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Item type:Publication, On Nörlund–Voronoi Summability and Instability of Rational Maps(Springer, 2020-12-01)We investigate the connection between the instability of rational maps and summability methods applied to the spectrum of a critical point belonging to the Julia set of a rational map. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Geometry of Horospherical Varieties of Picard Rank One(Oxford University Press, 2020-10-29)Abstract We study the geometry of smooth non-homogeneous horospherical varieties of Picard rank one. These have been classified by Pasquier and include the well-known odd symplectic Grassmannians. We focus our study on quantum cohomology, with a view towards Dubrovin’s conjecture. We start with describing the cohomology groups of smooth horospherical varieties of Picard rank one. We show a Chevalley formula for these and establish that many Gromov–Witten invariants are enumerative. This enables us to prove that in many cases the quantum cohomology is semisimple. We give a presentation of the quantum cohomology ring for odd symplectic Grassmannians. In the last sections, we turn to derived categories of coherent sheaves. We first discuss a general construction of exceptional bundles on horospherical varieties. We work out in detail the case of the horospherical variety associated to the exceptional group $G_2$ and construct a full rectangular Lefschetz exceptional collection in the derived category. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Foliations on the projective plane with finite group of symmetries(Mattioli 1885, 2020-03-09)Let $\mathcal{F}$ denote a singular holomorphic foliation on $\mathbb{P}^2$ having a finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of $\mathcal{F}$, we determine the maximal value that $|\mbox{aut}(\mathcal{F})|$ can take and explicitly exhibit all the foliations attaining this maximal value. Furthermore, we classify the foliations with large but finite automorphism group.3 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory(Mathematical Sciences Publishers, 2021-01-01)We produce a Grothendieck transformation from bivariant operational K-theory to Chow, with a Riemann-Roch formula that generalizes classical Grothendieck-Verdier-Riemann-Roch. We also produce Grothendieck transformations and Riemann-Roch formulas that generalize the classical Adams-Riemann-Roch and equivariant localization theorems. As applications, we exhibit a projective toric variety X whose equivariant K-theory of vector bundles does not surject onto its ordinary K-theory, and describe the operational K-theory of spherical varieties in terms of fixed-point data. In an appendix, Vezzosi studies operational K-theory of derived schemes and constructs a Grothendieck transformation from bivariant algebraic K-theory of relatively perfect complexes to bivariant operational K-theory. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Bi-traceable graphs, the intersection of three longest paths and Hippchen's conjecture(Cornell University, 2021-01-19)Let $P,Q$ be longest paths in a simple graph. We analyze the possible connections between the components of $P\cup Q\setminus (V(P)\cap V(Q))$ and introduce the notion of a bi-traceable graph. We use the results for all the possible configurations of the intersection points when $\#V(P)\cap V(Q)\le 5$ in order to prove that if the intersection of three longest paths $P,Q,R$ is empty, then $\#(V(P)\cap V(Q))\ge 6$. We also prove Hippchen's conjecture for $k\le 6$: If a graph $G$ is $k$-connected for $k\le 6$, and $P$ and $Q$ are longest paths in $G$, then $\#(V(P)\cap V(Q))\ge 6$. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Singular integral operators, a brief historical overview of its evolution(Universidad Nacional de Trujillo, 2022-06-30)In this work we give an analytical-historical view of the classical theory of singular integrals introduced by A.P. Calderón-A. Zygmund. Emphasis is given to their applications to PDEs and to some projections of the theory. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Bivariant K-theory of locally convex Z-graded algebras(Universidad Nacional de Trujillo, 2022-06-30)In the present work, we describe some results about the K-theory of Z-graded algebras. First, in the context of C* algebras, we begin with the Pimsner-Voiculescu sequence for crossed products and its generalizations. We will see that there are results analog to these in the context of locally convex algebras and we conclude with results for generalized Weyl algebras. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Statistical tables in Primary Education textbooks of Peru(Facultad de Ciencias de la Educacion, 2022-01-01)In recent years, the literature shows an increase in research analyzing statistical representation of data in textbooks, but in the Peruvian context is still scarce. Therefore, this research aims to analyze activities on statistical tables present in mathematics textbooks, published by the Ministry of Education and distributed free of charge to teachers and students of Primary Education in Peru. The methodology is qualitative and descriptive. For data analysis, the content analysis technique was used by analyzing types of statistical table, types of task, reading levels and semiotic complexity levels as units of analysis in a complete series of mathematics textbooks of Primary Education, from first to sixth grade, one per level, due to their wide national coverage. The results allow us to observe predominance of tally charts and data tables, completion and comparison tasks, reading level 2 (reading within data) and semiotic complexity level 3 (representation of data distribution). It is concluded that it is necessary to increase the number and variety of tasks related to statistical tables proposed in mathematics textbooks, as well as to reinforce the presence of the highest levels of reading and semiotic complexity in the last years of Primary Education in Peru. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Complete transversal and formal normal forms of germs of vector fields(Sociedade Brasileira de Matemática, 2022-12-26)In this work, inspired by the technique of the complete transversal, used for the classification of plane branches, developed by Hefez, A. and Hernandes, M., as well as Bruce, J.W., Kirk, N.P. and du Plesis, A.A., study the singularities of applications, we establish a classification of vector fields through their normal forms. In the case of vector fields with non zero linear part in $(\mathbb{C}^{2}, 0) $ and nilpotent fields in $(\mathbb {C}^{n}, 0), n\geq 2$ we recover the classical normal forms for those fields, and we provide a formal normal form different from Takens in dimension 2. Likewise, we obtain the normal form for the vector fields in $(\mathbb{C},0)$ of any multiplicity. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Transversely Product Singularities of Foliations in Projective Spaces(Academie des sciences, 2023-01-01)We prove that a transversely product component of the singular set of a holomorphic foliation on ℙ n is necessarily a Kupka component.
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