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.

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