Topics in Algebraic Number Theory Salahaddin University, Erbil
October 49, 2021
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 August 15, response on applications August 31):
Kurdish applicants
International and rest of Iraq applicants
Courses

Introduction to the Dedekind zeta function of a number field 
Mehdi Hassani (University of Zanjan)
 Riemann zetafunction;
 Dirichlet Lfunctions;
 Dedekindzetafunction;
 Functional equation and Analyic continuation.


Introduction to PariGP 
Elisa Lorenzo Garcia (Université de Rennes 1)
 Basic Number Theoretic functions with Pari: prime numbers, arithmetic functions,..
 Polynomials and Power Series with Pari
 Linear Algebra with Pari
 Sums, Products and Integrals
 Basic PARI/GP commands: standard operations, for, if, ...
 Algebraic Number Theory with Pari


Algebraic Number Theory I
Valerio Talamanca (Università Roma Tre)
 Generalities of Fields and Rings;
 Number fields;
 Norms, traces and discriminants;
 Ring of integers;


Algebraic Number Theory II
Peter Stevenhagen (Leiden University)
 Dedekind rings;
 Ideal factorization in Dedekind rings;
 Decomposition and ramification;
 Archimedean and non archimedean absolute values;
 Structure of Units;
 Class number and its finiteness;
 Artin reciprocity law.

 TBA
Sanhan M. Khasraw (Salahaddin UniversityErbil)

Galois Theory
Lea Terracini (Università di Torino)
 Separability and normality of field extensions:
 Finite Galois theory;
 The fundamental theorem of Galois theory;
 Explicit examples of Galois extensions;
 Cyclotomic extensions, radical extensions, solvable extensions;
 Solvable groups and the insolubility of the general quintic;
 Finite fields, Reduction modulo primes, Computation of Galois groups.

Organizing Commitee
 Saman Ahmed Bapir, Salahaddin UniversityErbil
 Rashad Rashid Haji, Salahaddin UniversityErbil
 Jabar Salih Hassan, Salahaddin UniversityErbil
 Sanhan M. Salih Khasraw, Salahaddin UniversityErbil
 Fuad Wahid Khdhr, Salahaddin UniversityErbil
 Gashaw A. Mohammed Saleh, Salahaddin UniversityErbil
 Andam Ali Mustafa, Roma Tre University and Salahaddin UniversityErbil
 Payman Abbas Rashed, Salahaddin UniversityErbil
Tentative Schedule

Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Saturday 
08:0009:00 
opening ceremony 

09:0009:50 
Galois Theory 
Galois Theory 
Algebraic Number Theory 
Algebraic Number Theory 
Algebraic Number Theory 
Algebraic Number Theory 
10:0010:50 
Algebraic Number Theory 
Algebraic Number Theory 
Galois Theory 
Dedekind zeta function

Dedekind zeta function

Dedekind zeta function

11:0011:30 
coffee break 
11:3012:20 
PARIGP 
PARIGP 
Algebraic Number Theory 
Algebraic Number Theory 
TBA 
TBA 
12:3015:00 
lunch break 
15:0015:50 
Galois Theory 
Galois Theory 
free afternoon 
PARIGP 
PARIGP 
closing ceremony 
16:0016:50 
Algebraic Number Theory 
Algebraic Number Theory 
PARIGP 
PARIGP 

 Topics in Commutative Algebra
University of Sulaimani, Sulaimani October 1116, 2021
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 August 15, response on applications August 31):
Kurdish applicants
International and rest of Iraq applicants
Courses

Introduction to commutative algebra
Sylvia Wiegand (University of Nebraska)

Rashid Zaare Nahandi (Institute for Advanced Studies in Basic Sciences)
 Ideals in a commutative ring;
 Operation on ideals;
 Zero divisors, nilpotent elements and units;
 Prime and maximal ideals;
 Nilradical and Jacobson radical;
 Localization in a prime ideal. Local properties;
 Primary decomposition;
 Integral dependance: Going up and going down theorems.

Noetherian rings
Roger Wiegand (University of Nebraska)

Kamran DivaaniAazar (IPM and Alzahra University)
 Chain conditions;
 Noetherian Modules;
 Noetherian ring;
 Hilbert's basis theorem, Hilbert's Nullstellensatz;
 Primary decomposition in Noetherian rings;
 Dimension of a Noetherian ring;
 Noetherian rings of dimension zero (Artinian rings);
 Primary decomposition in Noetherian rings of dimension one (Dedekind domains).

A gentle introduction to homological algebra
Amir Mafi (University of Kurdistan, Iran)

Lea Terracini (Università di Torino)

 Basic construction with modules and their submodules;
 Exact sequences of modules;
 Tensor product of modules;
 Free and projective modules;
 Cochain complexes, free and projective resolution of a module;
 EXT and TOR.

Basics notions in algebraic geometry
Valerio Talamanca (Università Roma Tre)

Francesco Pappalardi (Università Roma Tre)
 Affine spaces: Affine subset of affine spaces, Irreducible affine sets;
 The Zariski topology on A^{n};
 Affine varieties: coordinate rings and regular functions;
 Maps between affine varieties: polynomial functions, polynomial maps;
 Projective spaces: Algebraic subset of projective spaces, projective varieties;
 The Zariski topology on P^{n};
 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

Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
08:3009:00 
opening ceremony 

09:0009:50 
Commutative algebra 
Commutative algebra 
Algebraic Geometry 
Noetherian modules and rings 
Homological algebra 
10:0010:50 
Commutative algebra 
Commutative algebra 
Commutative algebra 
Noetherian modules and rings 
Homological algebra 
10:5011:20 
coffee break 
11:2012:10 
Homological algebra 
Noetherian modules and rings 
Homological algebra 
Commutative algebra 
Noetherian modules and rings 
12:2013:10 
Homological algebra 
Noetherian modules and rings 
Noetherian modules and rings 
Commutative algebra 
Noetherian modules and rings 
13:1015:00 
lunch break 
15:0015:50 
Algebraic Geometry 
Homological algebra 
free afternoon 
Algebraic Geometry 
Algebraic Geometry 
16:0016:50 
Algebraic Geometry 
Homological algebra 
Algebraic Geometry 
Algebraic Geometry 
