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Explore advanced mathematical concepts through this comprehensive focus program featuring mini-courses and workshops on analytic function spaces and their diverse applications. Delve into fundamental topics including Hardy spaces, Dirichlet spaces, Bergman spaces, and model spaces through structured multi-part lecture series. Master specialized areas such as interpolation and sampling theory, bounded mean oscillation, de Branges-Rovnyak spaces, and truncated Toeplitz operators. Investigate cutting-edge research in Blaschke products and inner functions, discrete and continuous semigroups of composition operators, and the corona problem. Advance your understanding of non-commutative function theory, Drury-Arveson spaces, and convergence of scattering data with non-linear Fourier transforms. Participate in two advanced course tracks covering Schramm Loewner Evolution and lattice models alongside reproducing kernel Hilbert spaces of analytic functions. Engage with contributed talks on polynomial inequalities, dominating sets on Bergman spaces, and various specialized topics. Learn from expert presentations on frames and Riesz bases, exponential frames, dynamical sampling, and phase retrieval for wide band signals. Examine operator theory applications including Toeplitz operators, composition operators, and spectral theory for non-self-adjoint operators. Study geometric function theory through topics like conformal mappings, harmonic functions, and complex analysis applications to boundary value problems.
