Short Intensive course

Course Title:

Fractal geometry – with a view towards number theory and dynamics

Resource Person: Dr. Simon Kristensen (Aarhus University, Denmark)

Starting Date: 05 February, 2020

Schedule:The course comprises of eight lectures of 90 minutes each on Wednesday (14:00 – 15:30) and Friday (14:30 – 16:00).

poster , For further information contact: info@sms.edu.pk


Course Title:

An Introduction to Dirichlet L-functions

Resource Person: Dr. Karl Dilcher (Dalhousie University, Canada)

Starting Date: 10 February, 2020

Schedule:The course comprises four lectures of 90 minutes each on Monday (14:00 – 15:30) and Friday (10:00 – 11:30).

poster, For further information contact: info@sms.edu.pk & karl.dilcher@dal.ca.


Course Title:

Introduction to representation theory of p-adic groups

Resource Person: Dr. Nadir Martinge ( Université de Poitiers, Laboratoire Mathématiques et Applications, France)

Starting Date: February 24, 2020

Schedule:The course comprises eight lectures of 90 minutes each on Monday (14:00 – 15:30) and Friday (10:00 – 11:30).

poster , For further information contact: info@sms.edu.pk


Course Title:

Quantum sl(2) : algebraic structure and topological applications.

Resource Person: Dr. Christian Blanchet (Université de Paris, France)

Starting Date: February 28 , 2020

Schedule:The course comprises of five lectures of 90 minutes each on Wednesday (14:00 – 15:30) and Friday (14:30 – 16:00).

Poster, For further information contact: info@sms.edu.pk


Course Title:

Short Course on Symmetry Methods for Differential Equations

Instructor:
Asghar Qadir

Textbook:
Differential Equations: Their Solution Using Symmetries

Author:
Hans Stefani

Publisher:
Cambridge University Press 1990

Referred as:
HS

Textbooks:
Differential Equations and the Calculus of Variations

Author:
L. Elsgolts

Publisher:
MIR Publishers 1970

Referred as:
LE

Course Description:

Whereas there are standard techniques for solving differential equations, apart from the first order equations there are no standard techniques for solving non-linear differential equations. Lie had developed an approach to try to determine substitutions, which could be used to reduce the order of an ODE, or the number of independent variables of a PDE. This field has made dramatic advances under the name of “symmetry analysis”. In this course the symmetries of ordinary differential equations (ODEs) will be discussed. Next the techniques for finding the symmetries of an ODE, and their use for solving it will be presented. This will be extended to systems of ODEs.

MDE-813 Symmetry Methods for Differential Equations

Detailed Syllabus

Week

Ch. Sect.

Topics

1

1,2

ODEs and PDEs of 1st order; formulations of
symmetries.

2

3.2-3.4

Lie symmetries of 1st and 2nd order
ODEs.

3

4.1-4.4

Lie symmetries of 2nd order ODEs; higher order
ODEs and linear nth order ODEs.

4

5.1, 5.2

The use of symmetries to solve 1st order ODEs.

5

6.1-6.5

Lie algebras for infinitesimal generators.

6

7.1-7.5

The use of symmetries for solving 2nd order ODEs
admitting a G2.

7

8.1-8.3

2nd order ODEs admitting more than 2 Lie point
symmetries.

8

9.1-9.5

Higher order ODES admitting more than one Lie point
symmetry.

9

LE 6.1-6.7

The optimization problem. The calculus of variations and
Lagrangians: first order, higher order and several
variables.

10

12.1-12.3

13.1-13.2

Noether symmetries and conservation laws.

Poster, For further information contact: info@sms.edu.pk