International Workshop in Complex and CR Geometry, Partial Differential Equations and Invariant Theory

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This U.S.-Czech mathematics workshop with mini-courses will bring together a group of pioneering mathematicians who will interact with graduate and post doctoral students to examine approaches for improving accuracy in models for mathematical physics. Organizers, David Tartakoff of the University of Illinois-Chicago and Czech partner, Vladimir Soucek of Charles University, will direct a four-day program of expert lectures and interactive sessions to investigate Cauchy-Riemann (CR) geometry, sometimes called complex-real geometry, suggesting real submanifolds of complex spaces. Invited U.S. participants include M.S. Baouendi, J. J. Kohn, L. Lempert and Y.-T. Siu. Among the invited Europeans are leading Czech mathematicians, M. Bures, M. Englis, M. Kolar and J. Slovak. With a goal of developing general systems for partial differential equations, the workshop agenda is designed to integrate current discussions on key unsolved problems while exposing junior workshop participants to an emerging branch of mathematics.The envisioned interaction should benefit from U.S. expertise in CR geometry, partial differential equations and analytic methods in complex algebraic geometry. Similarly, the Czechs will contribute complementary strengths in parabolic geometry and invariant differential operators on manifolds. One important workshop objective is to explore links between invariant differential operators and the generalized Bernstein-Gelfand-Gelfand (BGG) complexes and curved versions. Results from this and other exchanges are expected to help define mathematically accurate models for complex analysis, mapping and geometry problems. This workshop fulfills the program objective of advancing scientific knowledge by enabling experts in the United States, the Czech Republic, and other European countries to combine complementary talents and share research resources in areas of strong mutual interest and competence. Broader impacts include early career introduction of U.S. graduate and post doctoral students to leading theorists and mathematicians in the European research community.