## 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.

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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