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Mehtaab Sawhney, Anticoncentration in Ramsey graphs and a proof of the Erdős-McKay conjecture

September 21 Wednesday @ 4:30 PM - 5:30 PM KST

Zoom ID: 870 0312 9412 (ibsecopro)

An $n$-vertex graph is called $C$-Ramsey if it has no clique or independent set of size $C\log_2 n$ (i.e., if it has near-optimal Ramsey behavior). We study edge-statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a $C$-Ramsey graph. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős offered one of his notorious monetary prizes and the proof involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics, and low-rank approximation.

Joint w. Matthew Kwan, Ashwin Sah, and Lisa Sauermann

Details

Date:
September 21 Wednesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Venue

Zoom ID: 870 0312 9412 (ibsecopro)

Organizer

Joonkyung Lee (이준경)
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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