Hida Theory and Iwasawa Main Conjecture over Q (2023)

Convener(s)

 
Name: Aditya Karnataki Shaunak Deo
Mailing Address: Assistant Professor,
Chennai Mathematical Institute
H1, SIPCOT IT Park, Siruseri
Kelambakkam 603103		 Assistant Professor,
Department of Mathematics, Indian Institute of Science
Bangalore 560012
Email: adityack at cmi.ac.in shaunakdeo at iisc.ac.in

This program is intended for Ph.D students and postdocs interested in working in algebraic number theory. Some M.Sc students may also be able to attend depending on their background. The background required for this workshop includes basic algebraic number theory, commutative algebra, field theory and Galois theory, representation theory. There will be some preparatory lectures covering Herbrand-Ribet theorem, basic Iwasawa theory, p-adic L-functions. Along with that, the program will have lectures on the following topics: ordinary Λ-adic modular forms, Λ-adic Galois representations, proof of Iwasawa main conjecture.

Dates: 

Monday, December 4, 2023 - 19:00 to Saturday, December 9, 2023 - 19:00

Venue: 

Venue Address: 

 

Chennai Mathematical Institute

 

H1, SIPCOT IT Park, Siruseri

 

Kelambakkam 603103

 

India

 

 

Venue State: 

Venue City: 

PIN: 

603103

Chrono Order: 

430

Syllabus: 

 Syllabus to be covered in terms of modules of 6 lectures each :

Name of the Speakers
with their affiliation.

No. of
Lectures

Detailed
Syllabus

Dipramit Majumdar,
IIT Madras

4 (6 Hours)

Algebraic Number Theory and Iwasawa Theory

Ribet’s converse to Herbrand’s theorem, Basic Iwasawa Theory, and basic properties of p-adic L-functions.

Bharathwaj Palvannan,
IISc Bangalore

4 (6 Hours)

Iwasawa Theory and Hida Theory

Ordinary Λ-adic modular forms, Hida theory and Λ-adic Galois representations.

Mahesh Kakde,
IISc Bangalore

4 (6 Hours)

Hida theory and Iwasawa Main Conjecture

Λ-adic modular forms and the Iwasawa Main Conjecture : proof over Q, proof over totally real fields F if time permits.

 

References:

  1. C. Skinner, Galois Representations, Iwasawa Theory, and Special Values of L-functions, CMI notes.
  2. S. Lang, Cyclotomic Fields I and II.
  3. L. Washington, Introduction to cylotomic fields.
  4. .K. Ribet. A modular construction of unramified p-extensions of Q(μp). Invent. Math.,34(3):151–162, 1976.
  5. H. Hida, Elementary Theory of L-functions and Eisenstein Series.
  6. H. Hida. Galois representations into GL2(Zp[X]]) attached to ordinary cusp forms. Invent. Math., 85:545–613, 1986.
  7. .A. Wiles. On ordinary λ-adic representations associated to modular forms. Inv. Math.,94(3):529–573, 1988
  8. B. Mazur and A. Wiles, Class fields of abelian extensions of Q. Invent. Math. 76 (2) :179–330, 1984.
  9. 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 :

  1. Pratiksha Shingavekar, IIT Madras.
  2. Anand Chitrao, TIFR Mumbai.
  3. Ravitheja Vangala, IISc Bangalore.

 

 

Time Table: 

Tentative time-table, mentioning names of the speakers and tutors with their affiliation:  

Day

Date

Lecture 1

9:30
–
11:00

Tea

11:00
–
11.30

Lecture 2

11:30
–
13:00

Lunch

13:00
-
14:30

Tutorial 1

14:30
-
15:30

Tutorial 2

16:00
-
17:00

Snacks

17:00
 

 

(name of the speaker)

 

(name of the
speaker)

 

 

 

 
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

Selected Applicants: 

 

