The Subspace Theorem and its Applications (2024)

Convener(s)

 
Name: Purusottam Rath Anup Dixit
Mailing Address: Professor
Chennai Mathematical Institue
Kelambakkam- 603103		 Fellow E
Institute of Mathematical Sciences
Email: purusrath at gmail.com anupdixit at imsc.res.in

This program is intended for graduate students interested in diophantine approximation and in particular, the Subspace theorem. This is a powerful result with wide ranging ramifications. The primary goal is to have a gentle,
self-contained introduction to this theorem along with showcasing a few outstanding applications in seemingly diverse realms.

Dates: 

Monday, December 16, 2024 - 09:00 to Saturday, December 28, 2024 - 21:00

Venue: 

Venue Address: 

Purusottam Rath
Chennai Mathematical Institute H1,
SIPCOT IT Park, Siruseri
Kelambakkam 603103 India

Venue State: 

Venue City: 

PIN: 

603103

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

M. Ram Murty,
Queen’s University

V. Kumar Murty,
University of Toronto

6

Applications of Roth’s and subspace theorem

  1. On greatest prime factors of (ab+1)(ac+1).

  2. On a problem of Ruderman.

  3. On GCD of (an- 1) and (bn- 1).

Sinnou David,
Paris VI

4

Roth’s theorem, Ridout’s theorem and subspace theorem

  1. Statements, proof, applications and limitations.

  2. Schmidt’s theorem, Schlickewei’s theorem.

Purusottam Rath,
CMI

5

Applications of subspace theorem

  1. Polynomial exponential equations.

  2. Complexity and computability.

Sanoli Gun,
IMSc

3

Applications of subspace theorem

  1. Diophantine equations with power sums.

Anup Dixit,
IMSc

3

The theory of heights

  1. Introduction to Weil heights and basic properties.

  2. Algebraic numbers close to both 0 and 1.

  3. Lehmer’s Problem and Northcott property.

  4. Siegel’s theorem for integer points on curves.

Siddhi Pathak,
CMI

3

Introduction to Diophantine approximation

  1. Liouville, Dirichlet and Khinchine’s theorem, Duffin- Schaeffer conjecture.

  2. Well and Badly approximable numbers.

  3. Continued fractions and their basic properties.

References:
    1. W. M. Schmidt, Diophantine approximation
    2. W. M. Schmidt, Diophantine approximation and Diophantine equations
    3. S. Lang, Introduction to Diophantine approximation.
    4. E. Bombieri, W. Gubler, Heights in Diophantine geometry.

Names of the tutors with their affiliation :
    1. Rashi Lunia, IMSc.
    2. Dhananjaya Sahu, IMSc.
    3. Sushant Kala, IMSc.
    4. Preeti, CMI.
    5. Suhita Hazra, CMI.

Time Table: 

 

Day

Date

Lecture 1

9:30
to
11:00

Tea 11:00
to
11.30

Lecture 2

11:30
to
13:00

Lunch 13:00
to
14:30

Tutorial 1

14:30
to
15:30

Tea 15:30

to

16:00

Tutorial 2

16:00-17:00

Snacks 17:00

 

 

(speaker)

 

(speaker)

 

 

 

 

 

Mon

16/12/24

SP

 

AD

 

SP+SH+ DS

 

AD+SK+ RL

 

Tues

17/12/24

SP

 

AD

 

SP+SH+ DS

 

AD+SK+ RL

 

Wed

18/12/24

SP

 

AD

 

SP+SH+ DS

 

PR+SK+ RL

 

Thu

19/12/24

SG

 

PR

 

SG + SH

+ DS

 

PR+PT+ RL

 

Fri

20/12/24

SG

 

PR

 

SG + SH

+ DS

 

PR+PT+ RL

 

Sat

21/12/24

SG

 

PR

 

SG + SH

+ DS

 

PR+PT+ RL

 

 

Day

Date

Lecture 1

9:30
to
11:00

Tea 11:00
to
11.30

Lecture 2

11:30
to
13:00

Lunch 13:00
to
14:30

Tutorial 1

14:30
to
15:30

Tea 15:30
to
16:00

Tutorial 2
16:00
to
17:00

Snacks 17:00

 

