Number theory has been called the queen of mathematics, and it is known for its deep and challenging problems, for its unexpected connections to diverse branches of mathematics. On the other hand, number theory might not be the topic that you associate with pretty pictures. In this talk, Dr. Khoury aims to convince you that number theory abounds not only with beautiful ideas and intriguing problems but also with compelling visual appeal. Bertrand Russell famously wrote that mathematics possesses “a beauty cold and austere”; Mr. Russell will not be invited to this talk.
The main body of the talk will explore two of his favorite topics in number theory: integral Apollonian circle packings and modular forms. Each leads not only to some beautiful pictures, but also to beautiful mathematics and open questions, some suitable for undergraduate research. Time permitting, Michael will introduce further interesting problems for those interested in the beautiful mathematics of numbers. This is intended as a friendly and accessible talk with something to offer for faculty and students of mathematics alike.