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Nonlinear Dispersive and Wave Equations: Recent Developments and Future Directions

In the past two decades the field of dispersive and wave equations has witnessed a remarkable amount ofd. successful research that has been underlined by the use of tools for a broad spectrum of analytic areas: harmonic and Fourier analysis, hyperbolic theory, microlocal analysis, differential geometry, probability, analytic number theory and dynamical systems.

The conference will focus on a number of different areas, including well-posedness for critical and supercritical Schrödinger and wave equations, blow up, profile decomposition, soliton resolution conjecture, invariance of Gibbs measures and well-posedness of dispersive equations with random data, Strichartz estimates and related results in harmonic analysis, energy transfer and derivation of wave kinetic equations.

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Venue: Monash University

Mapping Class Groups: Pronilpotent and Cohomological Approaches

The mapping class group (in short, MCG) of a surface is a fundamental object of study in topology and in geometry, where it is regarded as the orbifold fundamental group of the moduli space of Riemann surfaces homeomorphic to the surface. Based on Tillman’s works, Madsen and Weiss proved that the stable part of the rational cohomology algebra is generated by the Mumford-Morita-Miller tautological classes. Before that, Johnson proposed to study the MCG through its action on the pro-nilpotent completion of the fundamental group of the surface. The two approaches to the mapping class group — cohomological and pro-nilpotent — were bridged in Morita’s works.

Recently, new developments occured: functor homology proved to be very useful to compute the twisted cohomology of the MCG, and the theory of “Johnson homomorphisms” benefited from explicit computations in small degrees. Furthermore, the theory was related to quite different topics:  the anabelian geometry of Grothendieck, the universal finite-type invariants of 3-manifolds, the Goldman-Turaev Lie bialgebra or the Kashiwara-Vergne problem.

The purpose of this conference is to strengthen these recent advances on cohomological and pro-nilpotent approaches of the MCG at the crossroad of algebraic topology, low-dimensional topology, group theory, number theory and Lie theory. Thought of as a sequel to the series of workshops “Johnson homomorphisms and related topics” held in Tokyo in the last years, it is intended to reach a wide community of mathematicians across Europe and beyond.

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Venue: SwissMAP Research Station

Elias M. Stein Memorial Conference

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Venue: Princeton University

Shape Optimization and Isoperimetric and Functional Inequalities

This workshop will bring together specialists working on topics involving geometric inequalities, isoperimetric and functional inequalities, partial differential equations on variable domains, with particular attention to the dependence of the solutions of the state equations (generally partial differential equations) on the geometry of their domain of definition and will include specialists on the following topics :

– shape optimization problems
– isoperimetric and functional inequalities
– free boundary problems ;
– spectral optimization problems ;
– convex geometric tools and geometric inequalities ; – free boundary regularity of optimal shapes
– numerical aspects of singular shapes ;
– geometric flows and PDE’s.

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Venue: Levico Terme, Italy

Young Topologists Meeting

The fifteenth edition of the Young Topologists Meeting will take place in July 2023 at EPFL, Lausanne, Switzerland. This meeting, which was organized for the first time in Switzerland in 2007, aims to bring together young researchers in topology in order to share and discuss their research. It has become an esteemed event in the field. 

Image: Mediacom EPFL, Wikimedia Commons

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Venue: EPFL

Noncommutative Geometry and Representation Theory

The aim of the meeting is to explore newly emerging interactions between C*-algebras and unitary representation theory on one side, and regularity properties of linear PDE, especially hypoellipticity, on the other, as well as current and future potential applications.

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Venue: National and Kapodistrian University of Athens

Iwasawa 2023: in Memory of John Coates

The Iwasawa conferences are an international conference series that has been taking place roughly biennially since 2004 and is the established regular conference that updates the research community on progress in Iwasawa theory. The focus of the 2023 meeting will be slightly wider to reflect the interests of John Coates. 

