AIS Diophantine Equations (2014)

Venue: Himachal Pradesh University, Shimla
Dates: 16th June to 4th July, 2014

 

Convener(s) Speakers, Syllabus and Time table Applicants/Participants

 

School Convener(s)
Name Prof. Shanta Laishram Prof. T N. Shorey Prof. P. L. Sharma
Mailing Address Stat Math Unit, Indian Statistical Institute, 7 SJS Sansanwal Marg, New Delhi Department of Mathematics, IIT Mumbai, Powai Mumbai Department of Mathematics, HP University, Shimla, Himachal Pradesh

 

Speakers and Syllabus 

A brief Description of the school
Diophantine Equations is one of the important areas of Number Theory. There are two aspects of Diophantine equations namely, checking if there are only finitely many solutions and in that case, explicitly solving it. A lot of techniques and theories have been developed to solve a number of Diophantine equations. In this school, we expect to cover some of the theories and teachniques starting from classical to modern techniques including combinatorial and transcendental techniques and elliptic and modular approaches.  

Speaker Lectures Detailed Syllabus
Prof. S. Akhtari, Oregon University, USA 9 Diophantine Analysis:Linear Forms in Logarithms and Applications; Thue Equations and Inequalities, Binary Forms; Integral points on a family of elliptic curves;
Prof.  S. Laishram, Indian Statistical Institute, New Delhi  9 Equations involving products of terms of an arithmetic progression:Sylvester's Theorem and improvements and generalizations;Application to Diophantine Equations; Erdos Conjecture: Results and Proofs; Connection of Dophantine Equations to Irreducibility of polynomials
Prof. A. Mukhopadhyaya, Institute of Mathematical Sciences, Chennai, India 6 Analytic Methods for Diophantine Equations: Prime Number Theory, Circle Methods, Counting points for Diophantine Equations; Linear Forms in Logarithms
Prof. C. S. Rajan, TIFR Mumbai, India 6 Modular Methods: Galois Representations
Prof. N. Saradha, TIFR Mumbai 7.5 Diophantine approximation methods:Liouville's theorem- applications; Thue's theorem; Siegel's improvement of Thue's result; Baker's result on cube root of 2; Baker's result on simultaneous approximation; Rickert's result on simultaneous approximation and application to
simultaneous Pell's equations;
Prof. A. Chandrakant Sharma, IISER Mohali 3 Basics of Modular Forms
Prof. R. Thangadurai, HRI Allahabad,  India 9 Elliptic Curves:  Elliptic Curves; Rank and Integral Points on Elliptic Curves;

References:

  1. A. Baker: Transcendental Number Theory, Cambridge University Press.
  2. H. Davenport: Analytic Methods of Diophantine Equations and Inequalities, Cambridge University Press
  3. L. J. Mordell: Diophantine Equations, Academic Press.
  4. T. N. Shorey and Tijdeman: Exponential Diophantine Equations, Cambridge University Press.
  5.  J. Silverman: Arithmetic of Elliptic Curves, Springer Verlag
  6. Henri Cohen: Number Theory Vo I: Tools and Diophantine Equations

Time- Table

    Lecture 1 Tea Lecturer 2 Lunch Tutorial or Guest Lecture Tea and Snacks
Day Date 9:30-11:00   11:30-1:00   2:00-4:00  
Mon 16 June 2014 SL   RT   To be decided with speakers  
Tue 17 June 2014 RT   SL      
Wed 18 June 2014 SL   RT      
Thu 19June 2014 RT   SL      
Fri 20 June 2014 SL   RT      
Sat 21 June 2014 RT   SL      
Mon 23June 2014 ACS   SA      
Tue 24 June 2014 SA   ACS      
Wed 25 June 2014 AM   SA      
Thu 26 June 2014 SA   AM      
Fri 27 June 2014 AM   SA      
Sat 28 June2014 SA   AM      
Mon 30 June 2014 NS   CSR      
Tue 1 July 2014 CSR   NS      
Wed 2 July 2014 NS   CSR      
Thu 3 July 2014 CSR   NS      
Fri 4 July 2014 NS   CSR      

Tutorial Assistants:

S. No. Name Affiliation
1   Pranabesh Das ISI Delhi
2 Saranya Nair IIT Mumbai
3 Ng Sudhir Singh Manipur University
4

R. Krishnan

Shiv Nadar University

 

 

Selected Applicants

 

SR.N SID Full Name Gender Affiliation City, State Position

University /Institute M.Sc. /M.A.

