Advanced Topics in Finite Fields (2023)

Convener(s)

 
Name: Prof. Amritanshu Prasad Dr. Sartaj Ul Hasan
Mailing Address: The Institute of Mathematical Sciences CIT Campus, Taramani, Chennai 600113 Department of Mathematics
Indian Institute of Technology Jammu Jammu 181221
Email: amri at imsc.res.in sartaj.hasan at iitjammu.ac.in

The theory of finite fields lies at the crossroads of algebra, combinatorics, and number theory. Finite fields play an important role in many application areas, such as coding theory and cryptography. The topics that will be covered in this workshop include the following: the structure of finite fields, matrices and linear operators over finite fields, polynomials over finite fields, sequences over finite fields, exponential sums over finite fields, and equations and varieties over finite fields. This workshop is intended for graduate students with a potential interest in finite fields and their applications.

Dates: 

Monday, July 10, 2023 - 09:00 to Saturday, July 29, 2023 - 18:00

Venue: 

Venue Address: 

 

 

The Institute of Mathematical Sciences, CIT campus, Taramani, Chennai 600113.

 

 

Venue State: 

Venue City: 

PIN: 

600113

Chrono Order: 

435

Syllabus: 

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Sartaj Ul Hasan
IIT Jammu

6x1.5hrs

The Structure of Finite Fields: Field extensions, Characterizations of finite fields, Roots of irreducible polynomials, Traces, Norms, Bases, Cyclotomic polynomials, Representation of elements of finite fields.

Amritanshu Prasad
IMSc, Chennai

 

6x1.5hrs

Counting subspaces and matrices by rank, similarity classes, JoRKan canonical form over finite field, similarity class type, centralizer caRKinality, counting invariant subspaces.

Mrinmoy Datta
IIT Hyderabad

6x1.5hrs

Order of polynomials, primitive polynomials, irreducible polynomials and their construction, linearized polynomials, permutation polynomials, Hermite and AGW criteria for permutation polynomials, special types of permutation polynomials.

Ayineedi Venkateswarlu
ISI Chennai

6x1.5hrs

Linear recurring sequences, Linear Feedback Shift Registers (LFSRs), Periodicity, Characteristic polynomial, Minimal polynomial, Generating functions, Maximal period sequences, Trace Representation, Golomb's randomness postulates, Linear complexity and related measures, Berlekamp-Massey algorithm, LFSR based cipher designs, Coding-theoretic connections, Modes of implementation of LFSRs, WoRK-oriented LFSRs and multi-sequences

Sudhir R. Ghorpade
IIT Bombay

6x1.5hrs

Equations and Varieties over Finite Fields: Elementary bounds, Theorems of Konig-Rados, Warning and Chevalley, Elementary estimates on the number of zeros of multivariate polynomial over finite fields, The case of system of multivariate polynomials of bounded degree, Variants of Nullstellensatz for algebraic varieties over finite fields, Outline of Weil bounds for the number of points of algebraic varieties over finite fields, and related results.

K Srinivas
IMSc, Chennai

6x1.5hrs

Characters, Gauss sums, Jacobi sums, and exponential sums over finite fields.

 References
    1. Lidl, R. and Niederreiter, H., Finite Fields, Cambridge University Press, 1997.
    2. Mullen, G. L. and Panario, D., Handbook of Finite Fields, CRC Press, 2013.

(Lecture notes from the speakers, if available)

 

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)

Tea

(3:35-3:55)

Tutorial

(4:00-5:00)

Snacks

(5:05-5:30)

 

 

speaker

 

speaker

 

speaker+tutors

 

speaker + tutors

 

Mon

10

SH

 

AP

 

SH+KG+RK

 

AP+SR+TB

 

Tues

11

SH

 

AP

 

SH+KG+RK

 

AP+SR+TB

 

Wed

12

SH

 

AP

 

SH+KG+RK

 

AP+SR+TB

 

Thu

13

SH

 

AP

 

SH+KG+RK

 

AP+SR+TB

 

Fri

14

SH

 

AP

 

SH+KG+RK

 

AP+SR+TB

 

Sat

15

SH

 

AP

 

SH+KG+RK

 

AP+SR+TB

 

SUNDAY OFF

Mon

17

MD

 

AV

 