 

(speaker)

 

(speaker)

 

 

 

 

 

Mon

23/12/24

PR

 

SD

 

PR+PT+ SH

 

SD+SK+ DS

 

Tues

24/12/24

PR

 

SD

 

PR+PT+ SH

 

SD+SK+ DS

 

Wed

25/12/24

RM

 

SD

 

RM+ SH

+ RL

 

SD+SK+ DS

 

Thu

26/12/24

KM

 

SD

 

KM + SH

+ PT

 

SD+SK+ DS

 

Fri

27/12/24

RM

 

KM

 

RM+ SH

+ RL

 

KM+SK+ PT

 

Sat

28/12/24

RM

 

KM

 

RM+ SH

+ RL

 

KM+SK+ PT

 

Speakers:  
RM: M. Ram Murty   
KM: V. Kumar Murty   
PR: Purusottam Rath  
SG: Sanoli Gun   
AD: Anup Dixit   
SP: Siddhi Pathak

Tutors:
RL: Rashi Lunia
DS: Dhananjaya Sahu
PT: Preeti
SH: Suhita Hazra
SK: Sushant Kala

Selected Applicants: 

 The selected candidates should confirm their participation to anupdixit@imsc.res.in by1st October 2024, failing which their selection shall be cancelled.

 

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 58446 Mr. Bal Bahadur Tamang Male Central Department of Mathematics PhD Student University MA 1999 11/02/2022
2 58549 Mr. Vivek Singh Male IIT Dharwad PhD IIT Patna 2022  
3 58604 Ms. Shruti Shreepati Hegde Female Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Ph.D. Karnatak University Dharwad 2013  
4 58643 Mr. Oais Ahmad Bhat Male Harish-Chandra Research Institute Prayagraj PhD University of Kashmir 2020  
5 58649 Ms Aparna Tripathi Female Harish-Chandra Research Institute Ph.D. - Math University of Delhi 2018  
6 58668 Ms. Sumita Gunri Female Indian Institute of Technology Madras PhD Student M.Sc.- Indian Institute of Technology Patna 2023  
7 58681 Ms. Parvathi S Nair Female National Institute of Technology Calicut PhD SVR NSS College, Vazhoor, Kottayam 2019  
8 58683 Mr Mrityunjoy Charan Male The Institute of Mathematical Sciences PDF Indian Institute of Technology Guwahati 2018 28/09/2023
9 58691 Mr. Shubhdeep Das Male NISER Bhubaneswar PhD IIT Indore 2023  
10 58705 Ms. Papiya Sur Female The Institute of Mathematical Sciences PhD Indian Institute of Technology, Kanpur 2023  
11 58721 Dr. Neelam Kandhil Female The University of Hong Kong Post-Doctoral Fellow IIT Madras 2017  
12 58747 Mr. Arighna Pan Male IISER Thiruvananthpuram Integrated PhD IISER TVM Appeared / Awaiting Result  
13 58755 Ms. Raveena Ganash Female National Institute of Science, Education and Research PhD Jawaharlal Nehru University    
14 58759 Mr. Aman Singh Male Indian Statistical Institute MSc Student Indian Statistical Institute    
15 58761 Dr. Rashi Sanjay Lunia Female Chennai Mathematical Institute Postdoctoral Fellow Sardar Patel University 2019 19/06/2024
16 58771 Mr. Gaurav Kumar Male Institute of Mathematical Sciences PhD University of Delhi 2023  
17 58778 Dr. Pasupulati Sunil Kumar Male The Institute of Mathematical Sciences Postdoctral Fellow IISER TVM 2018 01/09/2023
18 58783 Ms Amrutha C Female SRM University AP PhD Central University of Kerala 2020  
19 58813 Mr Jay Ram Thakur Male IISER Bhopal PHD University Of Delhi 2020  
20 58833 Mr. Subham Kundu Male Indian Institute of Science Education and Research Bhopal Integrated PhD Student Indian Institute of Science Education and Research Bhopal 2024  
21 58837 Mr. Sushant Kala Male IMSc, Chennai PhD IIT Ropar 2020  
