Spring 2026: Working Seminar in Contact and Symplectic Topology

Instructor: Bahar Acu

E-mail: baharacu [at] gmail [dot] com

Meetings:

Time: 11:00am-1:00pm

Place: Anderson Hall (Fen-Edebiyat Fakültesi), 

Second meeting point: TB120 (We will then move over to the new Math Library (TB115-7) altogether!)

Useful external links:

• See BU Academic Calendar for important dates.

Objectives:

This working seminar aims to provide a glimpse of two sister geometries that have earned a central role in mathematics interacting with other areas in the past two-three decades. Side by side, we will discuss basics of contact and symplectic manifolds, some key submanifolds (Legendrian and Lagrangian) and their topological characterizations via open book decompositions and Lefschetz fibrations, which have gained prominence as testing grounds for other theories. 

By giving talks about each geometry, typing up notes for those talks, and participating in talks by others, each participant will have the opportunity to get acquainted with the landscape of symplectic and contact worlds, expand their command of geometry and topology, and develop presentation and collaboration skills.

This course is designed to be an iteration of the successful working seminar at ETH Zürich titled Student Seminar in Symplectic vs. Contact Geometry

Topics: We will be covering basics of

• Morse Theory: Handlebody Calculus

• Lefschetz Fibrations

• Open Book Decompositions

• Symplectic and contact geometry

• Symplectic Mapping Class Groups

• Symplectic Fillings of Contact Manifolds

Prerequisites:

Prior knowledge of (basics of) differential geometry and point-set topology is required. Details of the seminar organization will be discussed during the organizational meeting on Monday, February 16, 2026.

Suggested references and readings:

1. An Introduction to Morse Theory by Yukio Matsumoto

2. Lectures on Symplectic Geometry by Ana Cannas

3. Introduction to Symplectic Topology by Dusa McDuff and Dietmar Salamon

4. Lecture Notes on Contact Geometry by Ko Honda

5. Introduction to Contact Topology by Hansjörg Geiges (c.f. brief version.)

6. From Stein to Weinstein and Back by Kai Cieliebak and Yasha Eliashberg

7. 4-Manifolds and Kirby Calculus by Robert Gompf and András Stipsicz

8. Contact Geometry: From dimension three to higher dimensions by Emmanuel Giroux

9. Convexity in Contact Topology by Emmanuel Giroux

10. Contact Open Books and Symplectic Lefschetz Fibrations, Bahar Acu

11. Surgery on Contact 3-Manifolds and Stein Surfaces by Burak Özbağcı and András Stipsicz

12. A Primer on Mapping Class Groups by Benson Farb and Dan Margalit

13. Constructions of Contact Manifolds by Hansjörg Geiges

Tentative Plan:

• The organizational meeting will take place on February 16, 2026.

• Weeks 7 through 12 will be devoted to student presentations. Each presentation will be preceded by a preparation phase, including a Zoom meeting with the instructor during Weeks 4 through 6. Please see the schedule below for a detailed description and timeline.

• Students will be asked to closely follow the notations and conventions file shared below.

• Prior to each presentation, presenters will share their LaTeX'd lecture notes to be uploaded to this website. Each presenter will then have a week following their presentation to submit their finalized notes.

_________

Tentative Weekly Plan:

For the sake of consistent presentations and lecture notes, please follow the notations and conventions here:

Notations and Convention (TBA)

1. Week 1: February 16, 2026

   • Organizational meeting and Overview @ TB120

2. Week 2:  February 23, 2026

   • Bahar Acu: Morse Theory and Handlebody Calculus

3. Week 3: March 2, 2026

   • Bahar Acu: Lefschetz Fibrations and Open Book Decompositions

4. Week 4: March 9, 2026

   • Preparation/Reading Week: Group Meetings

     • Meeting with Week 7 Speakers

     • Meeting with Week 8 Speakers

5. Week 5: March 16, 2026

   • Preparation/Reading Week: Group Meetings

     • Meeting with Week 9 Speakers

     • Meeting with Week 11 Speakers

6. Week 6: March 23, 2026

   • Preparation/Reading Week

     • Meetings with Week 12 Speakers

7. Week 7: March 30, 2026

   • An Introduction to Contact Manifolds and Legendrian Submanifolds 

     • Speaker 1: Şeyma Karadereli

     • Speaker 2: Ronahi Haykır

8. Week 8: April 6, 2026

   • Giroux Correspondence and Convexity in Contact Topology

     • Speaker 1: Kerem Kubilay

     • Speaker 2: Hasan Yılmaz

9. Week 9: April 13, 2026

   • An Introduction to Symplectic Manifolds and Lagrangian Submanifolds

     • Speaker 1: Kaan Çim

     • Speaker 2: Fatih Duymuş

10. Week 10: No Meeting! (Spring Break)

11. Week 11: April 27, 2026

    • An Introduction to Weinstein/Stein/Liouville Manifolds and Symplectic Fillings

      • Speaker 1: Cem Yalım Özel

      • Speaker 2: Cahit Erdem Anıl

12. Week 12: May 4, 2026 (Final Meeting)

    • An Introduction to Symplectic Mapping Class Groups

      • Speaker 1: Canan Özeren

      • Speaker 2: Berkay Taştan

      • Speaker/Mentor: Öykü Yurttaş

13. Week 13: No Meeting! IMBM Istanbul Topology Days, May 14-17, 2026.