MD+SM+HK

 

AV+DA+AA

 

Tues

18

MD

 

AV

 

MD+SM+HK

 

AV+DA+AA

 

Wed

19

MD

 

AV

 

MD+SM+HK

 

AV+DA+AA

 

Thu

20

MD

 

AV

 

MD+SM+HK

 

AV+DA+AA

 

Fri

21

MD

 

AV

 

MD+SM+HK

 

AV+DA+AA

 

Sat

22

MD

 

AV

 

MD+SM+HK

 

AV+DA+AA

 

SUNDAY OFF

Mon

24

SG

 

KS

 

SG+RL+SD

 

KS+MS+SV

 

Tues

25

SG

 

KS

 

SG+RL+SD

 

KS+MS+SV

 

Wed

26

SG

 

KS

 

SG+RL+SD

 

KS+MS+SV

 

Thu

27

SG

 

KS

 

SG+RL+SD

 

KS+MS+SV

 

Fri

28

SG

 

KS

 

SG+RL+SD

 

KS+MS+SV

 

Sat

29

SG

 

KS

 

SG+RL+SD

 

KS+MS+SV

 

 Tutorial Assistants:

S. No.

Name

Affiliation

1

Divya Aggarwal

IIIT Delhi

2

Akansha Arora

IIIT Delhi

3

Suhas Rao

IMSc Chennai

4

Subrata Manna

IIT Hyderabad

5

M. Subramani

IIITDM Kancheepuram

6

Rati Ludhani

IIT Bombay

7

Sakshi Dang

IIT Bombay

8

Kirpa Garg

IIT Jammu

9

Hridesh Kumar

IIT Jammu

10

Ramandeep Kaur

IIT Jammu

11

S Velmurugan

IMSc Chennai

12

Tirtharaj Basu

IMSc Chennai

 
Full forms for the abbreviations of speakers and tutors:

AP: Amritanshu Prasad SR: Suhas Rao TB: Tirtharaj Basu
SH: Sartaj Ul Hasan KG: Kirpa Garg RK: Ramandeep Kaur
MD: Mrinmoy Datta SM: Subrata Manna HK: Hridesh Kumar
AV: Ayineedi Venkateswarlu DA: Divya Aggarwal AA: Akansha Arora
SG: Sudhir R. Ghorpade RL: Rati Ludhani SD: Sakshi Dang
KS: K. Srinvas MS: M. Subramani SV: S Velmurugan

 

 

Selected Applicants: 

