Related papers: Topological equisingularity of function germs with…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…
We introduce a class of infinitely renormalizable, unicritical diffeomorphisms of the disk (with a non-degenerate "critical point"). In this class of dynamical systems, we show that under renormalization, maps eventually become…
The main question we target is the following: If one fixes a topological type of a complex normal surface singularity then what are the possible analytic types supported by it, and/or, what are the possible values of the geometric genus? We…
In this paper we will develop a very general approach which shows that critical relations of holomorphic maps on the complex plane unfold transversally in a positively oriented way. We will mainly illustrate this approach to obtain…
We consider the existence of the topological entropy of shift spaces on a finitely generated semigroup whose Cayley graph is a tree. The considered semigroups include free groups. On the other hand, the notion of stem entropy is introduced.…
We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…
We construct the analytic lattice cohomology associated with the analytic type of any complex normal surface singularity. It is the categorification of the geometric genus of the germ, whenever the link is a rational homology sphere. It is…
We consider pro-isomorphic zeta functions of the groups $\Gamma(\mathcal{O}_K)$, where $\Gamma$ is a unipotent group scheme defined over $\mathbb{Z}$ and $K$ varies over all number fields. Under certain conditions, we show that these…
We consider the simulation of finite temperature QCD with two flavors of dynamical overlap fermions in order to study the suppression of the axial U(1) symmetry breaking at the chiral phase transition point. As a preliminary study, pure…
Gambaudo and P\'ecou introduced the ``linking property'' to study the dynamics of germs of planar homeomorphims and provide a new proof of Naishul theorem in their paper "A topological invariant for volume preserving diffeomorphisms"…
Fix an o-minimal structure expanding the ordered field of real numbers. Let $(W_y)_{y\in\mathbb{R}^s}$ be a definable family of closed subsets of $\mathbb{R}^n$ whose total space $W = \cup_y W_y\times y$ is a closed connected $C^2$…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
We prove that the outer Lipschitz geometry of a germ $(X,0)$ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities…
We study the connection between topological order and degeneracy of the singular value spectrum by explicitly solving the two-dimensional dimerized quantum Heisenberg model in the form of tensor product state ansatz. Based on the ground…
We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincar\'e series of the minimal set of generators of the graded algebra of regular functions, provided that the link of the…
We consider an equisingularity problem for polynomial families of affine hypersurfaces $X_\tau \subset \mathbb C^n$ with (at worst) isolated singularities. We show that the constancy of the global polar invariants $\gamma^* (X_\tau)$ is…
In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…
The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical…
We give a complete classification of 1-dimensional exponential families $\mathcal{E}$ defined over a finite space $\Omega=\{x_{0}, ...,x_{n}\}$ whose Hessian scalar curvature is constant. We observe an interesting phenomenon: if…