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CASe SIGNED

Combinatorics with an analytic structure

Total Cost €

0

EC-Contrib. €

0

Partnership

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 CASe project word cloud

Explore the words cloud of the CASe project. It provides you a very rough idea of what is the project "CASe" about.

extend    connes    purely    tools    stanley    geometry    commutative    name    arrangement    ubiquity    translated       algebra    equipped    polytopes    deep    few    conjecture    counterexamples    combinatorial    contribution    initial    reverse    realized    designed    hochster    ahler    central    realization    deal    geometric    motivated    pure    combinatorics    relative    grothendieck    review    ancestors    caveat    modern    extends    hirsch    theorem    standard    of    intersection    topology    pdes    structures    subject    vital    interesting    objects    curvature    interplay    fascinated    branches    diameter    relation    questions    period    complements    ideas    enumerative    reliant    conjectures    isoperimetry    saito    shown    isoperimetries    neolithic    reisner    polyhedra    toric    stone    theory    made    spirit    embedding    guided    carvings    themselves    classification    wealth    subjects    settings    hodge    discrete    construct    mathematics    hard    lefschetz    solved   

Project "CASe" data sheet

The following table provides information about the project.

Coordinator
THE HEBREW UNIVERSITY OF JERUSALEM 

Organization address
address: EDMOND J SAFRA CAMPUS GIVAT RAM
city: JERUSALEM
postcode: 91904
website: www.huji.ac.il

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Project website http://www.math.huji.ac.il/
 Total cost 1˙337˙200 €
 EC max contribution 1˙337˙200 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-12-01   to  2021-11-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE HEBREW UNIVERSITY OF JERUSALEM IL (JERUSALEM) coordinator 1˙307˙200.00
2    UNIVERSITAET LEIPZIG DE (LEIPZIG) participant 30˙000.00

Map

 Project objective

'Combinatorics, and its interplay with geometry, has fascinated our ancestors as shown by early stone carvings in the Neolithic period. Modern combinatorics is motivated by the ubiquity of its structures in both pure and applied mathematics. The work of Hochster and Stanley, who realized the relation of enumerative questions to commutative algebra and toric geometry made a vital contribution to the development of this subject. Their work was a central contribution to the classification of face numbers of simple polytopes, and the initial success lead to a wealth of research in which combinatorial problems were translated to algebra and geometry and then solved using deep results such as Saito's hard Lefschetz theorem. As a caveat, this also made branches of combinatorics reliant on algebra and geometry to provide new ideas.

In this proposal, I want to reverse this approach and extend our understanding of geometry and algebra guided by combinatorial methods. In this spirit I propose new combinatorial approaches to the interplay of curvature and topology, to isoperimetry, geometric analysis, and intersection theory, to name a few. In addition, while these subjects are interesting by themselves, they are also designed to advance classical topics, for example, the diameter of polyhedra (as in the Hirsch conjecture), arrangement theory (and the study of arrangement complements), Hodge theory (as in Grothendieck's standard conjectures), and realization problems of discrete objects (as in Connes embedding problem for type II factors).

This proposal is supported by the review of some already developed tools, such as relative Stanley--Reisner theory (which is equipped to deal with combinatorial isoperimetries), combinatorial Hodge theory (which extends the ``K'ahler package' to purely combinatorial settings), and discrete PDEs (which were used to construct counterexamples to old problems in discrete geometry).'

 Publications

year authors and title journal last update
List of publications.
2018 Le, Quang-Nhat
Explicit computations of Fourier transforms of polyhedral cones
published pages: , ISSN: , DOI:
1 2019-05-14
2018 Le, Quang-Nhat
New irrational polygons with Ehrhart-theoretic period collapse
published pages: , ISSN: , DOI:
1 2019-05-14
2018 Karim Adiprasito, June Huh, Eric Katz
Hodge theory for combinatorial geometries
published pages: 381-452, ISSN: 0003-486X, DOI: 10.4007/annals.2018.188.2.1
Annals of Mathematics 188/2 2019-05-14
2017 Adiprasito, Karim
Lefschetz and Lower Bound theorems for Minkowski sums
published pages: , ISSN: , DOI:
1 2019-05-14
2018 Adiprasito, Karim; Bárány, Imre; Mustafa, Nabil H.; Terpai, Tamás
Theorems of Carath\'eodory, Helly, and Tverberg without dimension
published pages: , ISSN: , DOI:
1 2019-05-14
2019 Karim Adiprasito, Farhad Babaee
Convexity of complements of tropical varieties, and approximations of currents
published pages: 237-251, ISSN: 0025-5831, DOI: 10.1007/s00208-018-1728-2
Mathematische Annalen 373/1-2 2019-05-14
2018 Adiprasito, Karim; Liu, Gaku; Pak, Igor; Temkin, Michael
Log smoothness and polystability over valuation rings
published pages: , ISSN: , DOI:
2 2019-05-14
2018 Adiprasito, Karim; Nevo, Eran
Rigidity with few locations
published pages: , ISSN: , DOI:
1 2019-05-14
2017 Adiprasito, Karim; Benedetti, Bruno
Barycentric subdivisions of convex complexes are collapsible
published pages: , ISSN: , DOI:
1 2019-05-14
2017 Adiprasito, Karim; Benedetti, Bruno
A Cheeger-type exponential bound for the number of triangulated manifolds
published pages: , ISSN: , DOI:
Annals Institute Henri Poincare D 1 2019-05-14
2018 Adiprasito, Karim; Burens, Mikhail; Nevo, Eran
QGLBT for polytopes
published pages: , ISSN: , DOI:
1 2019-05-14
2017 Adiprasito,Karim
A note on the simplex-cosimplex problem
published pages: 5-12, ISSN: 0195-6698, DOI:
Eur. J. Comb. 66 2019-05-14
2017 Karim A Adiprasito, Philip Brinkmann, Arnau Padrol, Pavel Paták, Zuzana Patáková, Raman Sanyal
Colorful Simplicial Depth, Minkowski Sums, and Generalized Gale Transforms
published pages: 1894-1919, ISSN: 1073-7928, DOI: 10.1093/imrn/rnx184
International Mathematics Research Notices 2019/6 2019-05-14
2017 Adiprasito,Karim
Toric chordality
published pages: 783-807, ISSN: 0021-7824, DOI:
Journal de Mathématiques Pures et Appliquées 9 108.5 2019-05-14

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