Talbot 202One: Ambidexterity in Chromatic Homotopy Theory

Mentored by Jacob Lurie and Tomer Schlank

October 24-30, 2021
Plymouth→Boston, MA

Update April 2021: Due to the ongoing COVID-19 Pandemic, we are rescheduling the 2020 workshop to Fall 2021. We tentatively plan to hold the workshop in October, predicated on positive progress in the US related to vaccination and reopening.

Topic: A primary aim of chromatic homotopy theory is to understand the stable homotopy category by decomposing it into pieces (called chromatic localizations) which are, at least in principle, easier to understand. These chromatic localizations enjoy a certain duality property called ambidexterity, which guarantees that certain homotopy limits can be understood as homotopy colimits (and vice versa). The goal of this workshop is to explain the mathematics of ambidexterity and some of its applications.

Please see the preliminary syllabus for more detailed information.

Suggested prerequisites: Some knowledge of chromatic homotopy theory will be expected; while the workshop will feature a review lecture on the topic, this will be insufficient if the topic is entirely new to participants. Additionally, participants should have familiarity with the language of infinity categories.

Mentors: The 2020 Talbot workshop will be mentored by Prof. Jacob Lurie of the IAS and Prof. Tomer Schlank of The Hebrew University of Jerusalem.

Format: The workshop discussions will have an expository character and most of the talks will be given by participants. The afternoon schedule will be kept clear for informal discussions and collaborations. The workshop will take place in a communal setting, with participants sharing living space and cooking and cleaning responsibilities.

Update (September 2021): The workshop will be held in a hybrid format, with some in-person participants and some virtual participants. In-person participants should expect to follow mitigation measures such as regular Covid-19 antigen testing, masking in indoor common spaces, and meals taken in a socially distanced/outdoor setting. For virtual participants: we will do our best to create a virtual environment with resembles the workshops of the past. Both in-person and virtual participants will give talks.

Timeline: The 2020-21 Talbot workshop will take place in October 2021. The application is now closed.

Funding: We cover all local expenses, including lodging and food. We also have limited funding available for participant travel costs.

Who should apply: Talbot is meant to encourage collaboration among young researchers, particularly graduate students. To this end, the workshop aims to gather participants with a diverse array of knowledge and interests, so applicants need not be an expert in the field. In particular, students at all levels of graduate education are encouraged to apply. Our decisions are based not on applicants' credentials but on our assessment of how much they would benefit from the workshop. As we are committed to promoting diversity in mathematics, we also especially encourage women and minorities to apply.

Inclusiveness statement: In accordance with the Statement of Inclusiveness, this workshop will be open to everybody, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We are committed to ensuring that the Talbot Workshop is a supportive, inclusive, and safe environment for all participants, and that all participants are treated with dignity and respect.

Contact Information: Please email the organizers at talbotworkshop(at)gmail.com if you have any questions.