Gökova Geometry Topology Institute

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===== Summer Workshop 2021 (at a date to be announced later) ===== 

This summer workshop aims to provide an opportunity for advanced Ph.D. students, postdocs, and young researchers to interact in their research areas. There will be some mini-courses and research talks, followed by informal discussions.

The mini-courses will be given by Yi Ni, Çağrı Karakurt and Mustafa Korkmaz.

**Organizing Committee:** Fırat Arıkan, Çağrı Karakurt, Üstün Yıldırım, Eylem Zeliha Yıldız.

For further questions about this event please contact Eylem Zeliha Yıldız: [[eylem.yildiz@duke.edu]]



=== Mini Courses ===
^ Speaker ^ Title and Abstract ^
| Yi Ni | **Heegaard Floer homology and Dehn surgery**\\ In this course, we will give a brief introduction to Heegaard Floer homology, with focus on its applications to Dehn surgery. We may cover the following topics:  the construction of Heegaard Floer and knot Floer chain complexes, basic properties, surgery exact triangles, genus bound and fiberedness, the mapping cone formula for Dehn surgery, correction terms,  L-space surgery. |
| Çağrı Karakurt | **Correction terms in Heegaard Floer homology**\\ Correction term is a powerful invariant of 3-manifolds that is useful in answering a number of important problems in low-dimensional topology about Dehn surgery, homology cobordism `and knot concordance. In many cases, one can compute the correction term using purely combinatorial methods without a deep knowledge of the full  Heegaard Floer theory. In this mini-course I will introduce a few different computational techniques and discuss their applications. This series is accessible to those graduate students with a basic background in geometry and topology.|
| Mustafa Korkmaz | **Mapping class groups of surfaces**\\ The mapping class group Mod$(\Sigma_g)$ of a closed oriented surface $\Sigma_g$ of genus $g$ is defined as the group of isotopy classes of orientation-preserving diffeomorphisms $\Sigma_g \to \Sigma_g$. It is a fundamental object in low-dimensional topology. It is known that this group can be generated by finitely Dehn twists, torsion elements, and also by involutions. In these lectures, I will first discuss how to find \\ \\  * a finite set of Dehn twist generators, \\  * the minimal number of Dehn twist generators,\\  * the minimal number of torsion generators, \\  * the minimal number of involution generators, and \\  * the minimal number of commutator generators \\  \\ of the group Mod$(\Sigma_g)$, roughly in the chronological order. In the end, I am also planning to talk on low dimensional linear representations of the mapping class group.|
Gökova Geometry Topology Institute

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