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  1. Program Complementary Program 2021-22

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program.

    Updated on May 03, 2022 02:54 PM PDT
  2. Program The Analysis and Geometry of Random Spaces

    Organizers: LEAD Mario Bonk (University of California, Los Angeles), Joan Lind (University of Tennessee), Steffen Rohde (University of Washington), Eero Saksman (University of Helsinki), Fredrik Viklund (Royal Institute of Technology), Jang-Mei Wu (University of Illinois at Urbana-Champaign)
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    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.

    Updated on Dec 21, 2021 12:37 PM PST
  3. Program Complex Dynamics: from special families to natural generalizations in one and several variables

    Organizers: LEAD Sarah Koch (University of Michigan), Jasmin Raissy (Institut de Mathématiques de Bordeaux), Dierk Schleicher (Université d'Aix-Marseille (AMU)), Mitsuhiro Shishikura (Kyoto University), Dylan Thurston (Indiana University)
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    The mating of these two dendritic Julia sets is equal to the Julia set of a rational map of degree 2; that Julia set is equal to the entire Riemann sphere. Picture by Arnaud Chéritat

    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. 

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

    Updated on Jan 20, 2022 09:31 AM PST