## View abstract

### Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Thursday, July 15, 18:30 ~ 19:00 UTC-3

## Sets with rational linear patterns

### Malabika Pramanik

#### University of British Columbia , Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak05279b1f13093881e2e5820f2767b90e').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy05279b1f13093881e2e5820f2767b90e = 'm&#97;l&#97;b&#105;k&#97;' + '&#64;'; addy05279b1f13093881e2e5820f2767b90e = addy05279b1f13093881e2e5820f2767b90e + 'm&#97;th' + '&#46;' + '&#117;bc' + '&#46;' + 'c&#97;'; var addy_text05279b1f13093881e2e5820f2767b90e = 'm&#97;l&#97;b&#105;k&#97;' + '&#64;' + 'm&#97;th' + '&#46;' + '&#117;bc' + '&#46;' + 'c&#97;';document.getElementById('cloak05279b1f13093881e2e5820f2767b90e').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy05279b1f13093881e2e5820f2767b90e + '\'>'+addy_text05279b1f13093881e2e5820f2767b90e+'<\/a>';

How large does a set have to be in order to include a nontrivial solution of a translation-invariant linear equation with integer coefficients? Is it possible for a large set to avoid nontrivial solutions of many such equations? We will discuss answers to these questions under varying definitions of size, and report on ongoing work in this direction.

Joint work with Yiyu Liang (Beijing Jiaotong University).