Lei Xue, University of Washington

Online only via Zoom Link: https://washington.zoom.us/j/91547335974
Abstract:
In 1967, Grünbaum conjectured that any \$d\$dimensional polytope with \$d+s\leq 2d\$ vertices has at least $$\phi_k (d+s,d) = {d+1 \choose k+1} + {d \choose k+1}  {d+1s \choose k+1}$$ \$k\$faces. In the talk, we will prove this conjecture and discuss equality cases. We will then extend our results to lattices with diamond property (the inequality part) and to strongly regular normal pseudomanifolds (the equality part). We will also talk about recent results on \$d\$dimensional polytopes with \$2d+1\$ or \$2d+2\$ vertices.
Note: There will be no preseminar this week—the main talk will start at 3:30. This talk will be online only.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974