Eğitimciler: Selçuk Demir, Haydar Göral, Ahmet Batal, Doğa Can Sertbaş, Sadık Eyidoğan
Program:
Name: Prof. Selçuk Demir
Institution: İstinye University
Title of the course: Riemann-Roch Theorem
Level: Graduate, Advanced undergraduate
Language: English, Turkish
A short abstract or a daily curriculum: We will cover a version of the Riemann-Roch Theorem.
Prerequisites: Basic algebra
—————————
Name: Assoc. Prof. Haydar Göral
Institution: İzmir Institute of Technology
Title of the course: The Circle Method and Roth’s Theorem
Level: Graduate, Advanced undergraduate
Language: English, Turkish
A short abstract or a daily curriculum: We introduce the circle method and as an application we prove Roth’s theorem on arithmetic progressions.
Prerequisites: Calculus
————————
Name: Assoc. Prof. Ahmet Batal
Institution: İzmir Institute of Technology
Title of the course: Szemeredi’s Regularity Lemma
Level: Graduate, Advanced undergraduate
Language: English, Turkish
A short abstract or a daily curriculum: Szemeredi’s regularity lemma, triangle removal lemma, Roth’s theorem
Prerequisites: Calculus
——————————–
Name: Asst. Prof. Dr. Doğa Can SERTBAŞ
Institution: İstinye University
Title of the course: Probabilistic Number Theory
Level: Graduate, Advanced undergraduate
Language: English, Turkish
A short abstract or a daily curriculum: Basic Ramsey theory, lower bounds for Ramsey and van der Waerden numbers, basic probability theory, sum-free sets
Prerequisites: Elementary number theory and calculus
————————–
Name: Dr. Sadık Eyidoğan
Institution: Çukurova University
Title of the Course: Ramsey Theory and Ultrafilters
Language: Turkish
A Short Abstract: We introduce the space of ultrafilters βN and its topological properties. We also explain limits along ultrafilters. Then, we recall the relevant notions from Ramsey theory and give a proof that all partition regular properties correspond to ultrafilters. We define the addition of ultrafilters, which turns the space of ultrafilters βN into a left topological semigroup. Finally, we will collect information about the ideals of the semigroup βN to the point that we can give a proof of van der Waerden’s theorem.
Prerequisites: Topology and Basic group theory.
