About the Group. Within the framework of derived algebraic geometry, one can investigate well-known geometric structures presented in more generalized forms. For example, derived versions of Symplectic and Poisson geometries have been described and examined. The theory of contact structures has also been developing in the derived context. In this regard, we work on the following two main topics and neighboring subjects:
The developing theory of shifted contact structures on derived stacks
Facets of shifted symplectic structures and their applications
Our members, so far. Mehmet Fırat Arıkan, Kadri İlker Berktav, Ali Ulaş Özgür Kişisel, İrem Özge Saraç, Muhammed Şen, Yasemin Yıldırım, more to come (fingers crossed)...
Activities. We organize research meetings, seminars, working groups, and ongoing/upcoming projects.
We aim to promote higher categorical constructions (mainly in geometry, topology, and physics) and increase interest in these topics within our department, especially among graduate and (junior/senior) undergraduate students. Of course, everyone interested in these topics (or who wishes to stop by to just say hi) is very welcome and warmly invited! The tone will mostly be less technical and/or introductory.
This semester's plan: Our meetings will be held on Mondays at 18:00 (weekly or biweekly, starting October 13, 2025). Topics will include the basics of infinity categories (following Lurie's higher topos book—at least we will try the first few sections—), sheaf theoretic constructions and higher spaces (e.g., stacks and their applications in geometry and physics), fancy categorical constructions: functorial field theories/TQFTs, and informal discussions on derived geometry.
For more details or to subscribe to our mailing list, please contact KİB.
Fibrations in Derived Symplectic and Contact Geometries (TÜBİTAK-1001, 2025-2028, @METU)
Significant results have emerged in Derived Algebraic Geometry, a rapidly developing field of mathematics, in the past 20 years, including intersection theory and moduli problems. Within that framework, various derived geometries, such as derived symplectic, Poisson, and contact geometries, have been studied in the literature, and many significant results have been obtained. With the same spirit, this project aims to investigate fibrations in derived symplectic and contact geometries and provide new results. Our main techniques include analogous constructions in derived symplectic geometry, as well as higher category theory.
The center aims to do research and provide a collaborative environment in Physics and Mathematics. I have been a Higher Structures Research Group member at FGC for several years. The Center organizes periodic local and international activities. The Center is located in Boğaziçi University Campus, Istanbul, Türkiye. In 2023, the Center was selected as an "affiliated center" to the International Centre for Theoretical Physics.
FGC's webpage: see the link
For online seminars, see the group's seminar page or researchseminars.org. To subscribe to the mailing list, contact Kazım İlhan İkeda (FGC-Boğaziçi Univ.).
Here is the Center's YouTube channel, where you can find a playlist of the recordings.