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Thematic Program on Probability and PDEs

This research program will focus on two components of the interplay between differential equations and probability.  The first is how the introduction of randomness into differential equations affects their long-term behaviour.  The second component is how both probability and PDEs are used in mathematical models of group dynamics, and on the interplay between stochastic and PDE-based models.

Professor Kavita Ramanan (Brown) has been appointed as a Clay Senior Scholar to participate in this program.

CMI Enhancement and Partnership Program

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Venue: CRM, Université de Montréal

Complex Dynamics: From Special Families to Natural Generalizations in One and Several Variables

Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond. 

This semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. The organisers will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics. 

Professor Mikhail Lyubich (Stony Brook) has been appointed as a Clay Senior Scholar to participate in this program.

CMI Enhancement and Partnership Program

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Venue: MSRI

The Analysis and Geometry of Random Spaces

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers,  random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

Professor Nikolai Makarov (Caltech) has been appointed as a Clay Senior Scholar to participate in this program.

CMI Enhancement and Partnership Program

Details

Venue: MSRI