Coates made fundamental contributions to our understanding of elliptic curves, L-functions and the Birch–Swinnerton-Dyer conjecture, and was one of the founders of Iwasawa theory of elliptic curves and of non-commutative Iwasawa theory. He held the Sadleirian chair of mathematics at Cambridge until his retirement (1986–2012), was elected a fellow of the Royal Society in 1985, and served as the President of the London Mathematical Society in 1988–1990.

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Venue: University of Cambridge

String Math 2023

The University of Melbourne will host String Math 2023, an annual conference held in different locations around the world (and next year for the first time in Australia). Its aim is to cover the most important recent developments at the interface between string theory, quantum field theory and mathematics, while keeping a rough balance between physics and mathematics, stimulating interactions between the two communities.

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Venue: University of Melbourne

Foundations of Computational Mathematics, FoCM 2023

The FoCM 2023 Conference in Paris will build upon previous FoCM conferences and will make it a unique meeting point of specialists in computational mathematics and of researchers in mathematics and in computer science. The emphasis will be on multidisciplinary interaction across subjects and disciplines, in an informal and friendly atmosphere. The mornings are devoted to plenary lectures delivered by some of the foremost world authorities, and during the afternoons participants split into 7 workshops of the highest technical level. The organizers and committed participants of the conference have an outstanding history of intellectual and service contributions to the foundations of computational mathematics. Detailed planning of the conference program is well advanced. The organizers of the 21 workshops are chosen to include both established senior and talented junior researchers, their potential, diversity and creativity promising a vibrant scientific program.

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Venue: Sorbonne Université

A Panorama of Homotopy Theory

This conference will bring together three overlapping and interacting communities: equivariant and motivic homotopy theory, derived algebraic geometry, applications of homotopy theory in physics. The organizers will strive to represent the unity of the vast and still growing subject of homotopy theory. Sub-communities that have developed over time will thus again sit next to each other, their common history giving them a common language and tool set. This will enable mutual stimulation, exchange and cross-fertilisation.

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Venue: University of Oxford

Advances in Nonlinear Analysis and Nonlinear Waves: a Conference in Honor of Frank Merle

Since his early articles in the 1980s, Frank Merle’s work has been mostly centered on the mathematical analysis of nonlinear partial differential equations with Hamiltonian structure, like dispersive and wave equations, appearing in problems of wave propagation. In the 1980s, basic properties of these equations were established, notably the existence and stability properties of special solutions called solitons.  In the 1990s, the introduction of tools from harmonic analysis led to a refined understanding of the properties of the linear equations and how to extend them to nonlinear equations by perturbation. In this context, breakthrough works on the local well-posedness problem for such equations by Kenig-Ponce-Vega, Bourgain, Tao and others, were extremely influential. In particular, the notion of criticality appeared (invariance by scaling). The remaining problem of understanding qualita- tively the long-time dynamics of solutions, in relation with solitons have attracted considerable interest in the last thirty years. Frank Merle has enormously contributed to such questions in di↵erent directions : blowup in finite time, multi-solitons, collision of solitons, classification of solutions, soliton resolution conjecture. Very often, his surprising and disruptive ideas have strongly influenced the field. During the conference, Pierre Rapha ̈el (Herchel Smith Professor of Pure Mathematics at the University of Cambridge), former PhD student and long-term collaborator of Frank Merle, will give a talk summarizing Merle’s main contributions and ideas.  In this conference, several of the best worldwide experts in the field of dispersive and wave equations will present various aspects of their recent advances. 

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Venue: Institut des Hautes Études Scientifiques and Cergy Paris University

New Perspectives in Pure Mathematics

In recent years, reasearch in pure mathematics has flourished.  Often the most notable advances and breakthroughs have come from researchers drawing upon results and techniques from other areas, or finding applications in other areas.  This three-day conference will focus on the interaction between algebra, combinatorics, geometry, logic, number theory, and topology.  The invited speakers are excellent researchers whose work cuts across and combines various areas within pure mathematics and theoretical computer science.

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Venue: University of Bristol