Explore free boundary problems for incompressible fluids in this conference talk by Senjo Shimizu. Delivered as part of the Inaugural Meeting of Asian-Oceanian Women in Mathematics, the 39-minute presentation delves into complex mathematical concepts related to fluid dynamics. Gain insights into cutting-edge research in this field, presented by a distinguished mathematician at the International Centre for Theoretical Sciences. Engage with advanced topics in applied mathematics and fluid mechanics, contributing to the broader discussion on women's achievements in mathematics across the Asian-Oceanian region.