12th - 17th March, 2017 School

 

Topics in algebraic number theory and Diophantine approximation

 

 

 

To see the report about the school, please click here

and for the album of participants, please click here

 

 

 

 

 

Date:   (12th  - 17th) March 2017

 

Place: Mathematics Department, College of Science, Salahaddin  University/Erbil-Kurdistan Region/IRAQ.

 

 

Sponsored by

  CIMPA  &     Salahaddin University/ Erbil

cimpa

 

 

 

                                

 

 

 

 

Lecturers

Michel Waldschmidt

Emeritus Professor, Universit´e P. et M. Curie (Paris VI)

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Pierre Cartier

Emeritus Director of Research, Institut des Hautes Études Scientifiques 

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Francesco Pappalardi

 full Professor of Algebra, Università Roma Tre, Italy

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Valerio Talamanca

Professore a contratto, Università Roma Tre, Italy

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   Local Organizer Coordinator

Kawa M. A. MANMI

Head of the Mathematics Department, College of Science,

Salahaddin  University/Erbil-Kurdistan Region/IRAQ 

   Local committee

Director: Kawa M. A. MANMI

Head of the Mathematics Department, College of Science, Salahaddin University/Erbil-Kurdistan Region/IRAQ.

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Co-chair: Prof. Dr. Rostam Karim Saeed

Mathematics Department, College of Science, Salahaddin University/Erbil-Kurdistan Region/IRAQ.

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Member: Andam Ali Mustafa

Mathematics Department, College of Science, Salahaddin University/Erbil-Kurdistan Region/IRAQ.

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Member: Karzan Ahmed Perdawud

Mathematics Department, College of Science, Salahaddin University/Erbil-Kurdistan Region/IRAQ.

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Member: Ms Evar Lutfalla Sadraddin

Mathematics Department, College of Science, Salahaddin  University/Erbil-Kurdistan Region/IRAQ.

 

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Scientific Committee
1. Herish O. Abdullah, The Dean of College of Sciences, department of Mathematics,
     Salahaddin University/Erbil-Kurdistan Region/ - IRAQ
2. Kawa M. A. Manmi, Head of the Mathematics Department,
    College of Science, Salahaddin University, /Erbil-Kurdistan Region/IRAQ.
3. Valerio Talamanca, Università Roma Tre
4. Michel Waldschmidt, Université Paris 6    

Program of WAMS school in Erbil
Topics in algebraic number theory and Diophantine
approximation
Salahaddin University/Erbil-Kurdistan Region/IRAQ
March 12th  - March 17th  2017
Time Sunday, 12 March 2017 Lecturer
9:00-10:30 Group Theory Neshtiman N. Sulaiman
10:30-11:00 Coffee Break
11:00-13:00 Ring Theory Abdullah Abdul-Jabbar
Monday, 13 March 2017
9:00-10:30

Polynomial Ring

Download the Lecture

Sanhan Khasraw
10:30-11:00 Coffee Break
11:00-13:00 Field Parween A.Hummadi
Tuesday, 14 March 2017
9:00-10:30 Extension Field Parween A.Hummadi
10:30-11:00 Coffee Break
11:00-13:00 Continuing Extension Field Parween A.Hummadi
Wednesday, 15 March 2017
14:00-15:30

Introduction to continued fractions  

Download the Lecture

Michel Waldschmidt 

 

15:30-15:50 Coffee Break
15:50-17:20 Francesco Pappalardi
17:20-17:30 Coffee Break
17:30-19:00 Valerio Talamanca
Thursday 16 March 2017
9:30-11:00 Francesco Pappalardi
11:00-11:20 Coffee Break
11:20-12:50 Valerio Talamanca
12:50-14:00 Lunch
14:00-15:30 Pierre Cartier
Friday 17 March 2017
8:00-9:30 Continued fractions, transcendence, simultaneous approximation  Michel Waldschmidt
9:30-9:50 Coffee Break
9:50-11:20 Pierre Cartier

 

1.   A Promenade through Galois Theory, Pierre Cartier
2.
 Cyclotomy, Francesco Pappalardi
3.
 Mahler measure of polynomials, Valerio Talamanca
4.
 Introduction to Diophantine Approximation, Michel Waldschmidt

Description of each course

1. A Promenade through Galois Theory by Pierre Cartier

Starting from a description of Galois theory in the words of Galois himself, we shall mention a few open problems (including inverse Galois Theory) and describe various methods connected with these problems. Among the available methods, there are finite geometries (already known to Galois) and explicit computer algorithms. 

