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Université du Québec à Montréal (UQAM)

The proposed three-day workshop will focus on interrelated mathematical advances in each of the following highly active areas of current research: complex birational geometry (led by MMP), K-stability, and moduli spaces. These domains are of fundamental importance for the (birational) geometry and classification of complex projective varieties as well as for the understanding of their moduli spaces. The workshop will focus on some of the current frontiers that are of particular importance to each of these areas.

In addition to encouraging and stimulating interactions between relevant experts, the workshop will provide a valuable opportunity to explain to interested graduate students and young researchers the details of the techniques used through mini-courses and specialized lectures. Many speakers are renowned speakers in addition to being leading experts in their field. In particular, the workshop plans to have three mini-lectures, one by Sándor Kovács on the now classical and important KSBA (Kollar-Shepherd-Baron and Alexeev) compactification of moduli spaces, one by Chenyang Xu on the recent roles of the MMP on K-stability and one by Kenneth Ascher on K-moduli and the role of moduli space theory. In addition to our guest speakers, we intend to involve graduate students and postdocs.

minimal model program, K-stability, moduli space, varieties, birational geometry, GIT, Yau-Tian-Donaldson conjecture, PDE

Geometry and Topology,    Calculus, Differential Equations and Integration

Simons Laufer Mathematical Sciences Institute (SLMath)

The 2025 SMS will allow graduate students to learn about a number of recent trends and advances in the field of commutative algebra. The aim of the SMS is to provide an “on-ramp” for graduate students interested in algebra, combinatorics, and/or algebraic combinatorics to learn more about commutative algebra’s interaction with these fields. The introductory courses will introduce fundamental skills in commutative algebra, the more intermediate courses will expose students to cutting-edge research in the field. The school will focus on four topics within commutative algebra: Combinatorial Methods, Homological Methods, Computational Methods, and Characteristic p Methods. The SMS will provide both a series of introductory lectures and intermediate/advanced lectures from leaders in one of the four areas. The lectures will include a series of problem sessions that will allow participants to develop and hone their skills in these areas, which will be especially helpful for new people to the field. Participants will be encouraged to work collaboratively, both to enhance their own mathematical networks as well as to promote future collaborations beyond the school.

The Fields Institute for Research in Mathematical Sciences

Homotopy theory is in the midst of a renaissance as its usefulness in other areas of mathematics is becoming increasingly recognised. From polyhedral products in geometric group theory, to combinatorial methods in group theory, to topological properties of manifolds and spaces of embeddings, to Morava K-theory in symplectic geometry, to simplicial methods in topological data analysis, to a host of applications in mathematical physics - and these name only a few areas of interaction - homotopy theory over the past ten to fifteen years has significantly extended its reach. This program will assemble a wide range of leading experts to discuss the state of the art in current research, both in terms of core fundamental problems and crossover to other areas, and explore exciting new directions.