LEFSCHETZ FIBRATIONS DAY

January 10, 2020

Hacettepe University, Ankara

Speakers:

İnanç Baykur, UMass Amherst

Mustafa Korkmaz, METU

Nur Sağlam, Virginia Tech

Burak Özbağcı, Koç University

The talks will be in Yaşar Ataman Meeting Room on the second floor of Mathematics Department at Hacettepe University.

Schedule

09:30-10:30

Nur Sağlam

Constructions of Lefschetz fibrations using cyclic group actions

10:30-11:00

Coffee-Tea Break

11:00-12:00

Mustafa Korkmaz

Involution generators of mapping class groups

12:00-12:30

Coffee-Tea Break

12:30-13:30

İnanç Baykur

Symplectic Calabi-Yaus and exotic rational surfaces via pencils

13:30-14:30

Lunch Break

14:30-15:30

İnanç Baykur

Geography of surface bundles over surfaces

15:30-16:00

Coffee-Tea Break

16:00-17:00

Burak Özbağcı

Convexity in contact, symplectic and complex topology

17:30

Dinner at Bilkent Center

Abstracts

Nur Sağlam

Constructions of Lefschetz fibrations using cyclic group actions

We construct families of Lefschetz fibrations over S^2 using finite order cyclic group actions on the product manifolds Σ_gxΣ_g for g>0. We also obtain more families of Lefschetz fibrations by applying the rational blow-down operation to these Lefschetz fibrations. This is a joint work with Anar Akhmedov and Mohan Bhupal.

Mustafa Korkmaz

Involution generators of mapping class groups

İnanç Baykur

Symplectic Calabi-Yaus and exotic rational surfaces via pencils

We will discuss new ideas and techniques for producing positive Dehn twist factorizations of surface mapping classes, which yield novel constructions of symplectic Calabi-Yaus and exotic rational surfaces, via Lefschetz pencils. Parts of this research program is in collaboration with N. Hamada, K. Hayano, M. Korkmaz, and N. Monden.

İnanç Baykur

Geography of surface bundles over surfaces

An outstanding problem for surface bundles over surfaces, closely related to the symplectic geography problem in dimension four, is to determine for which fiber and base genera there are examples with non-zero signature. We will report on our recent progress (joint with M. Korkmaz), which resolves the question for all fiber and base genera except for about 25 pairs at the time of writing.

Burak Özbağcı

Convexity in contact, symplectic and complex topology

After giving a comparative review of convexity for contact, symplectic and complex manifolds, I will explain how it is related to Lefschetz fibrations and open books.