## January 17th talks

We have two talks to kick off the term. There will be dinner after the talks.
The first one (partly directed to Senior Problem Solving Students) is:

Time: 3:30pm
Speaker: Henry Segerman (Melbourne)
Title: Some mathematical sculptures
Abstract: I will talk about some 3d printed mathematical sculptures I have designed. I’ll say a little about the mathematical ideas behind them, and how they were produced. In the second half, I’ll talk about sculptures of space filling curves, how wobbly they are, and fractal graph structures designed to be more robust.

The second is:

Time: 5pm
Speaker: Jean Sun (Yale)
Title: Growth, projections and bounded generation of mapping class groups
Abstract: We investigate the non-bounded generation of subgroups of mapping class groups through the hierarchy in curve complexes developed by Masur and Minsky (2000). We compare the subsurface projections to nearest point projections in curve complexes and extend Behrstock’s inequality to include geodesics in curve complexes of subsurfaces in the Inequality on Triples in Bestivina-Bromberg-Fujiwara (2010). Based on this inequality, we can estimate translation lengths of words in the form $g_1^{n_1}\cdots g_k^{n_k}$ when $\sum |n_k|$ is sufficiently large for any given sequence $(g_i)_1^k$ in a mapping class group. With a growth argument, we further show that any subgroup of a mapping class group is boundedly generated if and only if it is virtually abelian.

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