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trevents:2021:summer_workshop
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. |
events/2021/summer_workshop.txt · Last modified: 2021/02/09 18:53 by ez_yildiz
