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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The researchers participating in this workshop come from several mathematical subdisciplines, including combinatorics, algebraic geometry, and theoretical computer science. Their work and common interest here is to investigate new interactions between discrete mathematics, algebra, algebraic geometry, tropical geometry, and combinatorial algorithms. Some participants have collaborated before in smaller groups, but this meeting will provide an opportunity to work together more intensively. Several recent mathematical breakthroughs will be highlighted in the workshop, including the recent resolution of some long-standing open problems about graphs and matroids. These breakthroughs used a surprising combination of interdisciplinary techniques which the organizers expect to have exciting further applications.

Geometry and Topology,    Information Theory, Foundations of Computer Science

The Fields Institute

This workshop will bring together those working in pure Borel combinatorics with those studying the ergodic theory, dynamics, and geometry of countable groups. Featured topics will include Gaboriau's theory of cost, Borel and measurable chromatic numbers, Borel matchings, and amenable and hyperfinite equivalence relations.

The Fields Institute

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds, begun by S. Lefschetz, and well established by the late 1950's. Many of the important Artinian graded algebras appear as cohomology rings of an algebraic variety or manifold, though recent important developments have demonstrated important cases of the Lefschetz properties beyond such geometric settings (such as Coxeter groups or matroids). This renews interest in understanding the Lefschetz property, and Artinian algebras that admit them, systematically.

Algebra,    Geometry and Topology

University of Manitoba and University of Winnipeg

The general topic of the conference is the theory and application of discrete structures. Its goal is to highlight the most salient trends in the field. The conference will bring together researchers from the various disciplines with which discrete and algorithmic mathematics interact. Particular areas of interest include graphs and digraphs, hypergraphs, matroids, ordered sets, designs, coding theory, enumeration, combinatorics of words, discrete optimization, discrete and computational geometry, lattice point enumeration, combinatorial algorithms, computational complexity, and applications of discrete and algorithmic mathematics, including (but not limited to) web graphs, computational biology, telecommunication networks, and information processing. The conference will follow its usual format. There will be eight plenary talks, one public interest talk, and invited mini-symposia, as well as contributed mini-symposia and talks

Local Organizing Committee co-chair;     Phone: [+1-204-474-7486];     Email: karen.gunderson@umanitoba.ca

graphs and digraphs, hypergraphs, matroids, ordered sets, designs, coding theory, enumeration, combinatorics of words, discrete optimization, discrete and computational geometry, lattice point enumeration, combinatorial algorithms, computational complexity

CRM / Université de Montréal

The mini-courses and research talks will address several themes, including: nonpositively-curved cube complexes, median spaces, (coarsely) Helly spaces and groups, and various combinatorial notions of nonpositive curvature. The first week of the workshop involves mini-courses by Elia Fioravanti (MPI Bonn), Thomas Haettel (Université de Montpellier), Nima Hoda (ENS Paris), Nir Lazarovich (Technion). The second week will be devoted to research talks.

Geometry and Topology,    Group Theory

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The workshop is concerned with geometric objects arising from polynomial equations known as algebraic curves. Such curves have been studied extensively since the 19th century, but recent developments in combinatorics have led to a plethora of new techniques and solutions to major problems in the field. Bringing together experts from classical algebraic geometry and the adjacent combinatorial areas, the workshop aims to bridge the different points of views, identify key open problems in the field, and to examine how progress can be achieved via a combination of old and new tools.

Geometry and Topology,    Calculus, Differential Equations and Integration

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Despite the enormous commercial potential that quantum computing presents, the existence of large-scale quantum computers also has the potential to destroy current security infrastructures. Post-quantum cryptography aims to develop new security protocols that will remain secure even after powerful quantum computers are built. This workshop focuses on isogeny-based cryptography, one of the most promising areas in post-quantum cryptography. In particular, we will examine the security, feasibility and development of new protocols in isogeny-based cryptography, as well as the intricate and beautiful pure mathematics of the related isogeny graphs and elliptic curve endomorphism rings. To address the goals of both training and research, the program will be comprised of keynote speakers and working group sessions.