Explore the structure of the Kakimizu complex for genus one hyperbolic knots in a conference talk by Luis Valdez from The University of Texas at El Paso. Delve into the properties of this simplicial complex, including its dimensions, contractibility, and finite nature. Learn about the various configurations of the complex for different dimensions, ranging from 0 to 4, and discover examples that illustrate distinct types of the complex MS(K). Gain insights into the construction methods, including maximal collections, simple pairs, and geometric presentations, as well as the challenges in finding additional vertices. Examine the connections to naval cipher surfaces, graph properties, and universal bounds in this comprehensive exploration of low-dimensional topology and circle-valued Morse functions.