This project will combine ellipses, the numerical range of square matrices, and Blaschke products around a single idea. We will explore how these objects connect and solve problems related to these ideas by using various tools of linear algebra, projective geometry, and complex analysis. We will explore specific questions such as

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• can we describe the interior curve generated by high degree Blaschke products,

• can we relate the interior curve generated by a Blaschke product and the distribution of its zeros,

• can we find a formula for the isogonal conjugate of any point in a given triangle?

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We will use the textbook Finding Ellipses as our reference point. There are many other project ideas and open problems in this book. We will supplement the book with articles and notes. Some of the subprojects will have computational flavor, and some others will be more theoretical. You can read the short description of the book on the AMS website to gain more information about the things we will investigate this summer. You can also have a look at the slides by one of the authors of the textbook here.

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