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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

Algebra,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

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.

The Fields Institute for Research in Mathematical Sciences

This workshop will accelerate development of new directions in chromatic and unstable homotopy theory and in the homotopy theory of polyhedral products. Key will be the exploration of areas of interaction: unstable homotopy theory and polyhedral products have substantial existing intersection while recent developments in chromatic homotopy theory suggest exciting new intersections with unstable homotopy theory and polyhedral products.

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Interactions between Group Theory and Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Interactions between Group Theory and Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

Kurse und Veranstaltungen für Studenten der Mathematik,    Gruppentheorie

The Fields Institute for Research in Mathematical Sciences

Group theory and topology have a long and rich history of interaction. This workshop will bring together experts working on different aspects of this interaction in order to share ideas and boost the development of new methods that can be applied to the topology of configuration spaces, braid groups, mapping class groups and manifolds, and spaces of commuting elements.

Gruppentheorie,    Kurse und Veranstaltungen für Studenten der Mathematik