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Geometric Flows in Riemannian and Complex Geometry

This workshop will concentrate on parabolic methods in both Riemannian and complex geometry.  Topics will include:

  • Ricci flow. Analytic questions about Ricci flow in three dimensions. Possible applications of Ricci flow to 4-manifold topology. Ricci flow in higher dimensions under curvature assumptions.
  • Kähler-Ricci Flow. Applications to the Kähler-Einstein problem. Connections to the minimal model program. Study of Kähler-Ricci solutions and limits of Kähler-Ricci flow.
  • Mean curvature flow. Singularity analysis. Generic mean curvature flow.
  • Other geometric flows such as Calabi flow and pluriclosed flow.

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Venue: MSRI

Kähler Geometry, Einstein Metrics, and Generalizations

The workshop will integrate elements from complex differential geometry with Einstein metrics and their generalizaitons.  Topics will include:

  • Existence of Kähler metrics and extremal Kähler metrics. Notions of stability in algebraic geometry such as Chow stability, K-stability, b-stability, and polytope stability. Kähler-Einstein metrics with conical singularities along a divisor.
  • Calabi-Yau metrics and collapsed limit spaces. Connections with physics and mirror symmetry.
  • Einstein metrics and their moduli spaces, ε-regularity, noncompact examples such as ALE, ALF, and Poincaré-Einstein metrics. Generalizations of the Einstein condition, such as Bach-flat metrics and Ricci solutions.
  • Sasaki-Einstein metrics and metrics with special holonomy. New examples and classification problems.

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Venue: MSRI

AIMS Conference on Quadratic Differentials

Holomorphic differentials on Riemann surfaces have long held a distinguished place in several areas of low dimensional geometry, dynamics and representation theory.  More recently they have emerged in intriguing ways in the study of billiards in polygons, special (so-called Hitchin) components of representation varieties, stability conditions on Fukaya-type categories, spectral networks, and asymptotic properties of Higgs bundle moduli spaces.  This workshop will bring together a small number of experts at the forefront of these diverse areas to explore common themes and in particular to investigate the use of techniques that could potentially cross disciplinary boundaries.

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Venue: African Institute for Mathematical Sciences

Women in Topology

The Women in Topology network is an international group of female mathematicians interested in homotopy theory whose main goal is to increase the retention of women in the field by providing both unique collaborative research opportunities and mentorship between colleagues.  This meeting will be organized as an afternoon of short talks from participants, followed by two days of open problem seminars and working groups designed to stimulate new collaborations, as well as to strengthen those already ongoing among the participants.

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Venue: MSRI

Geometric Functional Analysis and Applications Workshop

This is the main workshop of the program “Geometric Functional Analysis and Applications”. It will focus on the main topics of the program, including: convex geometry, asymptotic geometric analysis interaction with computer science, signal processing, random matrix theory and other aspects of probability.

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Venue: MSRI

Recent Developments in Harmonic Analysis

This topical workshop will bring together researchers from the forefront of the field of harmonic analysis to discuss recent breakthroughs.  Topics will include: 

  • Restriction, Kakeya, and geometric incidence problems
  • Analysis on nonhomogenous spaces
  • Weighted estimates
  • Quantitative rectifiability and other topics in PDE

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Venue: MSRI

Constructions and Obstructions in Birational Geometry

The main aims of this workshop include reviewing the most important recent developments in birational geometry, relating to the explicit methods and toric varieties and degenerations on the Constructions side, and Chow groups, derived categories and the Grothendieck ring of varieties on the Obstructions side, and subsequently initiating the discussion between experts, leading to further progress in these two neighboring fields.  

Professor Claire Voisin (Collège de France) will give the Clay Lecture at this event.

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Venue: ICMS, Edinburgh

Nairobi Workshop in Algebraic Geometry

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Venue: University of Nairobi

Emergent Trends in Complex Function Theory

This workshop will be held in conjunction with CRM’s Intensive Research Program Spaces of Analytical Functions: Approximation, Interpolation, Sampling.  The Program will bring together leading experts in topical domains in Complex Analysis, Functional Analysis, and Approximation Theory working in approximation, interpolation and sampling problems in spaces of analytic functions and in their applications to spectral theory, Gabor analysis and random analytic functions. This field is an example of a fruitful interplay of complex analysis, abstract functional analysis and operator theory. The workshop Emergent Trends in Complex Function Theory  will contain three advanced courses consisting of three one-hour lectures each, up to six one-hour invited talks, and contributed talks delivered, mainly, by promising young mathematicians.

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Venue: Centre de Recerca Mathemàtica, Bellaterra, Spain

Women in Numbers Europe 3

The aim of this workshop is to allow young women doing research in numbers theory — graduate students, post docs, junior faculty — to initiate collaborations with confirmed researchers in the area.  Addiitonally, senior faculy will have the orpportuynity to enlarge or strengthen their research network and gain new mentorship opportunities.  A broad spectrum of topics in algebraic and analytic number theory and arithmetic geometry will be covered, including abelian varieties, K3 surfaces, Teichmüller curves, L-functions, modular curves, and arithmetic dynamics.

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Venue: La Hublais Center, Rennes

Thermodynamic Formalism: Applications to Probability, Geometry and Fractals

Thermodynamic formalism is an area of dynamical systems which originated in the 1960s and 1970s with the introduction of ideas of mathematical physics.  In the past few years it has undergone something of a renaissance with applications to many different areas, including Riemannian geometry, microlocal analysis, and analytic number theory.  This is an active area of research which has both intrinsic elegance and useful applications to neighbouring areas.

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Venue: CIRM. Luminy

Young Geometric Group Theory IX

The school will focus on four main speakers, each giving a 4-hour mini-course. Their lectures will present a panoramic overview of some important developments in their field with the goal of enabling the participants to actively participate in the new directions of research emerging from these developments. Special time slots will be reserved for active discussions of the participants under the moderation of the main speakers.

Serge Cantat, Groups of polynomial transformations
Anna Erschler, Growth and amenability of groups
Peter Haissinksy, Convergence groups
Nicolas Monod, Spaces of the third kind

In addition to the four main lecture series, a number of shorter presentations will explore recent developments in geometric group theory not covered by the main lectures. This is to broaden the scope of the workshop, and to encourage the participants to explore the boundaries of the subject.

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Venue: Saint-Jacut-de-la-Mer, France