Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 23 for “"Betti numbers"”.
-
Betti numbers / Lambert series
Text includes handwritten formulas
-
GKM manifolds with low Betti numbers
A GKM manifold is a symplectic manifold with a torus action such that the fixed points are isolated and the isotropy weights at the fixed points are linearly independent. Each GKM manifold has a GKM graph which contains much of the topological information of the manifold, in particular the …
-
Maximum Betti Numbers for a Given Hilbert Function
… the most generators (that is, the largest first Betti number) of a homogeneous ideal with that Hilbert function. This thesis proves that the lex-segment ideal having a given Hilbert function always has the largest graded Betti numbers of any homogeneous ideal with that Hilbert function. We also …
-
Monomial Ideals, N-Lists, and Smallest Graded Betti Numbers
… thesis concerns the existence of smallest graded betti numbers. Given an Artinian Hilbert function H , consider all ideals I ⊂ R such that H(R/I) = H . Then the graded betti numbers which correspond to these ideals form a finite set which we partially order component-wise. It is known that …
-
Betti numbers of Koszul algebras and codimension two matrix factorizations
… of Avramov, Conca, and Iyengar about the Betti numbers of Koszul algebras. In Chapter 4, we study the codimension two matrix factorizations of Eisenbud and Peeva. Each matrix factorization compactly encodes the data of a free resolution of its corresponding matrix factorization module. By …
-
On lower bounds for the betti numbers of finite length modules
In this manuscript we consider multigraded modules. Chapter 1 gives the necessary definitions and examples that develop the theory of multigraded modules. A multigraded module has a multigraded minimal resolution. We give the necessary conditions for a matrix to correspond to a multigraded map and …
-
Compactness of the space of marked groups and examples of L2-Betti numbers of simple groups
This paper contains two parts. The first part will introduce Gn space and will show its compact. I will give two proofs for the compactness, the first one is due to Rostislav Grigorchuk [1], which refers to geometrical group theory and after the first proof I will give a more topological proof. In …
-
The Configuration Space of Two Particles Moving on a Graph
… on a graph Γ with a view to calculating the Betti numbers of this space. We develop an intersection theory for cycles in graphs inspired by the classical intersection theory for cycles in manifolds and we use this to develop an algorithm to calculate the second Betti number of F (Γ,2) for any …
-
Toric Varieties Associated with Moduli Spaces
… and Lunts to recover the intersection cohomology Betti numbers using the combinatorial information provided by the corresponding moment polytopes. The main contribution of this thesis is a computation of the intersection cohomology Betti numbers for the toric varieties associated to trinion …
-
Combinatorial Koszul Homology: computations and Applications
… and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals od this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to describe the structure of monomial ideals. Describe algorithms to perform efficient computations of the …
-
Hypersurface Sections: A Study of Divisor Class Groups and of the Complexity of Tensor Products
… of complexity, a measure of the growth of the Betti numbers of a module. We show that over a complete intersection R the complexity of the tensor product $M\otimes\sb{R}N$ of two finitely generated modules is the sum of the complexities of each if $Tor\sbsp{i}{R}(M,\ N)=0$ for $i\ge1.$ One of …
-
On the topology of the spaces of coverings
… analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on …
-
Free resolutions, combinatorics, and geometry
… of two cones: the first is the cone of graded Betti tables over a polynomial ring, and the second is the cone of cohomology tables of coherent sheaves over projective space. Each cone has a triangulation induced from a certain partial order. Our first result gives a module-theoretic …
-
A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices
… x 2 minors. For each possibility for the graded Betti numbers of B/I we describe an open cover of the parameter space of coefficients of the generators, and on each open set we describe the precise relationship between the coefficients of the forms g_i and the coefficients of the forms appearing …
-
Non-Commutative Probability for the Spectral Analysis of Simplicial Complexes
… the preprint reveals a new interpretation of Betti numbers for simplicial complexes in terms of distributions in an operator-valued probability space. This thesis is mostly an exposition of the areas of free probability and algebraic topology; here, we do not present cutting-edge research in …
-
Homological invariants of some special varieties
… about some homological invariants (e.g., graded Betti numbers, Hilbert function, regularity) of some special varieties. In particular, we focus on the codimension two ACM varieties in P1×P1×P1 (called varieties of lines), and the edge ideals of bicyclic graphs. We study the Hilbert function of …
-
Descent Systems, Eulerian Polynomials and Toric Varieties
… Sn . Therefore the Eulerian polynomials give the Betti numbers for certain smooth toric varieties associated with the permutohedra. In this thesis we derive recurrences for the h-vectors of a family of polytopes generalizing this. The simple polytopes we consider arise as the orbit of a …
-
Data-driven Methods for Resting-state fMRI Biomarker Discovery in Mental Illness
… spatial dynamics of fMRI data, revealing lower Betti numbers and higher Wasserstein distance in schizophrenia patients compared to controls, indicating reduced dynamism in resting-state fMRI studies.
-
Numerical simulations of dense granular systems with and without cohesive effects
… tools of persistence homology, and in particular Betti numbers, that allow to quantify the properties of the force networks, and make comparisons directly between experiments and simulations. This comparison is important in order to identify additional features that have to be included in …
Page 1 of 2