## View abstract

### Session S33 - Spectral Geometry

Tuesday, July 13, 13:00 ~ 13:20 UTC-3

## Towards hearing three-dimensional geometric structures

### Craig Sutton

#### Dartmouth College, United States of America   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakf66201dc5a20b87c50b84657a2a8b901').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyf66201dc5a20b87c50b84657a2a8b901 = 'cr&#97;&#105;g.j.s&#117;tt&#111;n' + '&#64;'; addyf66201dc5a20b87c50b84657a2a8b901 = addyf66201dc5a20b87c50b84657a2a8b901 + 'd&#97;rtm&#111;&#117;th' + '&#46;' + '&#101;d&#117;'; var addy_textf66201dc5a20b87c50b84657a2a8b901 = 'cr&#97;&#105;g.j.s&#117;tt&#111;n' + '&#64;' + 'd&#97;rtm&#111;&#117;th' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakf66201dc5a20b87c50b84657a2a8b901').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyf66201dc5a20b87c50b84657a2a8b901 + '\'>'+addy_textf66201dc5a20b87c50b84657a2a8b901+'<\/a>';

The positive resolution of the geometrization conjecture shows that geometric structures (i.e., complete locally homogeneous metrics) play a special role in our understanding of the taxonomy of three-dimensional manifolds. In light of this, we initiate the exploration of the extent to which three-dimensional geometric structures are determined by their spectra. For example, we find that among locally homogeneous manifolds, closed three-manifolds modeled on six of the eight Thurston geometries are determined up to universal Riemannian cover by their spectra, a result that includes all compact locally symmetric spaces. More generally, we obtain results concerning spaces modeled on metrically maximal geometries.''

Joint work with Samuel Lin (Dartmouth College, USA) and Benjamin Schmidt (Michigan State University, USA).