2. Cyclotomy
A Gaussian period is a certain kind of sum of roots of unity. The periods permit explicit calculations in cyclotomic fields connected with Galois theory and with harmonic analysis (discrete Fourier transform). They are basic in the classical theory called cyclotomy. Closely related is the Gauss sum, a type of exponential sum which is a linear combination of periods.


 - Reminders of the Galois Theory of cyclotomic polynomial
- Gauss sums and Gauss periods
- The determination of the quadratic Gauss Sum
- Gauss Theorem for expression of roots of unity via nested radicals
- The computation of 
- Kummer’s problem on cubic Gauss periods


3Mahler measure of polynomials

The Mahler measure of a polynomial (with integer coefficients) is a measure of its arithmetic complexity as well as the arithmetic complexity of its roots. Lehmer’s conjecture asserts that the Mahler measure of non cyclotomic polynomials is bounded below by an absolute constant. We willuse this very explicit problem to introduce a few concept of algebraic number theory.


- Mahler measure of a polynomial
- Algebraic integers and their minimal polynomial
- Absolute values and the height of algebraic numbers
- Lower bounds for the Mahler measure of totally real polynomials

4Introduction to Diophantine Approximation
Approximation Rational approximation to a real number: continued fractions and applications. Rational approximation to an algebraic number: transcendence theorem of Thue,Siegel, Roth. Simultaneous approximation. Schmidt Subspace Theorem. Diophantine approximation in fields of power series.

Second Exam Schedule

  download the file

3rd -5th May 2017 Workshop: Principles of Forecasting with R

Upcoming Workshop:

 

Principles of Forecasting with R

Date:- 3rd -5th May 2017

Place:- Mathematics Department, College of Science, Salahaddin University-Erbil, Kurdistan Region-IRAQ.

Sponsored by: Salahaddin University- Erbil

 

For registration, please click here

The Deadline will be  24th April 2017 at 9:00 PM

 

 

Instructor

Bahman Rostami-Tabar

Cardiff Business School, Cardiff University, UK

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Local Organizer Coordinator

1. Director, Khwazbeen Saida Fatah, Mathematics Department, College of Science, Salahaddin University - Erbil, Kurdistan Region/IRAQ.

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2- Member, Swar Omer Ahmed, Mathematics Department, College of Science, Salahaddin University - Erbil, Kurdistan Region/IRAQ.

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3- Member, Evar Lutfalla Sadraddin, Mathematics Department, College of Science, Salahaddin University - Erbil, Kurdistan Region/IRAQ.

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4- Member, Saman Ahmed Bapir, Mathematics Department, College of Science, Salahaddin University - Erbil, Kurdistan Region/IRAQ.

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Please install a recent version of R and RStudio

1. Download and install R: http://www.r-project.org

2. Download and install RStudio: http://www.rstudio.com/products/rstudio

 

 

 

 

 

The program of the workshop

Wednesday, 3rd May 2017
09:00 - 09:30 Registration and welcome
09:30 - 10:00 R, RStudio, RMarkdown
10:00 - 10:30 Forecasting and decision making
10.30 - 11:00  Data preparation
11:00 - 11:15 Break
11:15 - 12:15 Data exploration
12:15 - 13:00  Data visualization
13:00 - 14:00  Lunch
14:00 - 15:30 Practical forecasting : an overall view
15:30 - 15:45  Break
15:45 - 17:00 Reports with RMarkdown
Thursday, 4th May 2017
09:00 - 09:30 Time series components
09:30 - 11:00  Decomposition and forecasting
11:00 - 11:15 Break
11:15 - 13:00 Exponential smoothing models
13:00 - 14:00 Lunch
14:00 - 15:30 ARIMA models
15:30 - 15:45  Break
15:45 - 17:00 Neural networks and TBATS (Trigonometric Exponential Smoothing)
Friday, 5th May 2017
09:00 - 11:00 Regression
11:00 - 11:15 Break
11:15 - 13:00 Model selection
13:00 - 14:00 Lunch
14:00 - 15:30 Intermittent demand forecasting
15:30 - 15:45 Break
15:45 - 16:45 Forecasting by aggregation
16:45 - 17:00 Feedbacks, comments

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