AIS - An Introduction to p-adic Methods in Arithmetic (2023)
Speakers and Syllabus
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
Sazzad Ali Biswas SRM University AP |
05 |
1. Construction of p-adic numbers Detailed: |
Mihir Sheth IISc Bangalore |
04 |
1. Local Fields Detailed: |
Amiya Kumar Mondal IISER Berhampur |
04 |
Modular Forms Detailed: |
Santosh Nadimpally IIT Kanpur |
06 |
1. Construction of p-adic zeta functions Detailed: |
Manish Kumar Pandey SRM University AP |
02 |
Special values of the Riemann zeta functions Detailed: |
Shaunak Deo IISC Bangalore |
06 |
1. Cyclotomic Fields Detailed: |
C S Rajan Ashoka University |
(4+5)=09 |
(4 talks, in the first week of the program) Detailed: Polynomial over p-adic integers and their Solution, Quadratic Forms, Local- (5 talks, in the last week of the program) Stickelberger elements and annihilators of class groups. Ribet's converse to Herbrand and an indication of further developments towards the Main conjecture of Iwasawa theory. References: the Seminaire Bourbaki article of Serre on the work of Iwasawa; the two volumes of Washington; Ribet's article in Inv. on converse to Herbrand. |
References:
1. A course in Arithmetic by J.-P. Serre
2. Algebraic Number Theory by J. S. Milne
3. P-adic analysis by Neal Koblitz
4. Introduction to Cyclotomic Fields by Lawrence Washington
5. On p-adic L-function, Annals of Mathematics, Kenkich Iwasawa
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 (2.30–3.30) |
T ea (3 .3 5- 3. 5 5) |
Tutorial (4.00-5.00) |
Snacks 5.05- 5.30 |
(name of the speaker) | (name of the speaker) | (name of the speaker + tutors) | (name of the speaker + tutors) | ||||||
Mon | June 26 | CSR | SAB | CSR+AJ | SAB+AJ | ||||
Tues | June 27 | CSR | SAB | CSR+AJ | SAB+AJ | ||||
Wed | June 28 | CSR | SAB | CSR+AJ | SAB+AJ | ||||
Thu | June 29 | CSR | SAB | CSR+AJ | SAB+AJ | ||||
Fri | June 30 | MS | SAB | MS+AJ | SAB+AJ | ||||
Sat | July 01 | MS | MKP | MS+AJ | PKP+RV | ||||
SUNDAY: OFF | |||||||||
Mon | July 03 | MS | MKP | MS+AJ | MKP+MKP | ||||
Tues | July 04 | MS | AKM | MS+AJ | AKM+AJ | ||||
Wed | July 05 | SN | AKM | SN+RV | AKM+AJ | ||||
Thu | July 06 | SN | AKM | SN+RV | AKM+AJ | ||||
Fri | July 07 | SN | AKM | SN+RV | AKM+AJ | ||||
Sat | July 08 | SN | SN | SN+RV | SN+RV | ||||
SUNDAY: OFF | |||||||||
Mon | July 10 | SVD | SN | SVD+RV | SN+RV | ||||
Tues | July 11 | SVD | CSR | SVD+RV | CSR+SAB | ||||
Wed | July 12 | SVD | CSR | SVD+RV | CSR+SAB | ||||
Thu | July 13 | SVD | CSR | SVD+RV | CSR+SAB | ||||
Fri | July 14 | SVD | CSR | SVD+PV | CSR+SAB | ||||
Sat | July 16 | SVD | CSR | SVD+RV | CSR+SAB |
Tutorial Assistant
S. Name No. | Affiliation |
1 Dr. Arindam Jana | Postdoc, TIFR Mumbai |
2 Dr. Ravitheja Vangola | Postdoc, IIT Kanpur |
Full forms for the abbreviations of speakers and tutors:
MS: Mihir Sheth
CSR: C S Rajan
AM: Amiya Mondal
RV: Ravitheja Vangola
AJ: Arindam Jana
SAB: Sazzad Ali Biswas
MKP: Manish Kumar Pandey
PKD: Pallab Kanti Dey
SN: Santosh Nadimpalli
SVD: Shaunak Vilas Deo