 Year of Passing M.Sc. /M.A Ph.D. Degree Date
1 5514 Mr. Guddu Kumar Male IISER-Kolkata Kalyani, West Bengal MSc Student IISER-KOLKATA Appeared /Awaiting Result  
2 5549 Mr. Piyush Goyal Male SCD Govt. College
For Boys		 Ludhiana, Punjab Lecturer Panjab University, Chandigarh 2011  
3 5670 Ms. Srashti Dwivedi Female IIT Delhi Delhi Ph.D Delhi University 2012  
4 5671 Ms. Pooja Punyani Female IIT Delhi New Delhi PhD University Of Delhi/ St.Stephens College/ M.Sc. Mathamatics 2012  
5 5729 Dr. Jitendra Singh Male Central University of Bihar. Patna, Bihar Asst. Prof. C.S.J.M. University, Kanpur/ Nehru Degree College/ M.Sc. 2007 9 Nov 2012
6 5765 Mr Manjil Pratim Saikia Male Tezpur University Tezpur, Assam Integrated MSc Student Tezpur University Appeared /Awaiting Result  
7 5835 Mr. Vishal Gupta Male Zakir Husan Delhi College New Delhi, Delhi Asst. Prof. IIT GUWAHATI 2010  
8 5842 Mr. Subhash Chand Male MJP Rohilkhand University,Bareilly (u.p) Bareilly, U.P MSC Student MA Appeared /Awaiting Result  
9 5861 Mr. Bibekananda Maji Male Harish-Chandra research institute Allahabad, Uttar Pradesh Ph.D. Student IIT BOMBAY 2010  
10 5891 Ms. Neelam Saikia Female IIT Delhi New Delhi PhD Tezpur University 2012  
11 5900 Mr Lalit Vaishya Male Banaras Hindu University Varanasi, U.P M.SC. STUDENT Banaras Hindu University Appeared /Awaiting Result  
12 5912 Mr. Naeem Ahmad Pundeer Male Himachal Pradesh University Shimla, Himachal Pradesh MPHIL CCSU, Meerut 2008  
13 5927 Mr Kamalakshya Mahatab Male The Institute of Mathematical Sciences Chennai, Tamil Nadu PhD, SRF The Institute of Mathematical Sciences, Chennai. 2012  
14 5952 Mr. Pallab Kanti Deyy Male Harish-Chandra research institute Allahabad, U.P PhD University Of Calcutta 2010  
15 5953 Mr Balesh Kumar Male Harish-Chandra research institute Allahabad, U.P PhD Banaras Hindu University 2011  
16 5961 Ms Divyum Sharma Female TIFR, Mumbai Mumbai, Maharashtra Research Scholar IIT, Delhi 2011  
17 5969 Mr. Satish Kumar Male Govt. Degree College Solan Himachal Pradesh India Solan, Himachal Pradesh Asst. Prof. M.Sc. 2005  
18 5970 Dr. Raj Kumar Kanwar Male Deptt. of Mathematics Center of Excellence Govt. College Sanjauli Shimla-6 (H.P) Shimla, Himachal Pradesh Assoc. Prof. Panjab University Chandigarh 1980 11 Sep 2013
19 5985 Mrs. Mansi Rehan Female Himachal Pradesh University Shimla, Himachal Pradesh Ph. D. Research scholar Doaba College, Jalandhar, Punjab 2008  
20 5989 Mr. Ravinder Kumar Male Himachal Pradesh University Shimla, Himachal Pradesh Ph. D. Research scholar Himachal Pradesh University 2009  
21 5990 Mr. Bhagat Ram Male Himachal Pradesh University Shimla, Himachal Pradesh M.Phil. Student Himachal Pradesh University 2013  
22 5997 Mr . Arun A Male Cochin University of Science and Technology Kochi, Kerala MSc Student Cochin University of Science and Technology Appeared /Awaiting Result  
23 6009 Miss Neetu Dhiman Female Himachal Pradesh University Shimla, Himachal Pradesh Ph. D. Research scholar Regional Centre, Dharamshala, H. P. 2010  
