TeMoG

TeMoG:

TeMoG is a pure mathematics project which aims to study the groupoid named the “fundamental modular groupoid". Fundamental modular groupoid provides a common hybrid generalization of both Ptolemy groups and mapping class groups of punctured surfaces from the point of view of its connections to algebraic topology, combinatorial group theory, algebraic geometry and arithmetic. The acronym TeMoG is the short form of its Turkish translation. The isotropy groups of fundamental modular groupoid encode valuable information on Riemann surfaces of both finite and infinite type. Contrary to the fact that mapping class groups of surfaces of infinite type are uncountable, these groups are countable and it is possible to study them from diverse points of view. These groups are also conjectured to be finitely presented in many favourable cases.

Project Members:

Sena Özgünay - undergraduate student member
İlayda Serbes - undergraduate student member
Mustafa Burak Topal - undergraduate student member
A. Muhammed Uludağ (Researcher - R)
Özge Ülkem (Post-doc - PD)
Ayberk Zeytin (Principal Investigator - PI)

Open Positions :

There are two MSc positions available for those who are interested in writing a thesis within TeMoG. There are several topics available.
For undergraduate students at Galatasaray University, there is an undergraduate student position for those who are willing to contribute both to public outreach activities of the project as well as writing his/her senior year project in the context of TeMoG.

Those who are interested in any of the above positions should get in touch with PI. His contact information is available at math.gsu.edu.tr/azeytin.

Weekly Meetings (online)

There are several weekly meetings of our project. Anyone who is interested to participate can send an e-mail to PI.

Fridays at 14h00 we are holding a weekly study seminar. The duration is directly proportional to the energy of the participants. It is concentrated on a preprint of A.M. Uludağ and A. Zeytin where the fundamental modular groupoid is introduced.
Tuesdays at 14h00 with two undergraduate students (İlayda Serbes and Sena Özgünay), we meet and work on writing and expanding wikipedia articles on fundamental group and fundamental groupoid in Turkish. If time permits, we will work on a Turkish article on braid groups. This is a part of a public outreach activity of the project.
Thursdays at 15h15 with one undergraduate student (Mustafa Burak Topal), we meet to talk about units of real cyclotomic fields. We try to relate this to binary quadratic forms and çarks - possibly their higher dimensional generalizations. Çarks are one of the case studies we focused while studying the fundamental modular groupoid.
Thursdays at 14h00 there is a meeting with Begüm Gülşah Çaktı. In these meetings, we are trying to establish connections between Arakelov class groups of real quadratic number fields and çarks. We are hoping to publish a preprint soon.

Weekly Research Seminars (online)

We are planning to organize a research seminar on Tuesdays at 17h00. Main concentration is topics around mapping class groups, Teichmüller spaces, universal Teichmüller space, Thompson's groups, etc. If you are willing give a talk, please get in touch with PI. For participation, please fill in the form at :

https://forms.gle/5WFqgxobcX3GhPvP7

Here is a list of talks :

Speaker :
Title :
Abstract :