Workshop on birational geometry and stability of moduli stacks and spaces of curves

Workshop on birational geometry and stability of moduli stacks and spaces of curves

Thời gian: 08:30 đến 11:30 ngày 27/12/2013, 08:30 đến 11:30 ngày 26/01/2014, 08:30 đến 11:30 ngày 01/03/2014,

Địa điểm: C2-714

Báo cáo viên: Joe Harris, Jarod Alper, Ian Morrison, David Smyth, Emanuele Macri, Jack Huizenga, Ana-Maria Castravet, Angela Ortega, Arend Bayer, Gavril Farkas, Matthew Woolf

Tóm tắt:

Vietnam Institute for Advanced Study in Mathematics January 5-26 and February 9 – March 1, 2014

Overview and goals

We intend for the participants to shape the scientific agenda of the Workshop once at VIASM, but we anticipate areas of activity will include log minimal model programs and the associated Modularity Conjecture, GIT quotients with respect to linearizations of fixed degree, techniques for constructing weakly proper moduli stacks, bounds for ample and effective cones and connections to holomorphic differentials and Teichm¨ uller dynamics, applications of Bridgeland stability to related birational questions, and the clarification of empirically observed relations between these problems. Both the organization and the goals of the workshop will be unconventional, with the hope of creating mathematical opportunities not duplicated by other meetings with these themes. We have three main goals:

1. Introduce the Vietnamese mathematical community to the themes of the workshop through mini-courses of 2–4 lectures given by participants that progress from basic notions to more specialized ones.

2. Introduce the participants to Vietnam, its people and it scientific heritage, and initiate the development of longer term scientific connections between them and the Vietnamese mathematical community.

3. Facilitate intensive collaboration between participants on problems arising from their current research, and provide a sequel for the 2012 AIM workshop Log minimal model program for moduli spaces.

Organization

The unusual organization of the workshop is dictated by these goals and by the limited resources at VIASM’s disposal.

- Although workshop activities will take place over a 6 week period, most participants will be in residence in Hanoi only for 1–2 weeks.

- No formal conference is planned at any point during the workshop, although participants will be free to schedule research talks related to their collaborations in Hanoi. Participants will be free to devote the majority of their time to research activity of their choosing and the workshop will seek to facilitate this activity.

- The international visitors will offer two to three weekly seminars on basic notions connected with Workshop topics. These will begin at a level accessible to members of the Vietnamese audience who have a year or more of exposure at the graduate level to courses in commutative algebra and algebraic geometry, and each seminar will be followed by an informal hands-on problem session, led by one of the visitors.

- We also expect to arrange, with the guidance of the VIASM directorate, a program of two to three weekly field trips in Hanoi, led by Vietnamese participants in theWorkshop, to teach the international visitors some rudiments of Vietnamese language, life and culture.

We plan to post a calendar of dates for the international participants and a preliminary program for the weekly seminars here by the end of August.

Like any mathematical event, the success of the VIASM Workshop will depend on the energy of the participants. The organizers have heard much praise for the enthusiasm of VIASM students and faculty, and we know that many participants are equally excited about the opportunity to visit and work at the Institute. We are confident that theWorkshop will be both scientifically and personally rewarding both for the Vietnamese and international participants.