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It’s all about Moduli – Journal & Workshop

Published Feb 07, 2024

Our director Anna Wienhard is one of the Managing Editors of the newly launched open access journal 𝘔𝘰𝘥𝘶𝘭𝘪, and an organizer of the 2024 Summer Workshop in Mathematics at the Simons Center for Geometry and Physics, which is dedicated to the theme of moduli.

Moduli spaces appeared first in Riemann’s work to describe the quantities which parameterize (in modern terms) complex structures on a two-dimensional surface. Moduli spaces and their theory are now a fundamental topic that shows up in different forms across much of modern mathematics. Researchers approach the study of moduli problems using a vast array of techniques from algebraic, differential and arithmetic geometry, combinatorics, dynamical systems, gauge theory, geometric analysis, geometric group theory, mathematical physics, representation theory, and topology. Interactions across these different areas of mathematics are vital and the different perspectives add to the richness of the topic.

“With the journal Moduli we want to create a common forum, to bring researchers from different corners of mathematics together and build a community around the theme of moduli theory. We want to seize the opportunity to facilitate communications across disciplines, which subject specific journals might miss.”, says Anna Wienhard. The journal is led by a team of Managing Editors and supported by an Editorial Board of world-renowned researchers. It is owned by the Foundation Compositio Mathematica and published in collaboration with the LMS and Cambridge University Press. Further information about the journal and how to submit your paper can be found in the side box.

To promote this community-building, the editors of Moduli also plan to organize a series of events loosely affiliated with the journal. The first one will be the three-week 2024 Summer Workshop in Mathematics at the Simons Center for Geometry and Physics. It is dedicated to moduli and takes place from July 1-19, 2024. The workshop addresses both advanced graduate students as well as established researchers in other disciplines.  It will include several minicourses conducted by leading experts. It In addition, senior researchers will deliver talks sharing broad forward-looking perspectives. Each week will have a broad theme, but participants are encouraged to stay for multiple weeks, to allow for interactions between fields.

The weekly topics are:

  • Week 1 (July 1-5) - Moduli in differential and symplectic topology
  • Week 2 (July 8-12) - Moduli of Higgs bundles and the Langlands program
  • Week 3 (July 15-19) - Compactifications of moduli spaces

Applications for the workshop are open until March 1, 2024. Please visit the webpage of the Simons Center for Geometry and Physics to apply.