Kylerec 2017

Topic: Symplectic fillings of contact manifolds.

Date: May 19th-25th, 2017.

Location: A beautiful cabin on the top of a mountain near Truckee, CA.

Description: The focus of the workshop will be to study symplectic fillings of contact manifolds, both from the flexible and rigid viewpoints. A more detailed exposition of our mathematical goals can be found here.

Format: Kylerec is a student-led and student-run workshop. We will live in a communal setting, sharing cooking and cleaning responsibilities. Talks will be given by participants, with guidance from our mentors. Our vision is to curate a healthy, relaxed and creative atmosphere where we can learn mathematics together and make human connections in the process. There are no spectators, only participants! On one of the days there will be an afternoon hike through the beautiful peaks of the Sierra Nevada.

Mentors: Roger Casals, Steven Sivek, Laura Starkston

Organizing committee: Daniel Alvarez-Gavela, Roberta Guadagni, Oleg Lazarev, Kevin Sackel, Umut Varolgunes

Funding: Some funding may be available to cover travel expenses. Keep tuned.

Applications: Applications for Kylerec 2017 are open—please apply by filling out this form. The deadline for applications is April 8th. Our target participant is the young graduate student in symplectic topology, but all are welcome to apply. We are committed to promoting diversity in mathematics.

Contact: You are welcome to ask any questions by sending an email to kylerec2017@gmail.com

Schedule We will have four talks a day. The following is a tentative schedule:

Day 1 (5/20)—Introduction Introduction, types of fillings/fillability Weinstein handles, contact surgery Kirby calculus for Stein manifolds Lefschetz fibrations and open books
Day 2 (5/21)—Holomorphic curves Mapping class factorizations as Lefschetz fibration fillings J-holomorphic curves, intersection positivity, automatic transversality McDuff rational ruled classification Wendl planar open book filling result
Day 3 (5/22)—Mapping class factorizations High dimensional J-holomorphic curve classifications of fillings Applications of Wendl’s theorem to classifications of fillings Hike Hike
Day 4 (5/23)—Seiberg-Witten theory Intro to Seiberg-Witten invariants Symplectic Kodaira dimension 0 Fillings of unit cotangent bundles Lisca-Matic distinguishing fillings with SW
Day 5 (5/24)—High dimensions Flexible + loose SH, SH+, … Ustilovsky (application of SFT invariants, exotic contact) Oleg’s thesis (contact manifolds with flexible fillings and exotic contact structures)

About: Kylerec was born with the workshop on Lefschetz fibrations which was held in New Orleans during January 2016. We hope that this is the beginning of a long tradition. We are proud to draw inspiration from the long standing Talbot workshop in algebraic topology.

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New Orleans, January 2016

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Notes from the Kylerec 2017

Find below notes from the Kylerec 2017. Thank you to our note takers Orsola Capovilla Searle and Cédric De Groote. TALK 1 Roger Casals Introduction, types of fillings/fillability 01.roger.C 01.Roger.O TALK 2 Francois-Simon Fauteux-Chapleau Kirby calculus for Stein manifolds 02.francois-simon.C 03.francois-simon.O TALK 3 Orsola Capovilla-Searle Weinstein handles, contact surgery 03.orsola.C TALK 4 Alvin Jin Lefschetz … Continue reading Notes from the Kylerec 2017

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