Fri, 03 Nov 2023

15:00 - 16:00
L5

The Expected Betti Numbers of Preferential Attachment Clique Complexes

Chunyin Siu
(Cornell)
Further Information

Chunyin Siu (Alex) is a PhD candidate at Cornell University at the Center for Applied Mathematics, and is a Croucher scholar (2019) and a Youde scholar (2018).

His primary research interests lie in the intersection of topological data analysis, network analysis, topological statistics and computational geometry. He is advised by Prof. Gennady Samorodnitsky. Before coming to Cornell University, he was a MPhil. student advised by Prof. Ronald (Lokming) Lui at the Chinese University of Hong Kong.

Abstract

The preferential attachment model is a natural and popular random graph model for a growing network that contains very well-connected ``hubs''. Despite intense interest in the higher-order connectivity of these networks, their Betti numbers at higher dimensions have been largely unexplored.

In this talk, after a brief survey on random topology, we study the clique complexes of preferential attachment graphs, and we prove the asymptotics of the expected Betti numbers. If time allows, we will briefly discuss their homotopy connectedness as well. This is joint work with Gennady Samorodnitsky, Christina Lee Yu and Rongyi He, and it is based on the preprint https://arxiv.org/abs/2305.11259

Thu, 11 Jun 2020

14:00 - 15:00

Dense networks that do not synchronize and sparse ones that do.

Alex Townsend
(Cornell)
Abstract

Consider a network of identical phase oscillators with sinusoidal coupling. How likely are the oscillators to globally synchronize, starting from random initial phases? One expects that dense networks have a strong tendency to synchronize and the basin of attraction for the synchronous state to be the whole phase space. But, how dense is dense enough? In this (hopefully) entertaining Zoom talk, we use techniques from numerical linear algebra and computational Algebraic geometry to derive the densest known networks that do not synchronize and the sparsest networks that do. This is joint work with Steven Strogatz and Mike Stillman.


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