A pair of WAMS school in Kurdistan







Topics in Algebraic Number Theory
Salahaddin University, Erbil
August 22 - 28, 2022


The school aims at providing an introduction to various basic aspects of Algebraic Number Theory and it is directed at advanced undergraduate students of Salahaddin University and others from Kurdistan, Iraq and neighbouring countries Universities.
Application Forms (deadline July 10th)
Application form
Courses
  • Introduction to the Riemann zeta function and distribution of primes
    Mehdi Hassani (University of Zanjan)
    1. Riemann zeta-function;
    2. Dirichlet- L-functions;
    3. Dedekind-zeta-function;
    4. Functional equation and Analyic continuation.
  • Introduction to Pari-GP
    Elisa Lorenzo Garcia (Université de Rennes 1)
    1. Basic Number Theoretic functions with Pari: prime numbers, arithmetic functions,..
    2. Polynomials and Power Series with Pari
    3. Linear Algebra with Pari
    4. Sums, Products and Integrals
    5. Basic PARI/GP commands: standard operations, for, if, ...
    6. Algebraic Number Theory with Pari
  • Algebraic Number Theory I
    Francesco Pappalardi
    1. Generalities of Fields and Rings;
    2. Number fields;
    3. Norms, traces and discriminants;
    4. Ring of integers;
  • Algebraic Number Theory II
    Peter Stevenhagen (Leiden University)
    1. Dedekind rings;
    2. Ideal factorization in Dedekind rings;
    3. Decomposition and ramification;
    4. Archimedean and non archimedean absolute values;
    5. Structure of Units;
    6. Class number and its finiteness;
    7. Artin reciprocity law.
  • Introduction to Finite Groups
    Sanhan M. Khasraw (Salahaddin University-Erbil)
    1. Basic properties of finite groups (subgroups, homomorphisms, Lagrange Theorem, Cauchy Theorem);
    2. Cyclic and Abelian Groups;
    3. Symmetric Groups;
    4. Dihedral Groups;
    5. Properties of p-groups (Sylow Theorems);
    6. Simple groups (Alternate group).
  • Galois Theory
    Lea Terracini (Università di Torino)
    1. Separability and normality of field extensions:
    2. Finite Galois theory;
    3. The fundamental theorem of Galois theory;
    4. Explicit examples of Galois extensions;
    5. Cyclotomic extensions, radical extensions, solvable extensions;
    6. Solvable groups and the insolubility of the general quintic;
    7. Finite fields, Reduction modulo primes, Computation of Galois groups.
Organizing Commitee
  • Saman Ahmed Bapir, Salahaddin University-Erbil
  • Rashad Rashid Haji, Salahaddin University-Erbil
  • Jabar Salih Hassan, Salahaddin University-Erbil
  • Sanhan M. Salih Khasraw, Salahaddin University-Erbil
  • Fuad Wahid Khdhr, Salahaddin University-Erbil
  • Gashaw A. Mohammed Saleh, Salahaddin University-Erbil
  • Andam Ali Mustafa, Roma Tre University and Salahaddin University-Erbil
  • Payman Abbas Rashed, Salahaddin University-Erbil
Tentative Schedule
Monday Tuesday Wednesday Thursday Friday Saturday
08:00-09:00 opening ceremony
09:00-09:50 Finite Groups Finite Groups Algebraic Number Theory Algebraic Number Theory Algebraic Number Theory Algebraic Number Theory
10:00-10:50 Algebraic Number Theory Algebraic Number Theory Galois Theory Dedekind zeta function
 Dedekind zeta function
 Dedekind zeta function
11:00-11:30 coffee break
11:30-12:20 PARI-GP PARI-GP Algebraic Number Theory Algebraic Number Theory Galois Theory Galois Theory
12:30-15:00 lunch break
15:00-15:50 Finite Groups Galois Theory free
afternoon		 PARI-GP PARI-GP closing ceremony
16:00-16:50 Algebraic Number Theory Algebraic Number Theory PARI-GP PARI-GP
Topics in Commutative Algebra
University of Sulaimani, Sulaimani
September 3 - 7, 2022

