AIS Lie Algebras (2018)

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Venue: Harish Chandra Research Institute,  Allahabad, Uttar Pradesh
Date:  10th, Dec 2018 to 29th, Dec 2018

 

School Convener(s)

Name Prof. Punita Batra Dr. Umamaheswaran Arunachalam
Mailing Address Harish Chandra Research Institute, Allahabad. Harish Chandra Research Institute, Allahabad.

 


 Speakers with their affiliations:

Sl. No.

Speaker

Affiliation

1

Sachin Sharma

IIT Kanpur

2

PunitaBatra

HRI, Allahabad

3

B. Ravinder

CMI, Chennai

4

TanushreeKhandai

IISER Mohali

5

R. Venkatesh

IISc, Bangalore

6

S.E. Rao

Retired from TIFR, Mumbai

 Names of the tutors and their affiliation

 Sl. No.

Tutors

Affiliation

1

Souvik Pal

HRI, Allahabad

2

K.TejaGv

IISc, Bangalore

3

R. Venkatesh

IISc, Bangalore

4

S.E. Rao

Retired from TIFR, Mumbai

 


 Syllabus:

Sl. No.

Speaker

Actual syllabus covered by each speaker

1

Sachin Sharma

Linear Lie algebras, lie algebras of derivations, Ideals, homomorphism, Representations of lie algebras, Solvable and Nilpotent Lie algebras, Engel’s Theorem, Lie’s Theorem, Jordan chevalley decomposition.

2

PunitaBatra

Cartan’s Criterion – Killing Form, Criterion for semi-simplicity, Inner derivations, Abstract Jordan decomposition, Modules, Casimir element, Weyl’s Theorem, Preservation of Jordan decomposition, Representations of sl (2,F).

3

B. Ravinder

Maximal toralsubalgebras and roots, Orthogonality, Integrality and Rationality Properties of Roots, Root systems, Bases, Weyl chambers, The Weyl group, Irreducible Root Systems, Cartan Matrix.

4

TanushreeKhandai

Universal enveloping algebra,Coxeter graph, Dynkin diagrams, Classification Theorem, Construction of root systems and automorphisms, The theory of weights, Dominant weights, Isomorphism Theorem, CartanSubalgebras.

5

R. Venkatesh

Poincare-Birkhoff-Witt Theorem, Serre’s Theorem, Weights and maximal vectors, Verma modules, Finite dimensional irreducible modules, The finite dimensionality criterion, Multiplicity formula, characters of Verma modules, Weyl’s Character Formula.

6

S.E. Rao

Generalised Cartan matrices and Kac-Moody algebras, Affine Kac-Moody Lie algebras, Toroidal Lie algebras and representation theory.

 


 Time Table

 

Day

Date

Lecture 1

(9:30–11:00)

Tea

(11:00–11:30)

Lecture 2

(11:30–1:00)

Lunch

(1:00–3:00)

Tutorial 1

(03:00–4:00)

Tea & Snacks

(4:00-4:30)

Tutorial 2

(4:30-5:30)

Name of the Speaker

Name of the Speaker

Name of the Tutor

Name of the Tutor

Mon

10.12.18

S. Sharma

S. Sharma

-

-

Tues

11.12.18

S. Sharma

S. Sharma

-

Souvik Pal

Wed

12.12.18

S. Sharma

S. Sharma

Souvik Pal

K TejaGv

Thu

13.12.18

P. Batra

P. Batra

K TejaGv

Souvik Pal

Fri

14.12.18

P. Batra

S. Sharma

-

Souvik Pal

Sat

15.12.18

P. Batra

P. Batra

-

Souvik Pal

 

 

 

Sunday : Off

 

 

Mon

17.12.18

B. Ravinder

B. Ravinder

Souvik Pal

K TejaGv

Tue

18.12.18

B. Ravinder

B. Ravinder

-

K TejaGv

Wed

19.12.18

B. Ravinder

B. Ravinder

K TejaGv

K TejaGv

Thur

20.12.18

T. Khandai

T. Khandai

-

K TejaGv

Fri

21.12.18

T. Khandai

T. Khandai

-

K TejaGv

Sat

22.12.18

T. Khandai

T. Khandai

K TejaGv

K TejaGv

 

 

 

Sunday : Off

 

 

Mon

24.12.18

R. Venkatesh

R. Venkatesh

-

R. Venkatesh

Tue

25.12.18

R. Venkatesh

R. Venkatesh

-

R. Venkatesh

Wed

26.12.18

R. Venkatesh

R. Venkatesh

Souvik Pal

K TejaGv

Thu

27.12.18

S. E. Rao

S. E. Rao

-

-

Fri

28.12.18

S. E. Rao

S. E. Rao

-

S. E. Rao

Sat

29.12.18

S. E. Rao

S. E. Rao

-

-

 


