Abstract: In the mapping class group of a closed surface, every element may be written as a product of arbitrarily large number of right Dehn twists. A question of I.Smith related to the Stein fillings of contact 3-manifolds asks whether the same holds true if the surface has boundary components. Recently, R. İ. Baykur and J. Van Horn-Morris proved that the Dehn twist about the boundary component of the surface with one boundary admits such factorizations with arbitrarily large number of twists provided that the genus of the surface is at least 8. We entend this result all surfaces with one boundary. Our proof is more elementary. This work is a joint work with Elif Dalyan and Mehmetcik Pamuk.

Abstract: For any finitely presentable group G, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings whose fundamental group is isomorphic to G. Along the way, we also provide a new construction of a Lefschetz fibration over the 2-sphere whose total space has fundamental group G, using Luttinger surgery. (This is a joint work with Anar Akhmedov)

Abstract: In this talk, we will discuss techniques used in classification of Legendrian knots in contact 3-manifolds.The classification of Legendrian unknots with tight complements in 3-sphere is due to Eliashberg and Fraser. We will give an alternative proof for this classification. Then, using the same idea we will extend the classification result of Eliashberg and Fraser to rational unknots in lens spaces. (This is a joint work with H. Geiges)

Title: Branched cover surgery diagrams and real factorization of Lefschetz fibrations

Abstract: The most common constructions in 4-dimensional topology can be interpreted as double covers of the corresponding constructions with surfaces inside a 4-ball. I will discuss link diagram presentation of such surfaces and constructions, and in particular discuss them in the case of Real (i.e., symmetric) Lefschetz fibrations.