## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, November 8, 2018 — 4:00 PM EST

**Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo**

"Stable Regularity Lemma"

The Szemerédi regularity lemma tells us that any sufficiently large bipartite graph (V,W,E) can be partitioned into a small number of sets V_{1},...,V_{n} and W_{1},...,W_{m} such that for most pairs (V_{i,} W_{j)} the edge density between any pair of reasonably large subsets of V_{i} and W_{j} is close to the edge density between V_{i} and W_{j}. If we further assume a stability condition on (V,W,E), we can demand that the above hold for *every* pair, not just most; we can further demand that the edge density between each V_{i} and W_{j} be either close to zero or close to one. We present Pillay's proof of this stable variant of the regularity lemma.

MC 5403

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1