NCMW  Hida Theory and Iwasawa Main Conjecture over Q (2023)
Speakers and Syllabus
Syllabus to be covered in terms of modules of 6 lectures each :
Name of the Speakers 
No. of 
Detailed 
Dipramit Majumdar, 
4 (6 Hours) 
Algebraic Number Theory and Iwasawa Theory Ribet’s converse to Herbrand’s theorem, Basic Iwasawa Theory, and basic properties of padic Lfunctions. 
Bharathwaj Palvannan, 
4 (6 Hours) 
Iwasawa Theory and Hida Theory Ordinary Λadic modular forms, Hida theory and Λadic Galois representations. 
Mahesh Kakde, 
4 (6 Hours) 
Hida theory and Iwasawa Main Conjecture Λadic modular forms and the Iwasawa Main Conjecture : proof over Q, proof over totally real fields F if time permits. 
References:
 C. Skinner, Galois Representations, Iwasawa Theory, and Special Values of Lfunctions, CMI notes.
 S. Lang, Cyclotomic Fields I and II.
 L. Washington, Introduction to cylotomic fields.
 .K. Ribet. A modular construction of unramified pextensions of Q(μp). Invent. Math.,34(3):151–162, 1976.
 H. Hida, Elementary Theory of Lfunctions and Eisenstein Series.
 H. Hida. Galois representations into GL2(Zp[X]]) attached to ordinary cusp forms. Invent. Math., 85:545–613, 1986.
 .A. Wiles. On ordinary λadic representations associated to modular forms. Inv. Math.,94(3):529–573, 1988
 B. Mazur and A. Wiles, Class fields of abelian extensions of Q. Invent. Math. 76 (2) :179–330, 1984.
 A. Wiles, The Iwasawa conjecture for totally real fields. Ann. of Math. (2) 131 (3):493–540, 1990.
Names of the tutors with their affiliation :
 Pratiksha Shingavekar, IIT Madras.
 Anand Chitrao, TIFR Mumbai.
 Ravitheja Vangala, IISc Bangalore.
Time Table
Tentative timetable, mentioning names of the speakers and tutors with their affiliation:
Day 
Date 
Lecture 1 9:30 
Tea 11:00 
Lecture 2 11:30 
Lunch 13:00 
Tutorial 1 14:30 
Tutorial 2 16:00 
Snacks 17:00 

(name of the speaker) 

(name of the 





Mon 
04/12/23 
DM 

BP 

DM+PS 
BP+AC 

Tues 
05/12/23 
DM 

BP 

DM+ PS 
BP+AC 

Wed 
06/12/23 
DM 

BP 

DM+PS 
BP+AC 

Thu 
07/12/23 
DM 

MK 

DM+PS 
MK +RV 

Fri 
08/12/23 
BP 

MK 

BP+AC 
MK +RV 

Sat 
09/12/23 
MK 

MK 

MK+RV 
MK+RV 

Speakers: Tutors:
DM: Dipramit Majumdar PS: Pratiksha Shingavekar
BP: Bharathwaj Palvannan AC: Anand Chitrao
MK: Mahesh Kakde RV: Ravitheja Vangala