On mixing flows on finite-area translation surfaces

Key Points

• The aim is to find explicit examples of finite-area translation surfaces with strongly mixing vertical flows.
• Constructed an explicit family of translation surfaces
• Focused on finite-area and infinite-genus structures
• Demonstrated strong mixing properties of the vertical translation flow.
• Provided a positive answer to the mixing question posed by Lindsey and Treviño
• Showed that the constructed surfaces maintain strong mixing behavior under vertical flow.