Goals
This workshop will explore the foundations of the enumerative theory of pseudo-holomorphic curves. We will address the analytic theory (including basic linear elliptic theory, Sobolev spaces, and non-linear elliptic analysis), the derived geometry necessary to construct moduli spaces as derived smooth manifolds, and the interpretation of the resulting enumerative invariants in stable homotopy theory.

We also hope the workshop will help to (i) Strengthen the fabric of collaborators and young mathematicians, (ii) Prepare participants to engage with current and future research directions of the field, and (iii) Continue to create the foundations for a vibrant community of emerging researchers of varied interests.

Inclusiveness statement
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 workshop is a supportive, inclusive, and safe environment for all participants, and that all participants are treated with dignity and respect.

Format
This workshop is modeled on the Talbot workshop. All participants will spend the week in the Catskill foothills, sharing in both mathematical and communal activities such as giving talks, cooking meals, being on cleaning teams, and going for walks. Participants will be assigned their talk topics beforehand, and are strongly encouraged to prepare their talks in the months prior to the workshop with support from the organizer and mentor. In an effort to build community and to explore the mathematics, the workshop will aim to provide ample time for discussion and socializing.

Funding
We will provide lodging for all participants, and give some travel funding for students. Please indicate any requests for funding when you register. We strongly encourage all participants to explore other funding opportunities to help the workshop support as many participants as possible, and for potential participants to reach out to the organizer with any questions or concerns about financial support.

Applying The application deadline was Tuesday, December 10th, 2024. We will try to get back to applicants about acceptance decisions by January 1, 2025. We seek to gather a varied group of junior mathematicians (Master's and PhD students, post-docs, early career researchers, and some undergraduate mathematicians) of all backgrounds, with the main prerequisite being a willingness to engage with the learning and exploration of the mathematics.

The National Science Foundation (through Award DMS 2044557) and the Math Department of Texas State University (through substantial logistical support) have made this workshop possible.