The school aims at providing an introduction to various basic aspects of theory of commutative rings as well as a first introduction of its use in modern algebraic geometry. The school is directed at advanced undergraduate students of Sulaimani University and others from KAR, Iraqi and neighbouring countries Universities.
Application Forms (deadline July 10th)
application form
Courses
  • Introduction to commutative algebra
    Rashid Zaare Nahandi (Institute for Advanced Studies in Basic Sciences)
    1. Ideals in a commutative ring;
    2. Operation on ideals;
    3. Zero divisors, nilpotent elements and units;
    4. Prime and maximal ideals;
    5. Nilradical and Jacobson radical;
    6. Localization in a prime ideal. Local properties;
    7. Primary decomposition;
    8. Integral dependance: Going up and going down theorems.
  • Noetherian rings
    Kamran Divaani-Aazar (IPM and Alzahra University)
    1. Chain conditions;
    2. Noetherian Modules;
    3. Noetherian ring;
    4. Hilbert's basis theorem, Hilbert's Nullstellensatz;
    5. Primary decomposition in Noetherian rings;
    6. Dimension of a Noetherian ring;
    7. Noetherian rings of dimension zero (Artinian rings);
    8. Primary decomposition in Noetherian rings of dimension one (Dedekind domains).
  • A gentle introduction to homological algebra
    Kamran Divaani-Aazar (IPM and Alzahra University)
    Lea Terracini (Università di Torino)
    1. Basic construction with modules and their submodules;
    2. Exact sequences of modules;
    3. Tensor product of modules;
    4. Free and projective modules;
    5. Cochain complexes, free and projective resolution of a module;
    6. EXT and TOR.
  • Basic notions in algebraic geometry
    Valerio Talamanca (Università Roma Tre)
    1. Affine spaces: Affine subset of affine spaces, Irreducible affine sets;
    2. The Zariski topology on An;
    3. Affine varieties: coordinate rings and regular functions;
    4. Maps between affine varieties: polynomial functions, polynomial maps;
    5. Projective spaces: Algebraic subset of projective spaces, projective varieties;
    6. The Zariski topology on Pn;
    7. Morphism, rational and birational maps between projective varieties.
Organizing Commitee
  • Chwas Abas Ahmed University of Sulaimani (local coordinator)
  • Payman Mahmood Hama Ali University of Sulaimani
  • Dilan Faridun Ahmed University of Sulaimani
  • Hero M Salih University of Sulaimani
Tentative Schedule
Saturday Sunday Monday Tuesday Wednesday
08:30-09:00 opening ceremony
09:00-09:50 Algebraic Geometry Commutative algebra Noetherian modules and rings Noetherian modules and rings Noetherian modules and rings
10:00-10:50 Commutative algebra Commutative algebra Commutative algebra Noetherian modules and rings Noetherian modules and rings
10:50-11:20 coffee break
11:20-12:10 Homological algebra Homological algebra Homological algebra Commutative algebra Homological algebra
12:20-13:10 Homological algebra Homological algebra Algebraic Geometry Commutative algebra Homological algebra
13:10-15:00 lunch break
15:00-15:50 Homological algebra Algebraic Geometry free
afternoon		 Algebraic Geometry Algebraic Geometry
16:00-16:50 Noetherian modules and rings Noetherian modules and rings Algebraic Geometry Algebraic Geometry
17:00-17:30 Closing ceremony
SPONSORS
In early October 2021 a few days of on-line activities to prepare for the school were held.
Program of the on line activities
Topics in Algebraic Number Theory
Salahaddin University, Erbil
October 7-8, 2021


October 7th
Introduction to Finite Groups
Sanhan M. Khasraw 		90 minutes
Galois Theory
Lea Terracini		 90 minutes
Algebraic Number Theory I
Francesco Pappalardi		 90 minutes



October 8th
Algebraic Number Theory II
Peter Stevenhagen* 		90 minutes
Introduction to the Dedekind zeta
function of a number field
Mehdi Hassani		 90 minutes
Introduction to Pari-GP
Elisa Lorenzo Garcia		 90 minutes
Topics in Commutative Algebra
University of Sulaimani, Sulaimani
October 14-15, 2021


October 14th
Introduction to commutative algebra
Sylvia Wiegand and Rashid Zaare Nahandi* 		140 minutes
Noetherian rings
Roger Wiegand Kamran Divaani-Aazar*		 140 minutes



October 15th
A gentle introduction to homological algebra
Amir Mafi* and Lea Terracini 		140 minutes
Basics notions in algebraic geometry
Valerio Talamanca		 140 minutes
* = to be confirmed. The timing of the lectures will be decided soon.* = to be confirmed. The timing of the lectures will be decided soon.