2012 Arayıl Matematik Kışokulu Algebra and Arithmetic Eğitmen

2012 Arayıl Matematik Kışokulu Algebra and Arithmetic Eğitmen

2012 Arayıl Matematik Kışokulu
Algebra and Arithmetic
Eğitmen: Prof. Dr. Ali Nesin
Kurum: İstanbul Bilgi Üniversitesi
Tarihler: January 23 – February 13, 2012
Seviye: Graduate or advanced undergraduate
Kaynak: Arithmetic of Quadratic Forms by Goro Shimura (Springer 2019)
Program:
23 Ocak: Quadratic reciprocity Law
24 Ocak: Lattices in vector spaces and modules over pid’s.
25 Ocak: Valuations and p-adic numbers
26 Ocak: Hensel’s Lemma
27 Ocak: Integral elements
28 Ocak: Ideal theory in an algebraic number field
29 Ocak: Tensor products (of fields)
30 Ocak: Units and the class number of a field
31 Ocak: Units and the class number of a field
1 Şubat: Ideals in an extension of a number field
2 Şubat: The discriminant and different
3 Şubat: Adeles and ideles
4 Şubat: Galois extensions
5 Şubat: Cyclotomic fields
6 Şubat: Algebras over fields
7 Şubat: Central simple algebras
8 Şubat: Quaternion algebras
9 Şubat: Arithmetic of semisimple algebras I
10 Şubat: Arithmetic of semisimple algebras II
11 Şubat: Quadratic forms
12 Şubat: Clifford algebras
13 Şubat: Clifford groups and spin groups
Basic Functional Analysis
Eğitmen: Doç. Dr. Selçuk Demir
Kurum: İstanbul Bilgi Üniversitesi
Tarihler: January 23 – February 8, 2012
Seviye: Graduate or advanced undergraduate
Kaynak: Linear Analysis by Bela Bollobas (1999) and Functional Analysis by Rudin (1991)
Program:
23 Ocak: Normed vector spaces and linear operators
24 Ocak: Linear Functionals and the Hahn-Banach theorem.
25 Ocak: Finite dimensional spaces
26 Ocak: Open Mapping and Closed Graph Theorems
27 Ocak: Continuous functions on compact spaces
28 Ocak: Contraction Mapping Theorem
29 Ocak: Weak topologies and duality
30 Ocak: Hilbert Spaces
31 Ocak: Orthonormal systems
1 Şubat: Adjoint operators
2 Şubat: The algebra of bounded linear operators
3 Şubat: Compact operators on Banach spaces
4 Şubat: Compact normal operators
5 Şubat: Fixed point theorems
6 Şubat: Haar measure on compact groups
7 Şubat: Some Applications - 1
8 Şubat: Some applications - 2
Advanced Number Theory: Riemann-Roch and Abel-Jacobi Theorems
Eğitmen: Yard. Doç. Dr. Ayhan Günaydın
Kurum: Lizbon U.
Seviye: Advanced undergrads and grads
Kaynak: Introduction to Algebraic and Abelian Functions - Serge Lang
Tarihler: 23-31 January 2012
Program:
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31
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A little bit of valuation theory I
A little bit of valuation theory II
Curves, divisors and differential forms I
Curves, divisors and differential forms II
Riemann-Roch Theorem
Residues
Function fields
Riemann surface of a function field
Abel-Jacobi Theorem
Valued Fields
Eğitmen: Yard. Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Üniversitesi
Seviye: Lisans ve Lisansüstü
Tarih: 30 Ocak – 4 Şubat 2011
İçerik: Absolute values (archimedean and non-archimedian). Basic examples of valuations.
Ostrowski's Theorem. Completions and Hensel's Lemma. Krull valuations. Basic notions: ordered
abelian groups, valuation rings. Basic constructions of valuations: coarsening, completion.
Extensions of valuations: Chevalley's Theorem. Algebraic extensions, conjugation theorem in
normal extensions, fundamental inequality.