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Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 03/2020, Volume 2020, Issue 760, pp. 1 - 58
We initiate the study of intersection theory in real Grassmannians. We define the of the real Grassmannian as the average number of real -planes meeting... 
TOPOLOGY | MATHEMATICS | BETTI NUMBERS | INTERSECTION | FORMULA
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 05/2020, Volume 172, p. 105204
Using the concept of d-collapsibility from combinatorial topology, we define chordal simplicial complexes and show that their Stanley-Reisner ideals are... 
Linear resolution | Simplicial complex | Componentwise linear | Stanley-Reisner ideal | Chordality | Collapsibility | Betti number | MATHEMATICS | CLUTTERS | BETTI NUMBERS | SHELLABLE NONPURE COMPLEXES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 10/2015, Volume 284, pp. 21 - 53
The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. In this paper we investigate how Tarski... 
[formula omitted]-Betti number | Tarski number | Amenability | Cost | Golod–Shafarevich groups | Paradoxical decomposition | L 2 -Betti number | Golod-Shafarevich groups | MATHEMATICS | 1ST L-BETTI NUMBER | L-2-Betti number | EQUIVALENCE-RELATIONS
Journal Article
Nature Communications, ISSN 2041-1723, 01/2016, Volume 7, Issue 1, p. 10138
Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for... 
PERSISTENT HOMOLOGY | SEMI-ALGEBRAIC SETS | BETTI NUMBERS | STABILITY | MULTIDISCIPLINARY SCIENCES | COMBINATORIAL LAPLACIAN | COMPUTATION
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 2018
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2017, Volume 369, Issue 11, pp. 7549 - 7588
In this paper we show that totally geodesic subspaces determine the commensurability class of a standard arithmetic hyperbolic n-orbifold, n\ge 4. Many of the... 
DENSITY | MATHEMATICS | COMMENSURABILITY | EIGENVALUES | SUBGROUPS | 1ST BETTI NUMBER
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 03/2019, Volume 91, pp. 17 - 29
In this paper we compute Gröbner bases for determinantal ideals of the form I1(XY), where X and Y are both matrices whose entries are indeterminates over a... 
Determinantal ideals | Gröbner basis | Completely irreducible systems | Betti numbers
Journal Article
Fundamenta Mathematicae, ISSN 0016-2736, 2018, Volume 243, Issue 3, pp. 209 - 299
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 02/2019, Volume 223, Issue 2, pp. 571 - 579
Given an ideal I we investigate the decompositions of Betti diagrams of the graded family of ideals {Ik}k formed by taking powers of I. We prove conjectures of... 
BETTI-NUMBERS | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLICITY CONJECTURE | GRADED MODULES
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 12/2014, Volume 267, Issue 11, pp. 4264 - 4279
We prove that the first continuous L2-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of... 
Free group factors | von Neumann algebras | [formula omitted]-Betti numbers | Von Neumann algebras | Betti numbers
Journal Article
Journal of Algebra, ISSN 0021-8693, 06/2016, Volume 456, pp. 250 - 265
Let k be a field and let A be a standard N-graded k-algebra. Using numerical information of some invariants in the primary decomposition of 0 in A, namely the... 
Sequential Cohen–Macaulayness | Initial ideal | Hilbert series | Extremal Betti numbers | Sequential Cohen-Macaulayness | MATHEMATICS | MODULES | BETTI NUMBERS | RINGS | IDEALS | Algebra
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2015, Volume 143, Issue 1, pp. 121 - 128
We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-Soderberg theory to obtain... 
Gorenstein rings | Hilbert-Samuel multiplicity | Graded Betti numbers | BETTI-NUMBERS | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | graded Betti numbers | PURE
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 02/2014, Volume 163, Issue 3, pp. 465 - 488
An invariant random subgroup of the countable group Gamma is a random subgroup of Gamma whose distribution is invariant under conjugation by all elements of... 
MATHEMATICS | BETTI NUMBERS | RAMANUJAN GRAPHS | Mathematics - Group Theory | 22D40 | 05C81 | 35P20 | 53C24 | 20F69
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2013, Volume 277, Issue 3-4, pp. 709 - 723
Math. Z., Vol. 277 (3), (2014), 709--723 Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti... 
Arithmetic groups | Cohomology | Betti numbers
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2017, Volume 369, Issue 3-4, pp. 957 - 975
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 03/2014, Volume 266, Issue 5, pp. 3156 - 3169
We compute L2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in... 
Group von Neumann algebra | Plancherel measure | Type I groups | [formula omitted]-Betti numbers | Betti numbers
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 02/2018, Volume 222, Issue 2, pp. 387 - 413
We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the... 
MATHEMATICS | CONSEQUENCES | MATHEMATICS, APPLIED | ALGEBRAS | BETTI NUMBERS | HILBERT-FUNCTIONS | Algebra
Journal Article
by Erey, N
TURKISH JOURNAL OF MATHEMATICS, ISSN 1300-0098, 2019, Volume 43, Issue 5, pp. 2405 - 2414
The independence complex of a chordal graph is known to be shellable which is equivalent to the fact that cover ideal of a chordal graph has linear quotients.... 
MATHEMATICS | Chordal graph | shellable | linear quotients | cover ideal | Betti numbers
Journal Article
Advances in Mathematics, ISSN 0001-8708, 10/2018, Volume 337, pp. 363 - 416
In this paper we give a formula for the homotopy groups of (n−1)-connected 2n-manifolds as a direct sum of homotopy groups of spheres in the case the nth Betti... 
Loop space | Homotopy groups | Moore conjecture | Koszul duality | Quadratic algebra | MATHEMATICS | FREE LOOP SPACE | BETTI NUMBERS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2011, Volume 139, Issue 2, pp. 421 - 434
Journal Article
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