Geometry and Topology of Surfaces — Galatasaray University

Overview

Theme

The summer school focuses on a fundamental and modern area: the geometry and topology of surfaces.

Goals

Research-oriented introduction leading toward active research directions.
Suitable for multiple levels: topics that can support a Master’s thesis or serve as a starting point for PhD work.

Conference Committee

Athanase Papadopoulos (Université de Strasbourg)
Valdimir Turaev (Indiana University Bloomington)
Muhammed Uludağ (Galatasaray University)
Ayberk Zeytin (Galatasaray University)

Registration

Registration Information

Participants who are interested in attending are required to register by filling out the registration form.

Speakers & Topics

The lectures will be delivered in either French or English. In practice, the language of each lecture will be chosen according to the audience.

Georgios Daskalopoulos (Brown University) Lectures in English

Title: Harmonic maps between surfaces, measured foliations and geodesic laminations

Abstract: I will explain how certain techniques from Geometric Analysis can be used to describe topological objects like foliations and laminations which appear in topology and in particular in Thurston theory.

Yi Huang (Yau Mathematical Center, Tsinghua University) Lectures in English

Let us see how simple ideas and observations coming from doing trigonometry with hyperbolic polygons have blossomed into important developments in modern mathematics.

Hideki Miyachi (Institute of Science and Engineering, Kanazawa University) Lectures in English

To be announced.

Ken’ichi Ohshika (Gakushuin University, Tokyo) Lectures in French

structures hyperboliques de surfaces, les laminations géodésiques, les applications d’étirement et de tremblements de terre.

Athanase Papadopoulos (Université de Strasbourg) Lectures in French

Surface homeomorphisms and mapping classes. Measured foliations. The space of measured foliations. The piecewise-linear structure of the space of measured foliations. Thurston's classification of mapping classes.

Hugo Parlier (Université de Fribourg) Lectures in English

Title: Playing with moduli spaces

Abstract: Roughly speaking, a moduli space is a space of geometric objects up to some equivalence. For example, the space of triangles up to rigid motion is a simple moduli space. More complicated examples include moduli spaces of hyperbolic surfaces, which play an important role in geometric topology. These ideas can be very sophisticated, but some of the underlying principles can be approached without being an expert.

We’ll begin by playing around with examples coming from puzzles and drawings. It will be an excuse to explore how combinatorics often dovetails with geometry in surprising ways.

N.B. Participants are invited to “prepare" for class by playing Quadratis:

http://quadratis.app

Sumio Yamada (Gakushuin University, Tokyo) Lectures in English

A Finsler metric is equivalent to distributing a convex set to each tangent space of a manifold, and therefore a natural extension of the classical convex geometry. We will look into the relevance of convex geometry and concave geometry in this context, and discuss Finsler geometry as well as timelike finsler geometry.

Local Information

Istanbul’s historical and cultural heritage reaches back millennia, and the city stretches across both banks of the Bosphorus, linking Asia and Europe. Former capital of the Roman, Byzantine, and Ottoman Empires, Istanbul pairs striking natural beauty with a dense collection of historic landmarks.

Climate & Clothing

Istanbul has a mild Mediterranean climate. In late June, weather is generally warm—light, breathable summer clothing is recommended.

Visa Information

Citizens of many countries can obtain an e-visa online before traveling.
Official e-Visa application: evisa.gov.tr

Places to Visit in Istanbul

Historical landmarks

Shopping

Classical art

Modern art

Contact

For all questions, please contact: ayberkz@gmail.com