This page contains links and recordings for the Geometry-Topology Seminar series. G/T seminars usually take place on Mondays, 15:40.
To receive seminar notifications, you can subscribe to the mailing list via an e-mail to serge [at] metu.edu.tr.
Hybrid (Zoom+face-to-face)-Seminars (Fall 2021)
- Speaker:Burak Özbağcı (Koç Üniv)
Link: Zoom recording
- 18.04.22, Speaker:Mustafa Korkmaz (ODTÜ)
Link: Zoom recording
- 20.12.2021, Speaker: Sergey Finashin (METU), Signed count of real rational curves on real del Pezzo surfaces
Abstract: In joint work with V.Kharlamov, we proposed a real enumeration invariant for del Pezzo surfaces based on a signed count of real rational curves, in which the signs are Welschinger invariants combined with the Pin-weights. It has strong invariance property (independence of the real structures) and is ``magically'' related to the corresponding Gromov-Witten count. Starting with a motivational example of a projective plane, I will introduce basic ingredients, describe our counting method, and present our ``magic'' relation.
Link: Zoom recording
13.12.2021, Speaker: Mustafa Korkmaz (METU), Constructing Lefsechetz fibrations with arbitrary signature
Link: Zoom recording
- 06.12.2021, Speaker: Alexander Degtyarev (Bilkent U.), Conics on polarized K3-surfaces
- 29.11.2021, Speaker: Özgür Kişisel (METU), On Complex 4-Nets
Abstract: Nets are certain special line arrangements in the projective plane that naturally occur in the study of resonance varieties, homology of Milnor fibers and fundamental groups of curve complements. It has been conjectured that the only 4-net realizable in the complex projective plane is the Hesse configuration. In this talk, I will outline our joint work with A. Bassa for proving this conjecture.
Link: Zoom recording, Passcode: 7+eSl$MN
- 08.11.2021, Speaker: Turgut Önder (METU), Existence of Almost Complex Foliations on Spheres
Abstract: An almost complex foliation is a foliation whose tangent bundle admits a complex structure. The existence problem of foliations on closed manifolds is reduced to the existence problem of plane fields in 1970’s by W.Thurston which can be attacked by algebraic topological methods. However, not much has been written about the existence problem of almost complex foliations. On spheres, I. Dibağ’s results provide concrete necessary conditions in terms of the dimension of the sphere and the dimension of the foliation. In this talk, we will present some results in the other direction, i.e about the sufficient conditions for the existence of almost complex foliations on spheres.
Link: Zoom recording, Passcode:
Zoom-Seminars (Spring 2021)
03.05.2021, 15:40, Speaker: Ferit Öztürk (Boğaziçi U.)
Title: Real contact 3-manifolds and isolated surface singularities
Abstract: We will present our work on real contact 3-manifolds the accumulated in time in collaboration with several colleagues (Nermin Salepci, Merve Seyhun Cengiz, Sinem Onaran). We will discuss a partial classification result on the real Milnor fillability of lens spaces. We will focus on some surprising negative results related with equivariant convexity of surfaces in real contact 3-manifolds.
Link: Zoom recording Passcode: 7J%EJ+%h
- 26.04.2021, 15:40, Speaker: Speaker: Nur Saglam
Title: Families of Lefschetz Fibrations via Cyclic Group Actions and Applications
Abstract: Using various diagonal cyclic group actions on the product manifolds Σ_gxΣ_g for g>0, we obtain some families of Lefschetz vibrations over S^2. Then, we study the monodromies of these families applying the resolution of cyclic quotient singularities. We also realize some patterns of singular fibers and study deformations of these Lefschetz vibrations. Some cases give rise to nice applications using rational blow-down operation. This is a joint work with Anar Akhmedov and Mohan Bhupal.
Link: Zoom recording Passcode: 3n&!HwU*
- 19.04.2021, 15:40, Speaker: Ferihe Atalan (Atılım U.)
Title: Connectedness of the cut system complex on nonorientable surfaces
Abstract: After introducing the cut system complex of a nonorientable surface N, I will mention its connectivity (j.w. Fatema Ali).
- 12.04.2021, 15:40, Speaker: Ergun Yalcin (Bilkent U.)
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