AIS Algebraic Number Theory (2018)

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Venue: Indian Institute of Technology Guwahati,  Guwahati, Assam
Date:  14th, May 2018 to 2nd, Jun 2018

 

School Convener(s)

Name Anupam Saikia Rupam Barman
Mailing Address Professor, Department of Mathematics
IIT Guwahati, PIN 781039
Associate Professor,
Department of Mathematics,
IIT Guwahati, PIN 781039

 


 Speakers with their affiliations:

Sr. Speaker Affiliation
1 Prof. Dilip P. Patil IISc, Bangalore
2 Dr. Debopam Chakraborty Tezpur University
3 Dr. Rupam Barman IIT Guwahati
4 Prof. Anupam Saikia Panjab University, Chandigarh
5 Dr. U. K. Anandavardhan IIT Bombay

 


 Syllabus:

Sr. Speaker Topics covered
1 Prof. Dilip P. Patil, (Six lectures)
  1. Dedekind domains
  2. Prime Factorization in Dedekind Domain
  3. Ideal Class Group of Dedekind Domain
2

Dr. Debopam Chakraborty (Six lectures)

  1. Algebraic numbers and integers
  2. Number fields and ring of integers
  3. Integral basis and discriminant
  4. The ring of integers as Dedekind domain
  5. Quadratic fields: integral basis and units
3 Dr. Rupam Barman (Eight lectures)
  1. Minkwoski’s theory
  2. Finiteness of Class group of Number Fields
  3. Computation of class group
  4. Dirichlet’s Unit Theorem
  5. Regulator
4 Prof. Anupam Saikia (Nine lectures)
  1. Cyclotomic polynomials
  2. Ring of integers of cyclotomic extensions
  3. Discriminant
  4. Ramification
  5. Cycolotomic units
  6. Fermat’s Last Theorem for regular primes
5 Dr. U. K. Anandavardhan
  1. Dirichlet characters
  2. Dirichlet L-series
  3. Bernoulli numbers
  4. Dedekind zeta function
  5. Class number formula

 

In addition to the speakers, the following took tutorial classes:
(1) Dr. Prem Prakash Pandey, Assistant Professor, IISER Berhampur
(2) Dr. Neelam Saikia, Inspire Faculty, IIT Guwahati
(3) Dr. Azizul Haque, Post-Doctoral Fellow, HRI, Allahabad
(4) Dr. Gautam Borisagar, Assistant Professor, IITRAM, Ahmedabad
(5) Dr. Sneh Bala Sinha, NPDF, IIT Guwahati.
(6) Mr. Naba Kanta Sarma, Assistant Professor, Assam University, Silchar

 


 Time Table

Day Date Lecture 1
(09.30-11.00)
Tea Lecture 2
(11.30- 01.00)
Lunch Tutorial
(02.30-3.30)
Tea Tutorial
(4-5)
Snacks
MON 14.05.2018 DP-1   DC-1   (DP, NKS)   (DP, NKS)  
TUE 15.05.2018 DP-2   DC-2   (DC, NS)   (DC, NS)  
WED 16.05.2018 DP-3   DC-3   (DP, NKS)   (DP, NKS)  
THU 17.05.2018 DP-4   DC-4   (DC, NS)   (DC, NS)  
FRI 18.05.2018 DP-5   DC-5   (DP, NKS)   (DP, NKS)  
SAT 19.05.2018 DP-6   DC-6   (DC, NS)   (DC, NS)  
MON 21.05.2018 RB-1   AS-1   (RB, AH)   (RB, AH)  
TUE 22.05.2018 AS-2   RB-2   (AS, PPP)   (AS, PPP)  
WED 23.05.2018 RB-3   AS-3   (RB, AH)   (RB, AH)  
THU 24.05.2018 AS-4   RB-4   (AS, PPP)   (AS, PPP)  
FRI 25.05.2018 UKA-1   RB-5   (RB, AH)   (RB, AH)  
SAT 26.05.2018 UKA-2   RB-6   (UKA)   (UKA)  
MON 28.05.2018 UKA-3   AS-5   (UKA)   (UKA)  
TUE 29.05.2018 RB-7   UKA-4   (AS, PPP)   (AS, PPP)  
WED 30.05.2018 UKA-5   AS-6   (RB, AH)   (RB, AH)  
THU 31.05.2018 UKA-6   RB-8   (UKA)   (UKA)  
FRI 1.06.2018 UKA-7   AS-7   (AS, PPP)   (AS, PPP)  
SAT 2.06.2018 UKA-8   AS-8   (UKA)   (UKA)  
DP: Prof. Dilip Patil DC: Dr. Debopam Chakraborty RB: Dr. Rupam Barman
AS: Dr. Anupam Saikia UKA: Dr. U.K. Anandavardhanan

 


List of Participants

Sr. Name Affiliation
1 Ms. Prachi Gupta Department of Mathematics, Delhi University
2 Ms. Sehra Sahu National Institute of Technology, Surathkal
3 Ms Pratiksha Satish Shingavekar Indian Institute of Technology Madras
4 Ms Deepshikha Chatterjee Ambedkar University, Delhi
5 Ms. Shalini Rana Ambedkar University, Delhi
6 Ms. Shivani Sharma Ambedkar University, Delhi
7 Ms. Sudipa Mondal Indian Institute of Science Education and Research Pune
8 Ms. Sampurna Satpati Indian Institute of Technology (Indian School of Mines) Dhanbad
9 Ms Rubayya University of Hyderabad
10 Dr. Saroj Rani S.A. Jain College, Ambala
11 Mr Tarun Dalal Indian Institute of Technology Hyderabad
12 Mr. Suneel Kumar Indian Institute of Science Education and Research, Mohali
13 Mr. Mohit Mishra Harish-Chandra Research Institute, Allahabad
14 Mr. Arpit Bansal Jawaharlal Nehru University, Delhi
15 Mr. Rishabh Agnihotri Harish-Chandra Research Institute, Allahabad
16 Mr Sumukha S National Institute of Technology, Karnataka
17 Mr. Sujeet Kumar Singh NISER, Bhubaneswar
18 Mr. Mansoor Ali K S University of Hyderabad
19 Mr. Rijubrata Kundu Indian Institute of Science Education and Research Pune
20 Mr Subhasis Panda Indian Institute of Technology Madras
21 Mr. Mahesh Kumar Ram Indian Institute of Science Education and Research Berhampur
22 Mr Arjun Singh Chetry Indian Institute of Inofrmation Technology Guwahati
23 Mr. Hridoyananda Saikia Indian Statistical Institute, Bangalore
24 Mr. Debakanta Buragohain Tinsukia College, Assam
25 Mr. Vipul Arora Indian Institute of Science, Bangalore
26 Mr. Vivek Dabra Thapar Institute of Engineering & Technology
27 Mr Nilanjan Bag Indian Institute of Technology Guwahati
28 Mr. Shamik Das Indian Institute of Technology Guwahati
29 Kumar Abhinav Mishra Indian Institute of Technology Guwahati
30 Ronit Neogy Indian Institute of Technology Guwahati
31 Subhaajyoti Bhattacharya Indian Institute of Technology Guwahati
32 Abhishek Kumar Sharma Indian Institute of Technology Guwahati
33 Mohit Tripathi Indian Institute of Technology Guwahati
34 Archana S. Pondichery University

 


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