## View abstract

### Session S28 - Knots, Surfaces, 3-manifolds

Wednesday, July 14, 16:00 ~ 16:30 UTC-3

## Cyclic quadrilaterals and smooth Jordan curves

### Joshua Greene

#### Boston College, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakbc87f0cf3cbb976fc15400340bc8331b').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addybc87f0cf3cbb976fc15400340bc8331b = 'j&#111;sh&#117;&#97;.gr&#101;&#101;n&#101;' + '&#64;'; addybc87f0cf3cbb976fc15400340bc8331b = addybc87f0cf3cbb976fc15400340bc8331b + 'bc' + '&#46;' + '&#101;d&#117;'; var addy_textbc87f0cf3cbb976fc15400340bc8331b = 'j&#111;sh&#117;&#97;.gr&#101;&#101;n&#101;' + '&#64;' + 'bc' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakbc87f0cf3cbb976fc15400340bc8331b').innerHTML += '<a ' + path + '\'' + prefix + ':' + addybc87f0cf3cbb976fc15400340bc8331b + '\'>'+addy_textbc87f0cf3cbb976fc15400340bc8331b+'<\/a>';

I will discuss the context and proof of the following result: for every smooth Jordan curve and for every four points on a circle, there exists an orientation-preserving similarity taking the four points onto the curve. The proof involves symplectic geometry in a surprising way.

Joint work with Andrew Lobb (Durham University).