Abstract:
The Generalized Lower Bound Theorem states that the \$g\$-numbers of any simplicial \$(d-1)\$-sphere are nonnegative. Moreover, equality \$g_i = 0\$ holds for some \$1 \le i \le d/2\$ if and only if the sphere is \$(i-1)\$-stacked. Such a sphere must have missing faces in dimension greater than \$d-i\$. This naturally leads to the following question: what lower bounds can be established for the \$g\$-numbers of simplicial spheres with no large missing faces?
In this talk, I will discuss several open problems related to this question and describe recent progress. A central tool in our approach is stress theory; I will explain how stress spaces can be used to derive lower bounds on the \$g\$-numbers. As an application, I will present a complete characterization of simplicial \$5\$-spheres with no missing faces of dimension \$>3\$ that satisfy \$g_3 = 1\$. This is joint work with Isabella Novik.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974