List of actual participants

Sr.n SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg
1 16889 Mr. Jaitra Chattopadhyay Male Harish-Chandra Research Institute PhD Ramakrishna Mission Vidyamandira 2015  
2 17011 Ms Shushma Rani Female iiser mohali PhD Punjabi University Patiala 2015  
3 17012 Mr. Niranjan Nehra Male iiser mohali PhD IIT Kanpur 2017  
4 17196 Mr. Bharat Talwar Male University of Delhi PhD student Ramjas college, University of Delhi 2016  
5 17234 Mr. Bhagwat Sharan Male university of lucknow Phd Student Bundelkhand University Jhansi 2011  
6 17250 Mr. Ravi Dwivedi Male University of Lucknow PhD Student C S J M University Kanpur 2012  
7 17266 Ms. Sheere Farhat Ansari Female Lucknow University Student M.Sc. 2011  
8 17277 Mr. Rahul Ghosh Male Indian Statistical Institute, Bangalore B.Math.(Hons.)      
9 17521 Mr. Mahesh Krishna K Male (NITK) Surathkal Ph.D. STUDENT Mangalore University 2014  
10 18888 Mr. Saikat Panja Male IISER Pune PhD First year IISER-Kolkata 2017  
11 19117 Mr. Shashank Vikram Singh Male IIT Bombay M.Sc.-Ph.D dual degree IIT Bombay 2017 7/16/2017
12 20040 Dr. Dilpreet Kaur Female IISER Pune Post Doc Fellow Panjab University Chandigarh 2009 5/29/2015
13 20223 Mr. Sushil Singla Male NA NA Shiv Nadar University 2016  
14 20751 Ms. Neha Malik Female IISER Integrated PhD student IISER 2017  
15 21105 Mr. Rijubrata Kundu Male IISER Pune Research Scholar IIT Guwahati 2016  
16 21223 Mr Jayakumar Ravindran Male The Institute of Mathematical Sciences PhD Ramanujan Institute for Advanced Study in Mathematics 2016  
17 21587 Mr Nishant Rathee Male Harish chandra research institute Phd IIT MADRAS 2016  
18 21604 Ms Shilpi Mandal Female University of Hyderabad MSc Student University    
19 21673 Mr Samir Kumar Hazra Male Shiv Nadar University PhD IIT BOMBAY 2011  
20 21827 Mr. Himanshu Setia Male Indian Institute Of Technology , Ropar PhD University Of Delhi 2017  
21 21893 Mr. Ratheesh T V Male The Institute of Mathematical Sciences phD Pazhasi Raja Nss College Mattanur 2016  
22 22064 Ms Papi Ray Female IIT Guwahati PhD Kolkata University 2015  
23 22123 Ms Amthul Muqheet Female Jain University PhD student PSG College of Arts and Science, Coimbatore M.Sc 2006  
24 22261 Mr. Pritam Majumder Male TIFR PhD IIT Kanpur 2014  
25 22317 Mr. Philip Koppara Thomas Male IISc B.Sc(Research) student      
26 22338 Mr. Souvik Pal Male HCRI PhD IMSc 2016  
27 22352 Ms. Soniya Takshak Female IIT, Delhi PhD University of Rajasthan,Jaipur 2015  
28 22353 Ms. Pooja Gahlyan Female IIT,Delhi PhD SCHOLAR Deenbandhu Chotu Ram University Of Science And Technology-Murthal(Sonipat) 2016  
29 22357 Mr. Sujeet Ganesh Bhalerao Male IISER Pune BSMS Student IISER Pune Appeared / Awaiting Result  
30 22370 Mr Supravat Sarkar Male Indian Statistical Institute B.Stat.      
31 22377 Mr. Prashant Shivaji Arote Male TIFR, Mumbai. Ph. D. Department of Mathematics, University of Pune. 2015  
32 22388 Mr Prasad H M Male Mangalore University, Mangalagangothri PhD Student Mangalore University 2014  
33 22417 Mr Krishna Teja Gv Male Indian Institute of Science PhD Central University of Tamil Nadu 2016  
34   Mr. Priyanshu Chakraborty   HRI        
35   Mr. Santanu Tantubay   HRI        
36   Mr. Debasish Karmakar (HRI)   HRI        
37  

Ms. PranjalPandurangWarade

 

Indian Institute of Science, Bangalore.

BSc (Research) student

     

 


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