Shoemaker Lecture Series with Dr. Christopher Halcon, "On the Geometry of Polynomial Equations"

Lecture I of the Fall 2026 Shoemaker Lecture Series, featuring renowned mathematician Dr. Christopher Hacon of the University of Utah. Hacon is a leading expert in algebraic geometry, a member of the National Academy of Sciences and a Fellow of the Royal Society. He also shared the 2018 Breakthrough Prize in Mathematics for his contributions to birational algebraic geometry. Abstract: Algebraic geometry is the study of geometric objects given by the solutions of polynomial equations. One can consider solutions given by rational numbers, real numbers, complex numbers and so on. In this talk I will discuss solution sets given by complex numbers. In complex dimension one, smooth projective curves give rise to compact Riemann surfaces of genus g ≥ 0, which look like spheres with g handles. While the Riemann sphere is the only example with genus zero, there is a one-parameter family of Riemann surfaces of genus one and a (3g − 3)-parameter family of Riemann surfaces of genus g ≥ 2. Remarkable recent advances show that a similar picture holds in all dimensions. Visitor parking on campus requires payment through the ParkMobile app , a parking meter or a daily permit via ParkUToledo. Visit the ParkUToledo website for more information.