This page contains links and recordings for the Geometry-Topology Seminar series.
Zoom-Seminars (Spring 2021)
- 12:04.2021, 15:40, Speaker: Ergun Yalcin (Bilkent)
Title: Higher limits over the fusion orbit category
Abstract: An homology decomposition of a discrete group is sharp if certain higher limits vanish. For the subgroup decomposition, these higher limits are either over the orbit category or over the fusion orbit category of a discrete group. I will introduce these categories and discuss how the higher limits over an orbit category can be calculated. At the end, I will state some results for the vanishing of higher limits over the fusion orbit category of a discrete group.
Link: Zoom recording Passcode: %N11jNHk
- 29.03.2021, 15:40, Speaker: Hakan Doga (University at Buffalo, SUNY)
Title: A Combinatorial Description of the Knot Concordance Invariant Epsilon
Abstract: Sitting at the intersection of 4-dimensional topology and knot theory, the knot concordance group is an important object in low-dimensional topology whose structure is not yet fully explored and understood. One approach to study knot concordance is to use knot Floer homology, introduced by Ozsvath-Szabo and Rasmussen independently in early 2000s, and the invariants obtained from this theory. In this talk, I will describe the knot concordance, introduce some basic definitions of the combinatorial knot Floer homology called the "grid homology", explain our method of computing the concordance invariant epsilon and talk about some results. This is a joint work with S. Dey.
Link: Zoom recording Passcode: XPS9=s5%
Zoom-Seminars (Fall 2020)
21.12.2020, Speaker: Melih Üçer (Bilkent U.)
Title: Monodromy Alexander Modules of Trigonal Curves
Zoom video link Passcode: ^2?xx6XG
- 14.12.2020, Speaker: Burak Ozbagci
Title: Lefschetz fibrations on nonorientable 4-manifolds.
Abstract: I will discuss a few results about nonorientable 4-manifolds, using Lefschetz fibrations---with some applications to nonorientable 3-manifolds. This is a joint work with Maggie Miller.
Zoom link: Recorded video
- 7.12. 2020, Speaker: Bülent Tosun
Title: Symplectic and complex geometric aspects of the 3-manifold embedding problem in 4-space.
Abstract: The problem of embedding one manifold into another has a long, rich history, and proved to be tremendously important for the development of geometric topology since the 1950s. In this talk, I will focus on the 3-manifold embedding problem in 4-space. Given a closed, orientable 3-manifold Y, it is of great interest but often a difficult problem to determine whether Y may be smoothly embedded in R^4. This is the case even for integer homology spheres, and restricting to special classes such as Seifert manifolds, the problem is open in general, with positive answers for some such manifolds and negative answers in other cases. On the other hand, under additional geometric considerations coming from symplectic geometry (such as hypersurfaces of contact type) and complex geometry (such as the boundaries of holomorphically and/or rationally convex Stein domains), the problems become tractable and in certain cases a uniform answer is possible. For example, recent work shows for Brieskorn homology spheres: no such 3-manifold admits an embedding as a hypersurface of contact type in R^4, which is to say as the boundary of a region that is convex from the point of view of symplectic geometry. In this talk I will provide further context and motivations for this result, and give some details of the proof. This is joint work with Tom Mark.
Zoom-link: Recorded video, Passcode: @KXu3U4x
- 23.11.2020, Speaker: M.Korkmaz
Title: The lowest-slope Lefschetz fibrations
Abstract: In a joint work with Adalet Cengel, we obtained the lowest possible slopes, much lower than the known previous slopes. I am planning to explain this work.
Zoom video link
- 9.11.2020, Speaker: Inanc Baykur
Title: Lefschetz fibrations and symplectic geography
Abstract: We will discuss how to build symplectic Lefschetz vibrations with prescribed signatures and spin type, along with novel applications to the geography of symplectic 4-manifolds. This is joint work with N.Hamada.
Zoom video link