Yuqing Shi

Reading Seminar on Synthetic Spectra

From December 2021 till March 2021, Jack Davies and I ran a reading seminar on synthetic spectra. Our goal is to study the basics of synthetic spectra and discuss some of its applications. You're welcome to contact me or Jack if you are interested in participating the seminar.

Time and Location

The seminar will take place weekly on Mondays on Microsoft Teams. You can find the concrete time slot (CET) for each talk in the schedule below. Please contact Jack Davies or I if you want to be added to the MS Team.

Schedule

Basic notion on synthetic spectra

• Prerequisites on sheaves of spectra. 30.11.2020, Yuqing Shi. Notes.
• Adams-type homology theories and synthetic spectra. 07.12.2020, Jack Davies. Notes.
• Properties of synthetic spectra. 14.12.2020, Tommy Lundemo. Notes.

Synthetic spectra and motivic homotopy theory

• Synthetic spectra in motivic homotopy theory. 10:00 - 12:00, 25.01.2021. Achim Krause. Notes.

Synthetic spectra and manifold topology

• The metastable homotopy of MO<4n>. 17:00 - 19:00, 01.02.2021. Jeremy Hahn.
• The Thom spectrum MO<4n>. 16:00 - 18:00, 08.02.2021, Yuqing Shi. Notes.
• Proofs of Theorem 1.4 of 1910.14116v2. 16:00 - 18:00, 15.02.2021, Gijs Heuts. Notes.
• Studying the Toda bracket w using synthetic spectra. 16:00 - 18:00, 22.02.2021, Mingcong Zeng. Notes.

Synthetic spectra and chromatic algebraicity

• Introduction to chromatic algebraicity. 15:15 - 17:00, 01.03.2021, Haoqing Wu. Notes.
• Franke's algebraicity conjecture. 17:00 - 19:00, 08.03.2021, Piotr Pstrągowski. Notes.

More applications

• Classifying Morava K-theories as Azumaya algebras via synthetic modules. 16:00 - 18:00, 15.03.2021, Lennart Meier. Notes.
• Power operations and Balmer spectra of module categories 16:00 - 18:00, 22.03.2021, Robert Burklund.
• The chromatic structure of F_p-synthetic category 16:00 - 18:00, 29.03.2021, Robert Burklund.

Reference

• Robert Burklund, Jeremy Hahn, Andrew Senger. On the boundaries of highly connected, almost closed manifolds. Version 2. Dec. 02, 2019. arXiv:1910.14116v2.
• Bogdan Gheorghe, Daniel C. Isaksen, Achim Krause, Nicolas Ricka. C-motivic modular forms. Version 1. Oct. 25, 2018. arXiv:1810.11050v1.
• Michael Hopkins, Jacob Lurie. On Brauer groups of Lubin--Tate spectra I. Available online.
• Jacob Lurie. Spectral algebraic geometry. Available online.
• Piotr Pstrągowski. Chromatic homotopy is algebraic when p>n²+n+1. Version 2. Nov. 14, 2018. arXiv:1810.12250v2.
• Piotr Pstrągowski. Synthetic spectra and the cellular motivic category. Version 1. Mar. 08, 2018. arXiv:1803.01804v1.