Opendata, web and dolomites


Combinatorics with an analytic structure

Total Cost €


EC-Contrib. €






 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.

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

Project "CASe" data sheet

The following table provides information about the project.


Organization address
postcode: 91904

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
 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


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
2    UNIVERSITAET LEIPZIG DE (LEIPZIG) participant 30˙000.00


 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).'


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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