24 6017 Dr. Gautam Kalita Male Darrang College. Tezpur, Assam Asst. Prof. Tezpur University, Assam. 2010 28 Feb 2014
25 6019 Dr. Ajaib Singh Banyal Male Sidharth Govt. College Nadaun, Dist. Hamirpur, (HP) Nadaun (Hamirpur) H.P., Himachal Pradesh Associate Professor H.P. University Shimla 1988 24 Nov 1994
26 6023 Ms Saranya G Nair Female IIT BOMBAY Mumbai, Maharashtra PhD Cochin University of Science and Technology 2010  
27 6029 Mr Sudhansu Sekhar Rout Male National Institute of Technology Rourkela Rourkela, Orissa Research Scholar Utkal University, Bhubaneswar. 2007  
28 6037 Mr. Neeraj Sangwan Male IISER Mohali Mohali, Punjab Integrated MS student IISER Mohali Appeared /Awaiting Result  
29 6039 Miss Kiran Devi Female Himachal Pradesh University Shimla, Himachal Pradesh M.Phil. Student Himachal Pradesh University 2011  
30 6042 Mr Ravi Kumar Davala Male National Institute of Technology - Rourkela Rourkela, Orissa Ph.D - Student IIT, kanpur 2007  
31 6050 Mr Manish Kumar Pandey Male Himachal Pradesh University Allahabad, U.P PhD ISI 2011  
32 6052 Mrs. Neha Devi Female Himachal Pradesh University Shimla, H.P M.Phil. Student S.B.S.D. College, Bhatoli, Una, H. P. 2009  
33 6053 Miss Shabnam Sharma Female Himachal Pradesh University Shimla, H.P Ph. D. Research scholar Himachal Pradesh University 2010  
34 6054 Mr Nitin Serwa Male IISER Mohali Mohali, Punjab Student IISER,Mohali Appeared /Awaiting Result  
35 6058 Mrs. Priyanka Kaushal Female Rayat Bahra College of Engineering & Biotechnology for Women Mohali, Punjab Assoc. Prof. Himachal Pradesh University, Shimla 2001  
36 6062 Dr. Vizender Singh Sihag Male GJUS&T Hisar Hisar, Haryana Asst. Prof. GJUS&T Hisar 2008 3 Sep 2013
37 6074 Mr. Sada Ram Male Himachal Pradesh University Shimla, H.P Research Scholar Ph.D H P U SHIMLA 2008  
38 6075 Mr. Sanjay Kumar Kalta Male ABVGIET, Pragatinagar, (HP). Shimla, H.P Asst. Prof. Himachal Pradesh University 2004  
39 6080 Mrs. Shalini Garga Female Bahra University Solan, Himachal Pradesh Asst. Prof. University of Roorkee 1991  
40 6084 Mr. Pramod Eyyunni Male Harish-Chandra research institute Allahabad, U.P PhD student IIT Madras 2012  

 

How to reach

The Himachal Pradesh University(HPU) Shimla is situated in Summer Hills, Shimla. The airport at Jubar-Hatti is 23 km away. The main Bus Stand is at a distance of 4 km and Railway Station is 4 km. Local buses and taxis are available from railway station and bus stand to Summer Hill.

1. From Delhi, there is direct service of buses (Volvo/AC/Deluxe) from Delhi to Shimla.  Here are some bus sites:

http://www.hptdc.nic.in/bus.htm

www.redbus.in

2. Train facility is also available from Delhi to Shimla via Kalka.

www.indianrail.gov.in

 

Some possible train route from Delhi to Shimla is

  • 14095 Himalayan Queen Delhi 05:45- Kalka 11:10
  • 12011 Kalka Shatabdi  Delhi 07:45 - Kalka 11:45
  • 52455 Himalayan Queen Delhi Kalka 12:10 to Shimla 17:20

  
3. One can also travel by train to Kalka and take a number of buses to Shimla. Also the distance  is just 70 km and there are number of taxi available from Kalka to Shimla.