HI-DIM COMBINATORICS

High-dimensional combinatorics

 Coordinatore THE HEBREW UNIVERSITY OF JERUSALEM. 

Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.

 Nazionalità Coordinatore Israel [IL]
 Totale costo 1˙754˙600 €
 EC contributo 1˙754˙600 €
 Programma FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call ERC-2013-ADG
 Funding Scheme ERC-AG
 Anno di inizio 2013
 Periodo (anno-mese-giorno) 2013-10-01   -   2018-09-30

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    THE HEBREW UNIVERSITY OF JERUSALEM.

 Organization address address: GIVAT RAM CAMPUS
city: JERUSALEM
postcode: 91904

contact info
Titolo: Ms.
Nome: Hani
Cognome: Ben-Yehuda
Email: send email
Telefono: +972 2 6586676
Fax: +972 72 2447007

IL (JERUSALEM) hostInstitution 1˙754˙600.00
2    THE HEBREW UNIVERSITY OF JERUSALEM.

 Organization address address: GIVAT RAM CAMPUS
city: JERUSALEM
postcode: 91904

contact info
Titolo: Prof.
Nome: Nathan
Cognome: Linial
Email: send email
Telefono: +972 2 5494548
Fax: +972 7 22447007

IL (JERUSALEM) hostInstitution 1˙754˙600.00

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

simplicial    theory    geometric    discrete    view    graph    objects    dimensional    random    graphs    giant    interactions    permutations    combinatorial    perspective    transition    complexes    computer    mathematical    mathematics   

 Obiettivo del progetto (Objective)

'This research program originates from a pressing practical need and from a purely new geometric perspective of discrete mathematics.. Graphs play a key role in many application areas of mathematics, providing the perfect mathematical description of all systems that are governed by pairwise interactions, in computer science, economics, biology and more. But graphs cannot fully capture scenarios in which interactions involve more than two agents. Since the theory of hypergraphs is still too under-developed, we resort to geometry and topology, which view a graph as a one-dimensional simplicial complex. I want to develop a combinatorial/geometric/probabilistic theory of higher-dimensional simplicial complexes. Inspired by the great success of random graph theory and its impact on discrete mathematics both theoretical and applied, I intend to develop a theory of random simplicial complexes. This combinatorial/geometric point of view and the novel high-dimensional perspective, shed new light on many fundamental combinatorial objects such as permutations, cycles and trees. We show that they all have high-dimensional analogs whose study leads to new deep mathematical problems. This holds a great promise for real-world applications, in view of the prevalence of such objects in application domains. Even basic aspects of graphs, permutations etc. are much more sophisticated and subtle in high dimensions. E.g., it is a key result that randomly evolving graphs undergo a phase transition and a sudden emergence of a giant component. Computer simulations of the evolution of higher-dimensional simplicial complexes, reveal an even more dramatic phase transition. Yet, we still do not even know what is a higher-dimensional giant component. I also show how to use simplicial complexes (deterministic and random) to construct better error-correcting codes. I suggest a new conceptual approach to the search for high-dimensional expanders, a goal sought by many renowned mathematicians.'

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