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International Colloquium on Randomness, Geometry, and Dynamics

The International Colloquium (IC) is the flagship conference of the School of Mathematics at TIFR Mumbai, organized once every four years.

The theme for IC 2024 is probability, geometric group theory and dynamics. Recent years have seen spectacular progress in these areas. Much of this progress has taken place at their interface, and connections between these fields have thrived. The IC 2024 will bring together experts from these research areas and cover topics including probability, hyperbolic geometry, geometric group theory, holomorphic dynamics, and homogeneous dynamics.

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Venue: IISER Pune

Aggregation-Diffusion Equations and Collective Behavior: Analysis, Numerics and Applications

The aim of this conference is to foster the development of new theoretical mathematical tools and methods of analysis, numerics, and applications in the field of nonlinear nonlocal aggregation-diffusion and kinetic equations within the broad area of PDEs.

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Venue: CIRM, Luminy

Renormalization and Visualisation in Geometry, Dynamics and Number Theory

In many areas of dynamics and geometry, the ideas of renormalization and self-similarity play a crucial role. These ideas involve rescaling dynamical or geometric phenomenon to observe behaviors at multiple scales. This conference will focus on the following problems:

  • Geometric models of digit algorithms
  • Symbolic models of unipotent dynamics
  • Renormalization in Interval exchanges and dynamical systems
  • Number theory and circle and sphere packings

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Venue: CIRM, Luminy

British Mathematical Colloquium

The University of Manchester is proud to host the 75th British Mathematical Colloquium, having organised the 1st, 25th and 50th editions as the Victoria University of Manchester and the 48th as UMIST. As well as bringing some of the world’s leading mathematicians, the organisers aim to provide the opportunity for postgraduate and early career researchers to present their work and mix with the British mathematical community.

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Venue: University of Manchester

Visions in Arithmetic and Beyond: Celebrating Peter Sarnak’s Work and Impact

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Venue: Princeton University and IAS

Young Geometric Group Theory XII

The purpose of this conference is to gather together early-career researchers working in the area of geometric group theory, to give them the opportunity to learn from each other and the senior mathematicians invited, to broaden their knowledge of geometric group theory, and to share their own research.

The main activity of the conference will be three mini-courses, each four hours long, which are intended to give an overview of key areas in geometric groups theory. These will be supplemented by four plenary talks in a colloquium-style format, and four research talks by early-career speakers.

As usual for YGGT, there will be a number of discussion sessions, which are informal parallel sessions on topics suggested by participants. There will also be an opportunity for lightning talks, as well as a poster session.

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Venue: University of Bristol

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