22 58842 Dr. Gorekh Prasad Sena Male Harish-Chandra Research Institute Post Doctoral Fellow University of Hyderabad 2015 26/09/2023
23 58857 Ms Suhita Hazra Female CMI PhD ISI Bangalore 2021  
24 58858 Ms. Preeti Goyat Female Chennai Mathematical Institute PhD Chaudhary Ranbir Singh University 2020  
25 58861 Mr. Kushal Bhowmick Male Harish-Chandra Research Institute PhD Student Indian Statistical Institute, Bangalore Centre 2017  
26 58873 Mr. Aviral Srivastava Male IIT Gandhinagar Phd University of Hyderabad,M.Sc. 2022  
27 58888 Mr. Venkatasubbareddy Kampamolla Male University of Hyderabad PhD scholar Andhra University, Visakhapatnam 2019  
28 58953 Dr. Karthick Babu C G Male ISI Bangalore Post Doctoral Fellow Madurai Kamaraj University 2014 23/12/2021
29 59011 Mr Karishan Kumar Male IIT, Ropar PhD M.Sc 2020  
30 59014 Mr. Prashant Tiwari Male Harish-Chandra Research Institute Post Doctoral Fellow IISER Bhopal 2018 03/07/2022
31 59023 Ms. Akanksha Gupta Female Indian Institute of Technology Delhi PhD Student IIT ISM Dhanbad 2021  
32 59024 Mr. Divyanshu Kala Male Indian Institute of Technology Delhi PhD H.N.B. Garhwal University Srinagar Garhwal Uttarakhand 2020  
33 59025 Ms. Diksha Rani Female IIT Indore PhD Indian Institute of Technology Indore 2022  
34 59066 Mr Ravi Kalwaniya Male IIT Madras PhD IIT KGP 2022  
35 59069 Mr. Aishik Chattopadhyay Male Ramakrishna Mission Vivekananda Educational and Research Institute(RKMVERI) PhD Pondicherry University 2018  
36 59078 Ms. Meghali Garg Female IIT Indore Ph.D. IIT Gandhinagar 2019 19/12/2020
37 59080 Mr Archit Agarwal Male IIT Indore PhD IIT Gandhinagar 2018  
38 59112 Mr. Bittu . Male IIIT Delhi PhD IIT Roorkee 2019  
39 59143 Ms. Shivani Goel Female Chennai Mathematical Institute Postdoctoral Fellow Chaudhary Charan Singh University, Meerut 2018 16/08/2024
40 59151 Dr. Priyanka Majumder Female ISI Bangalore Centre Research Associate IIT Hyderabad 2016 17/12/2021
41 59167 Dr. Amrinder Kaur Female Harish-Chandra Research Institute Post Doctoral Fellow Thapar University 2017 03/07/2024
42 59206 Mr Abhishek Thyagarajan Bharadwaj Male Na Na Bangalore university 2013 22/06/2020
43 59217 Mr. Dhananjaya Sahu Male Institute of Mathematical Sciences Senior research fellow M.Sc. 2018  
44 59233 Mr. Arunabha Mukhopadhyay Male IMSc PhD Indian Institute of Technology Kanpur 2019  
45 58838 Dr. Shubham Gupta Male Indraprastha Institute of Information Technology Delhi Visiting Researcher Indian Institute of Technology Kanpur 2018  
Waitlist
1 58904 Mr Prashantkumar Jamanbhai Makadiya Male Institute of Infrastructure, Technology, Research And Management (IITRAM) PhD Saurashtra University Rajkot 2019  
2 59221 Mr Vikas Vikas Male Birla Institute of Technology and Science PhD Visvesvaraya National Institute Of Technology, Nagpur 2022  
3 59223 Mr. Mohit Mittal Male Birla Institute of Technology and Science Pilani (Pilani Campus) PhD IIT Roorkee 2017  

 

 

 

How to Reach: 

TBA

School Short Name: 

tstia

Last Date Application: 

Sunday, May 14, 2023

School Type: 

AIS

Separate faculty form: 

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