The HADES seminar on Tuesday, **April 16th**, will be at **3:30pm** in **Room 939.**

**Speaker**: Lizhe Wan, University of Wisconsin-Madison

**Abstract**: In this talk I will discuss the Cauchy problem of two-dimensional gravity water waves with constant vorticity. The water waves system is a nonlinear dispersive system that characterizes the evolution of free boundary fluid flows. I will describe the balanced energy estimates by Ai-Ifrim-Tataru and show that using this method, the water waves system is locally well-posed in $H^{\frac{3}{4}}\times H^{\frac{5}{4}}$. This is a low regularity well-posedness result that effectively lowers $\frac{1}{4}$ Sobolev regularity compared to the previous result.