Abstract: In this talk I will present a complete solution to the Ovals problem, which corresponds to determining the best constant in a Poincare-type inequality on functions defined on the unit circle and subject to an angular constraint. This problem has attracted a lot of attention in the past 30 years due to its connections to certain Schrodinger operators and Lieb-Thirring inequalities. The solution relies on an optimal control approach. This is joint work with J. Denzler, F. Jean and E. Trelat