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. Degree Date
1 51234 Ms. Muskan Bansal Female Harish-Chandra Research Institute PhD NIT, Warangal    
2 51242 Mr. Rohit Pokhrel Male HRI Prayagraj PhD Sikkim University 2019  
3 51320 Mr. Ajay Prajapati Male Indian Institute of Science, Bangalore Ph.D. Indian Institute of Technology, Kanpur 2022  
4 51352 Dr. Lalit Vaishya Male The Institute of Mathematical Sciences Chennai Post Doctoral Fellow Banaras Hindu University Varanasi India 2014 13/8/2021
5 51402 Mr. Subham De Male IIT Delhi Graduate Student IIT Delhi Appeared  
6 51519 Prof. Guhan Venkat Male Ashoka University Assistant Professor IISER Pune 2012 26/6/2015
7 51742 Mr. Ashutosh Suresh Jangle Male Indian Institute of Science, Bangalore PhD IISER Pune 2021  
8 51905 Mr. Pranjal Vishwakarma Male IISER Pune Integrated PhD IISER PUNE 2019  
9 51907 Mr Rajat Kumar Mishra Male IIT Gandhinagar PhD IISER Kolkata 2019  
10 51947 Mr Mrityunjoy Charan Male The Institute of Mathematical Sciences PDF Indian Institute of Technology Guwahati 2018 25/9/2023
11 51996 Mr. Srijan Das Male IISER Pune PhD Student Indian Statistical Institute, M.Math 2020  
12 52088 Mr Selvam V Male Harish Chandra Research Institute PhD Student IIT Madras 2023  
13 52192 Mr. Dhrubajyoti Das Male IISER PUNE PHD JADAVPUR UNIVERSITY 2021  
14 52262 Mr. Arup Mondal Male INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH Integrated PhD INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH Appeared  
15 52294 Dr. Priyanka Majumder Female IISER Pune Post-doc IIT Hyderabad 2016 17/12/2021
16 52308 Mr. Mabud Ali Sarkar Male The University of Burdwan PhD student The University of North Bengal 2015  
17 52570 Mx Sanskar Agrawal Male IISER Tirupati BSMS student IISER Tirupati Appeared  
18 52737 Ms. Priyanka Dey Female IISER PUNE MSc Student IISER PUNE    
19 52837 Ms Arathy Venugopal Female IISER TIRUPATI PhD Indian Institute of Science Education and Research, Tirupati 2021  
20 52932 Mr Nandagopal Ramachandran Male University of California San Diego PhD student Indian Statistical Institute Bengaluru 2017  
21 52964 Mr. Pratik Ashok Jadhav Male Indian Institute of Science PhD Second year Chennai Mathematical Institute 2022  
22 52997 Ms. Dwipanjana Shit Female Indian Institute of Technology Hyderabad PhD Indian Institute of Technology Hyderabad 2021  
23 53083 Mr. Rishabh Agnihotri Male Indian Institute of Science, Bangalore, India Post-doc Fellow IIT Kanpur, Kanpur 2017 8/3/2022
24 53095 Mr Mahesh Garg Male Indian Institute of Science Phd Indian Institute of Technology Delhi 2022  
25 53143 Mr. Manodeep Raha Male Tata Institute of Fundamental Research, Mumbai PhD Tata Institute of Fundamental Research 2021  
26 53171 Mr. Clifford J. Rodrigues Male IISER Pune PhD IIT Ropar 2021  
27 53294 Mr Lalit Thuwal Male IISc Bangalore PhD Kumaun University 2019  
28 53388 Mr. Prabhat Kumar Mishra Male Indian Institute of Technology Jammu PhD Indian Institute of Technology Guwahati 2021  
29   Mr. Rieshikesh Rajendra Ghatage Male   PhD      
30   Dr. C. S. Rajan Male   Professor      
31   Dr. Neha Malik Female   Postdoc      

 

 

 

 

 

 

How to Reach: 

TBA

School Short Name: 

htimcoq

Last Date Application: 

Monday, August 15, 2022

School Type: 

NCMW

Separate faculty form: 

0