Coordinator: Ramesh Gautam, Mathematical Biology Research Centre (MBRC), Nepal
2025
Applied Mathematics for Real-Life Phenomenon
Coordinators: Gourav Arora (India), Youcef Mammeri (France)
Lattices and codes : arithmetic for communication systems
Frédérique Oggier
Summary: In this course, we taught show how lattices and codes, both independently and jointly, are used in the context of communication systems. The course was structured as follows :
- Introduction to lattices and geometry of numbers
- Introduction to linear codes and lattices from codes
- Introduction to number fields and lattices from number fields
- Introduction to quaternion algebras and codes from quaternion algebras
- Practical aspects : channel modeling
Numbers Theory
Francesco Pappalardi
Summary:
Elementary Numbers Theory:
- Quadratic reciprocity
- Arithmetic fonctions
Analytic Numbers Theory :
- Dirichlet Arithmetic progression
- Prime Number Theorem
Integrable systems
Maciej Dunajski
Summary: Integrable systems are nonlinear differential equations which ‘in principle’ can be solved analytically. This means that the solution can be reduced to a finite number of algebraic operations and integrations. Such systems are very rare - most nonlinear differential equations admit chaotic behaviour and no explicit solutions can be written down. Integrable systems nevertheless lead to a very interesting mathematics ranging from differential geometry and complex analysis to quantum field theory and fluid dynamics.
Theories of Ordinary Differential Equations (ODEs): Special Topics
Abdulhakeem Yusuf
Summary: The following topics were covered during the period of stay
1. GENERAL FIRST-ORDER EQUATION i. General Introduction of ODE ii. iii. Equivalence of an Initial Value Problem Existence & Uniqueness Theorem
2. LINEAR SYSTEM OF FIRST-ORDER EQUATION i. Characrerisation of the Fundamental Matrix ii. iii. iv. v. vi. vii. Properties of Linear Systems Adjoint systems Homogeneous and non-homogeneous system Autonomous Differential equations LINEAR SYSTEMS WITH PERIODIC COEFFICIENTS THEORY OF OSCILLATION
Research Methodology
Patrick Tchepmo Djomegni
Mathematical epidemiology
Patrick Tchepmo Djomegni
Introduction to real dynamical systems with applications
Jorge Mozo Fernández
Summary: The idea of this course is to give an introduction to the theory of real dynamical systems from scratch, focusing on the main elements of qualitative theory: equilibria, periodic orbits, limit cycles, … An outline of the contents is as follows: