Related papers: Recent Developments in the Penrose Conjecture
We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…
In This paper, we survey recent progress on the theory of Gromov- Witten invariants on Hilbert schemes of points mainly on elliptic surfaces and simply connected minimal surface of general type. In particular, we focus on the aspects of…
I report on recent theoretical developments at Quark Matter 2006.
In this thesis, we scrutinize the literature to trace the evolution of the concepts surrounding the weak cosmic censorship conjecture and the attempts to prove or disprove it. We discuss its development over the years, its conceptual…
We prove the Penrose-Wall singularity theorem in the full semiclassical gravity regime, significantly expanding its range of validity. To accomplish this, we modify the definition of quantum-trapped surfaces without affecting their…
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
Closely following recent ideas of J. Borcea, we discuss various modifications and relaxations of Sendov's conjecture about the location of critical points of a polynomial with complex coefficients. The resulting open problems are formulated…
We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.
The main aim of this thesis is to study the properties of trapped surfaces in spacetimes with symmetries and their possible relation with the theory of black holes. We will concetrate specially on one aspect of this possible equivalence,…
We study quasi-lisse vertex (super)algebras and establish new finiteness conditions for the convergence of genus-zero and genus-one $n$-point correlation functions.
Recent developments in Seiberg-Witten theory and relations with Complex Geometry.
We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the…
Identifying a general quasi-local notion of energy-momentum and angular momentum would be an important advance in general relativity with potentially important consequences for mathematical and astrophysical studies in general relativity.…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
This is a report of the author's talk at Kinosaki Algebraic Geometry Symposium 2018. We discuss some recent progress on the geometry of thin exceptional sets in Manin's Conjecture.
In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer…
In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus…
Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.