How many links can you fit in a box? & An explicit packing of links in a box and some progress in quantitative embeddings

Speaker 1: Michael Freedman, Harvard CMSA (from 3:00pm to 4:00pm)

Title 1: How many links can you fit in a box?

Abstract 1: I’ll discuss a “made up” problem on the interface of topology and packing, which may well be classified as “recreational math”. Here is the first question suppose you have a unit box, how many unlinked (split) copies of the Hopf link (c_1,i,c_2,i) and be embedded so that for each copy the two components c_1,i and c_2,i maintain a distance of at least some fixed \epsilon >0. Is this number even finite?

Speaker 2: Elia Portnoy, MIT (from 4:00pm to 5:00pm)

Title 2: An explicit packing of links in a box and some progress in quantitative embeddings

Abstract 2: Following Freedman’s talk, I’ll begin by showing how to pack a large number of links in a box with certain geometric and topological constraints (joint with Fedya Manin). If time permits, I’ll also discuss some progress and open questions for the following quantitative embedding problem: given a simplicial complex X, what is the smallest size of a map from X to R^n so that the preimage of each unit ball intersects a small constant number of simplices?

Time: Wednesday, March 12th from 3:00pm to 5:00pm

Location: Room G-10 at Harvard CMSA and Zoom (hybrid)
Zoom link: https://harvard.zoom.us/j/96691023299
Password: cmsa