List of selected applicants

Sr. SID Full Name Gender Affiliation Position in College / Univ. Univ. / Institute M.Sc./ M.A. Year of
Passing
M.Sc. / M.A		 Ph.D.
Deg
Date
1 47044 Dr. Anuj Jakhar Male IIT Madras Assistant Professor IISER Mohali 2014 21 May 2018
2 46982 Mr Amritanshu Rai Male Bits Pilani Hyderabad Campus, Hyderabad PhD Dr. R L Avadh University Ayodhya Faizabad UP India 2017  
3 48116 Mr Sridhar Rajagopal Male VIT Chennai Research Scholar Madras University D.G Vaishnav College 2010  
4 48553 Mr. Tejbir Lohan Male IISER Mohali PhD Student IIT Kanpur 2018  
5 48874 Ms. Tiasa Dutta Female IIT Hyderabad PhD student Ramakrishna Mission Vivekananda Educational and Research Institute 2021  
6 47266 Ms. Astha Agrawal Female IIT Delhi PhD Student Banasthali Vidyapith 2018  
7 46864 Mr. Soham Pal Male CMI, Chennai BSc Student      
8 46577 Mr. Anuj Kumar Bhagat Male IIT Delhi. PhD University of North Bengal 2020  
9  49534 Mr.N Abhilash  Male  SRM Institute of Science and Technology  PhD  Pondicherry University 2017  
10 47757 Ms. Prachi Saini Female IISER Pune PhD IIT Hyderabad 2021  
11 48941 Mr. Biplab Chatterjee Male NIT Jamshedpur Ph.D. Visva-Bharati 2020  
12 49737 Ms Sampa Dey Female ISI Kolkata Postdoc IIT Madras 2014 19 Mar 2021
13 46600 Ms. Akanksha Tiwari Female IIT Delhi Ph.D. University Of Delhi 2021  
14 49892 Ms. Krishna Mallick Female NIISER Bhubaneswar PhD student Central University of Jharkhand, Ranchi 2016  
15 46469 Mr. Mrinal Kanti Bose Male IIT (ISM) Dhanbad PhD Student Burdwan University Golapbug Campus 2018  
16 48180 Ms. Anitha Valliappan Female IISER TVM I-PhD student IISER TVM App / Awaiting Result  
17 46665 Mr. Ankit - Male IIT, Delhi PhD Student Indian Institute of Technology, Delhi 2022  
18 49727 Mr. Ranit Dutta Male IIT, Jodhpur PhD M.Sc. (Jadavpur University) 2021  
19 50155 Ms. Anwita Bhowmik Female IIT Guwahati PhD Jadavpur University 2017  
20 46594 Mr. Rohit Yadav Male IIT Jammu Junior Research Fellow University of Allahabad 2021  
21 50089 Mr. Saheb Dnyaneshwar Navghare Male School of Mathematical Sciences PhD Student School Of Mathematical Sciences, SRTM University 2020  
22 49142 Ms Bidushi Sharma Female Tezpur University Ph.D Scholar Indraprastha college for women ,University of Delhi 2021  
23 48910 Mr. Saikat Panja Male HRI Post-Doc Indian Institute of Science Education and Research Kolkata 2017 13 Oct 2022
24 50322 Dr. Abhishek Kesarwani Male IIT Kanpur Cryptanalyst University of Allahabad 2014 24 Sep 2021
25 47452 Ms Ayantika Laha Female IIT ROPAR PhD UNIVERSITY OF CALCUTTA 2016  
26 46668 Mr. Nithish Kumar R Male Manipal Institute of Technology (MAHE) - Manipal PhD Mangalore University 2018  
27 46632 Ms Shashirekha G Female Manipal Institute of Technology, Manipal Academy of Higher Education Manipal, Karnataka Ph.D University of Mysore / M.Sc 2019  
28 48360 Mr. Amit Phogat Male IIT Madras Msc Student Indian Institute of Technology Madras App / Awaiting Result  
29 46620 Mr. Sagar Vinayak Male Himachal Pradesh University PhD Research Scholar Central University of Punjab 2020  
30 46616 Mr. Manpreet Singh Male Himachal Pradesh University PhD Punjabi University/ Punjabi University/ M.Sc. 2017  
31 46496 Mr. Sathish Kumar V Male The Institute of Mathematical Sciences PhD Student Ramanujan Institute for Advanced Study in Mathematics 2018  
32 46701 Mr Ravi Kalwaniya Male IIT Madras PhD Indian Institute of Technology kharagpur 2022  
33 46996 Mr Gyanendra Kumar Verma Male IIT Delhi PhD M.Sc. 2018  
34 47770 Mr Arpan Chandra Mazumder Male Tezpur University PhD UNIVERSITY OF HYDERABAD 2021  
35 47906 Mr. Abul Kalam Male IIT Madras PhD VISVA - BHARATI 2022  
36 47939 Ms Anitha G Female VIT - Chennai PhD PRESIDENCY COLLEGE 2019  
37 47987 Mr. Kevinsam B Male VIT - Chennai PhD Madras Christian College 2013  
38 48049 Mr. Anik Bhowmick Male IIT Madras Graduated student Indian Institute of Technology, Madras 2021  
39 48282 Mr. Rahul Ata Male IISER TVM IPHD STUDENT IISER TVM App / Awaiting Result  
40 49143 Ms. Shikhamoni Nath Female Tezpur University PhD Tezpur University 2022  
41 49499 Mr. Akshay Dhan Male ISI, Chennai centre PhD Indian Institute of Science Education and Research, Tirupati 2021  
42 50325 Mr. Varun Kaushal Shah Male IISER, Pune BS-MS Student IISER Pune    
43 49535 Ms. Sivaranjani N U Female SRM Institute of Science and Technology PhD Ramanujan Institute of Advanced Study in Mathematics, University of Madras 2020  

 

 

How to Reach: 

TBA

School Short Name: 

atff

Last Date Application: 

Friday, March 31, 2023

School Type: 

AIS

Separate faculty form: 

0