Explore a lecture on homological mirror symmetry and logarithmic geometry presented by Bernd Siebert from the University of Texas. Delve into the development of a natural logarithmic analogue of the ordinary Hilbert scheme, a collaborative effort with Mattia Talpo and Richard Thomas. Discover immediate applications, including induced good degenerations of Hilbert schemes of points, and gain insights into the potential definition of tropical Hilbert schemes. Examine how logarithmic methods can be applied to coherent sheaves in maximal degenerations within mirror symmetry. Cover topics such as parabolic sheets, plot schemes, logarithmic structures and ideals, tropical curves, and basic minimal art structures throughout this in-depth, hour-long presentation.