Our website: Higher Structures Research Group at METU
About the Group. Within the framework of derived algebraic geometry, we can investigate certain well-known geometric structures in more general forms. For example, the literature describes and examines derived versions of symplectic and Poisson geometries. The theory of contact structures has also been developing in the derived context. In this regard, we work on the following two main directions:
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, Berat Geven, Emirhan Gür, Efe İzbudak, Saliha Kıvanç, Ali Ulaş Özgür Kişisel, Muhammed Şen, Hena Üçkum, Yasemin Yıldırım, more to come (fingers crossed)...and also all friends in the mailing list.
(I occasionally update the names; apologies if some are missing)
Activities. We organize research meetings, seminars, working groups, and ongoing/upcoming projects.
For more details or to subscribe to our mailing list, please contact KİB.
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 just wants to stop by and say hi) is very welcome and warmly invited! The tone will be mostly introductory, but sometimes technical.
This semester's plan: This semester features organizational innovations: We form 2 (+1) groups with different but related motivations:
Group A: HS for beginners. This group focuses on the basics of categorical constructions and introductory discussions. We aim to increase interest in categorical constructions and related topics within our department, especially among graduate and (junior/senior) undergraduate students. Group A will meet on Wednesdays at 18:00 (weekly or biweekly, starting Oct. 07, 2026). Topics mostly include the basics of category theory, an introduction to sheaf-theoretic constructions, and a glance at the formulation of higher spaces.
Group B: HS for advanced studies. This group focuses on topics related to ongoing research. It serves as preparation for the current research directions of the HS Research Group. Group B will meet on Tuesdays at 18:00 (weekly or biweekly, starting Oct. 13, 2026). Here is the link to the group page.
Group C: This secret society conducts ongoing research projects on derived geometry in an underground, top-secret lab. To get clearance for this level of secrecy, you need to hang out with us more and complete some Group A and Group B tasks!
See below for the schedule.
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, yielding many significant results. 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 and higher category theory.
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Schedule: almost every Tuesday (Group B) and Wednesday (Group A) at 18:00, lasting 2 hours, @İkeda room
Meeting 21 (Oct. 13, 2026): Group B -- Recent results on shifted (contact) structures (Speaker: KiB)
Meeting 20 (Oct. 07, 2026): Group A -- Intro to categorical constructions (Speaker: Emirhan Gür)
Topics usually include the basics of infinity categories, sheaf-theoretic constructions and higher spaces (e.g., stacks and their applications in geometry and physics), fancy categorical constructions (e.g., functorial field theories/TQFTs), and some discussions on derived geometry.
Schedule: Every (mostly )Wednesday or Thursday at 18:00, lasting 2 hours, @ikeda room
Meeting 19 (Apr. 14-15, 2026): Intro to higher category theory-V II(Speaker: Efe İzbudak)
Meeting 18 (Apr. 30, 2026): Intro to higher category theory-VI (Speaker: Efe İzbudak)
Meeting 17 (Apr. 22, 2026): Intro to higher category theory-V (Speaker: Efe İzbudak)
Meeting 16 (Apr. 17, 2026): Guest Speaker: Kürşat Sözer (Université de Lille), Extended TFTS.
Meeting 15 (Apr. 08, 2026): Intro to higher category theory-IV (Speaker: Efe İzbudak)
Meeting 14 (Apr. 01, 2026): Intro to higher category theory-III (Speaker: Muhammed Şen)
Meeting 13 ( Mar. 27, 2026): Guest Speaker: Kazım İlhan İkeda (BOUN-FGC), Condensed TQFTs
Meeting 12 (Mar. 12, 2026): Intro to higher category theory-II (Speaker: Muhammed Şen)
Meeting 11 (Mar. 04, 2026): Intro to higher category theory (Speaker: Muhammed Şen)
Our meetings are 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.
Meeting 10 (Dec. 22): Introduction to TQFTs, Speaker: Muhammed Şen
Meeting 9 (Dec. 22): Constructing spaces, Speaker: Efe İzbudak
Meeting 8 (Dec. 15): Moduli problems and stacks-II, Speaker: Efe İzbudak
Meeting 7 (Dec. 07): Moduli problems and stacks, Speaker: Efe İzbudak
Meeting 6 (Dec. 01): More examples of stacks, Speaker: KİB
Meeting 5 (Nov. 24): On presheaves of groupoids and stacks, Speaker: KİB
Meeting 4 (Nov. 10): Fancy things to do with 2-categories at home, Speaker: Hena Üçkum
Meeting 3 (Oct. 27): Civil War: 2-categories vs. Bicategories, Speaker: Emirhan Gür
Meeting 2 (Oct. 20): A Bluffer's Guide Part-II: Ways to talk about infinity categories at parties, Speaker: KİB
Meeting 1 (Oct. 13): A Bluffer's Guide Part-I: Ways to talk about infinity categories at parties, Speaker: KİB
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" of the International Center 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.