BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Noriyoshi Sukegawa (Tokyo University of Science) DTSTART:20210527T150000Z DTEND:20210527T153000Z DTSTAMP:20260414T235812Z UID:MIP2021/28 DESCRIPTION:Title: Recent Advances in Diameter of Polyhedra\nby Noriyoshi Sukegawa (Toky o University of Science) as part of Mixed Integer Programming Workshop 202 1\n\n\nAbstract\nThe diameter of polyhedra has attracted attention for yea rs due to its connection with the complexity of the simplex algorithm. In particular\, giving sharp bounds on the diameter in terms of specified par ameters is a central topic in mathematical optimization and computational geometry. In this talk\, we will survey some recent results on the diamete r of polyhedra with emphasis on those for lattice polytopes. A lattice pol ytope means a polytope whose vertices are drawn from {0\,1\,...\,k}d (name ly\, here\, k and d are the parameters). It is known since the 1990s that the diameter of lattice polytopes behaves as Θ(k2/3) in dimension 2. We g ive an explicit expression for the diameter of lattice zonotopes in fixed dimension for infinitely many k\, which implies that the diameter of latti ce polytopes behaves as Ω(kd/(d+1)) in dimension d. This talk is based on joint work with Antoine Deza and Lionel Pournin.\n LOCATION:https://researchseminars.org/talk/MIP2021/28/ END:VEVENT END:VCALENDAR