IST Algebraic Number Theory (2016) - Speakers and Syllabus

Speakers and Syllabus

Name os Speaker Affiliation Topic
Ganesh Kadu S. P. Pune University 1)Field Theory (2 and half hours)
2) Algebraic Numbers and Algebraic Integers, Algebraic Number Fields,
Integral Basis and Discriminant (5 hours)
S. A. Katre S. P. Pune University 1) Newton's theorem on symmetric polynomials (1 hour)
2) Divisibility (1 hour)
3) Euclidean Fields and Units (3 and half hours)
4) Divisibility in Quadratic Fields (1 hour)
5) Quadratic reciprocity law (1 hour)
S. D. Adhikari H.R.I., Allahabad 1)Ideals, Divisors, Factors (1 hour)
2)Fundamental Theorem of Ideal Theory and its consequences (4 hours)
3)Fractional Ideals, Inverse of an Ideal (1 hour)
4)Second Proof of Fundamental Theorem of Ideal Theory (1 hour)
(Relevant theory of Dedekind domains)
R. Thangadurai H.R.I., Allahabad 1)Congruences, Norm of an Ideal, Ideals in Different Number Fields (2 hours)
2)Ramification Index and Degree of a Prime Ideal , Splitting of Rational Primes in  Algebraic Number Fields (3 hours)
3)Splitting of Primes in Quadratic Fields (2 hours)
Anirban Mukhopadhyay IMSc, Chennai 1)The ideal class group (1 hour)
2)Minkowski's Theorem (1 hour)
3)Finiteness of class number and its consequences (3 hours)
4)Class number computations (2 hours)
Note: The guidelines for the course are provided herewith. The teachers may do a variation in the topics as per need.

First 5 days:

Day Lecture1
9:30-11
Tea break
11-11:30
Lecture2
11:30-1:00
3 -10-2016 Ganesh Kadu        S. A. Katre
4-10-2016 Ganesh Kadu S. A. Katre
5 -10-2016 Ganesh Kadu S. A. Katre
6 -10-2016 Ganesh Kadu S. A. Katre
7-10-2016 Ganesh Kadu S. A. Katre

 Last 7 days:

Day Lecture1
9:30-10:30
Tea break
10:30-10:45
Lecture2
10:45-11:45

Lecture3

12:00-1:00

Lunch
1:15

8 -10-2016 S. D. Adhikari       R. Thangadurai Anirban Mukhopadyay  
10-10-2016 S. D. Adhikari R. Thangadurai Anirban Mukhopadyay
11 -10-2016 S. D. Adhikari R. Thangadurai Anirban Mukhopadyay
12 -10-2016 S. D. Adhikari R. Thangadurai Anirban Mukhopadyay
13-10-2016 S. D. Adhikari R. Thangadurai Anirban Mukhopadyay
14-10-2016 S. D. Adhikari R. Thangadurai Anirban Mukhopadyay
15-10-2016 S. D. Adhikari R. Thangadurai Anirban Mukhopadyay

Tutorials:
(Time: 2.30 -3.30 and 3.45-4-45)

First Week

Monday Tuesday Wednesday Thursday Friday Saturday
03/10/16 4/10/2016 5/10/2016 6/10/2016 7/10/2016 8/10/2016
GK+2 SAK+2 GK+2 SAK+2 GK+2 SAK+2

 

Second Week

Monday Tuesday Wednesday Thursday Friday Saturday
10/10/16 11/10/2016 12/10/2016 13/10/2016 14/10/2016 15/10/2016
SDA+2 RT+2 AM+2 SDA+2 RT+2 AM+2

Snacks: 5.00 pm
Dinner: 8 pm

GK: Ganesh Kadu
SAK: S. A. Katre
SDA: S. D. Adhikari
RT: R. Thangadurai
AM: Anirban Mukhopadhyay
Associate Teachers:

sr Name Affiliation
1 A. Satyanarayan Reddy Shiv Nadar Univ., U.P.
2 Dilpreet Kaur Symbiosis College, Pune
3 Deepa Krishnamurty St. Mira’s College, Pune