TITLE: Asymptotic depth of invariant chains of edge ideals
ABSTRACT: We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes. This is joint work with T.Q. Hoa, D.T. Hoang, D.V. Le and T.T. Nguyen.
TITLE: Asymptotic depth of invariant chains of edge ideals
ABSTRACT: We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes. This is joint work with T.Q. Hoa, D.T. Hoang, D.V. Le and T.T. Nguyen.
Telegram has exploded as a hub for cybercriminals looking to buy, sell and share stolen data and hacking tools, new research shows, as the messaging app emerges as an alternative to the dark web.An investigation by cyber intelligence group Cyberint, together with the Financial Times, found a ballooning network of hackers sharing data leaks on the popular messaging platform, sometimes in channels with tens of thousands of subscribers, lured by its ease of use and light-touch moderation.
Telegram Gives Up On Crypto Blockchain Project
Durov said on his Telegram channel today that the two and a half year blockchain and crypto project has been put to sleep. Ironically, after leaving Russia because the government wanted his encryption keys to his social media firm, Durov’s cryptocurrency idea lost steam because of a U.S. court. “The technology we created allowed for an open, free, decentralized exchange of value and ideas. TON had the potential to revolutionize how people store and transfer funds and information,” he wrote on his channel. “Unfortunately, a U.S. court stopped TON from happening.”
