the level set topology optimization method has been drawing attention as a method to integrate conceptual design to manufacturing. the use of level set method has a distinct advantage in naturally handling splitting and merging of boundaries. topology optimization has been identified as the ideal design method for additive manufacturing and many case studies quote revolutionary weight saving or performance improvement in the order of 20% - 80%. my research has been developing the level set topology optimization method for engineering design problems. this seminar will present the existing challenges that will potentially benefit from collaboration with mathematics.