## View abstract

### Invited talk

Friday, July 23, 12:15 ~ 13:15 UTC-3

## Hardy fields and Transseries

### Lou van den Dries

#### University of Illinois at Urbana-Champaign, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakc0e922840f932fc786e06bb52361b350').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyc0e922840f932fc786e06bb52361b350 = 'vddr&#105;&#101;s' + '&#64;'; addyc0e922840f932fc786e06bb52361b350 = addyc0e922840f932fc786e06bb52361b350 + '&#105;ll&#105;n&#111;&#105;s' + '&#46;' + '&#101;d&#117;'; var addy_textc0e922840f932fc786e06bb52361b350 = 'vddr&#105;&#101;s' + '&#64;' + '&#105;ll&#105;n&#111;&#105;s' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakc0e922840f932fc786e06bb52361b350').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyc0e922840f932fc786e06bb52361b350 + '\'>'+addy_textc0e922840f932fc786e06bb52361b350+'<\/a>';

This concerns joint work with Matthias Aschenbrenner and Joris van der Hoeven. The focus of our book Asymptotic Differential Algebra and Model Theory of Transseries '' (Annals of Mathematics Studies 195, 2017, Princeton University Press) is on understanding the differential field of transseries. To deal with Hardy fields we recently refined the general theory from that book considerably. This has benefits beyond Hardy fields. I will start from scratch by introducing Hardy fields and state our main result about Hardy fields, which basically amounts to a complete theory about extending Hardy fields. I will include some material on transseries and on how they relate to Hardy fields.

Joint work with Matthias Aschenbrenner (University of Vienna, Vienna, Austria) and Joris van der Hoeven (Ecole Polytechnique, Paris, France).