This project will be run by Nathan Wagner and Yunus Zeytuncu.

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The project aims to unite ellipses, the numerical range of square matrices, and Blaschke products under a cohesive framework. We will explore the intricate connections between these mathematical objects and address related problems using tools from linear algebra, projective geometry, and complex analysis. In addition to these theoretical and classical inquiries, we will introduce several new directions using experimental mathematics and artificial intelligence tools. The project will focus on various properties of Toeplitz operators on Bergman spaces. We will focus on properties such as zero-products, Lₚ mapping properties, spectral analysis, Berezin transform, and compactness. We will study these operators on various domains in ℂⁿ where we will explore the relationship between these analytical properties of the operators and the geometry of the underlying domain.

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