

Tea

PC+AM

 

(Tutorial)

Snacks

Tue

06/08

KG-2

Tea

PC-2

Lunch

 

SM-2

Tea

KG+SM

 

(Tutorial)

 

Snacks

Wed

07/08

KG-3

Tea

PC-3

Lunch

 

PC-4

Tea

AM

Snacks

Thurs

08/08

SB-1

Tea

CM-1

Lunch

 

KB-1

Tea

KB+SB

 

(Tutorial)

 

Snacks

Fri

09/08

KB-2

Tea

CM-2

Lunch

 

SB-2

Tea

KG-4

 

Sat

10/08

CM-3

Tea

Discussion

AM+CM

Lunch

Free

 

Note:

  • Sayani Bera- SB
  • Kuntal Banerjee: KB
  • Pralay Chatterjee- PC
  • Krishnendu Gongopadhyay- KG
  • Chandan Maity: CM
  • Sudeb Mitra: SM
  • Abhishek Mukherjee-AM

Tutors :

  • Sayani Bera- SB
  • Kuntal Banerjee: KB
  • Pralay Chatterjee- PC
  • Krishnendu Gongopadhyay- KG
  • Chandan Maity: CM
  • Sudeb Mitra: SM
  • Abhishek Mukherjee-AM

 

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