A pair of WAMS school in Kurdistan



Topics in Algebraic Number Theory
Salahaddin University, Erbil
October 4-9, 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)
    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
    Valerio Talamanca (Università Roma Tre)
    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.
  • TBA
    Sanhan M. Khasraw (Salahaddin University-Erbil)
  • 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 Galois Theory Galois Theory 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 TBA TBA
12:30-15:00 lunch break
15:00-15:50 Galois Theory 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
October 11-16, 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)
    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
    Roger Wiegand (University of Nebraska)
    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
    Amir Mafi (University of Kurdistan, Iran)
    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.
  • Basics notions in algebraic geometry
    Valerio Talamanca (Università Roma Tre)
    Francesco Pappalardi (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
Monday Tuesday Wednesday Thursday Friday
08:30-09:00 opening ceremony
09:00-09:50 Commutative algebra Commutative algebra Algebraic Geometry Noetherian modules and rings Homological algebra
10:00-10:50 Commutative algebra Commutative algebra Commutative algebra Noetherian modules and rings Homological algebra
10:50-11:20 coffee break
11:20-12:10 Homological algebra Noetherian modules and rings Homological algebra Commutative algebra Noetherian modules and rings
12:20-13:10 Homological algebra Noetherian modules and rings Noetherian modules and rings Commutative algebra Noetherian modules and rings
13:10-15:00 lunch break
15:00-15:50 Algebraic Geometry Homological algebra free
afternoon
Algebraic Geometry Algebraic Geometry
16:00-16:50 Algebraic Geometry Homological algebra Algebraic Geometry Algebraic Geometry

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