Pedro Morales-Almazan

Pedro Morales-Almazan
University of California, Santa Cruz | UCSC · Department of Mathematics

PhD Mathematics

About

13
Publications
561
Reads
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41
Citations
Introduction
My work has been directed towards the application of spectral zeta functions in calculations of the Casimir Effect. I have studied spectral zeta functions arising from Laplace type differential operators defined on different types of Riemannian manifolds, their relation with heat kernel coefficients and zero point energy.
Additional affiliations
July 2018 - present
University of California, Santa Cruz
Position
  • Professor (Assistant)
January 2013 - June 2018
University of Texas at Austin
Position
  • Lecturer
January 2013 - present
University of Texas at Austin
Position
  • Lecturer
Education
January 2008 - December 2011
Baylor University
Field of study
  • Mathematics
January 2008 - August 2012
Baylor University
Field of study
  • Mathematics
January 2003 - May 2008
University of San Carlos of Guatemala
Field of study
  • Electronics

Publications

Publications (13)
Article
This article explores the parallels between improvisational theater, commonly known as improv, and active teaching. Specifically, it focuses in the impact of improv techniques on instructor and teaching assistant professional development. The implementation of an active teaching seminar is analyzed, where improv techniques were used in developing t...
Preprint
This article explores the parallels between improvisational theater (Improv) and teaching in an Active Learning environment. It presents the notions of Active Teaching as a natural complement to Active Learning, and discusses how unexpected situations give rise to valuable Teaching Moments. These Teaching Moments can be strategically utilized follo...
Article
In this article, we consider the functional determinant on an annulus and elliptic regions with a variety of boundary conditions. Known results for the annulus are rederived and extended using contour integration techniques. Conformal transformations are then used to relate these results to ellipsoidal annuli, providing very explicit answers. Simil...
Article
Full-text available
In this paper, we explore the zeta function arising from a small perturbation on a surface of revolution and the effect of this on the functional determinant and on the change of the Casimir energy associated with the surface.
Article
Full-text available
In this article we consider a spherical piston modeled by a spherically symmetric potential. The piston is positioned between two spherical shells and the corresponding Casimir energy and force are computed. Zeta function regularization based upon suitable contour integral representations is utilized. A numerical analysis of the Casimir force is pr...
Article
Full-text available
We present a geometric way of describing the irrationality of a number using the area of a circular sector $A(r)$. We establish a connection between this and the continued fraction expansion of the number, and prove bounds for $A(r)$ as $r\to\infty$ by describing the asymptotic behavior of the ratios of the denominators of the convergents.
Article
Full-text available
In this paper we explore the Zeta function arising from a small perturbation on a surface of revolution and the effect of this on the functional determinant and in the change of the Casimir energy associated with this configuration.
Article
Full-text available
In this work the Casimir effect is studied for scalar fields in the presence of boundaries and under the influence of arbitrary smooth potentials of compact support. In this setting, piston configurations are analyzed in which the piston is modeled by a potential. For these configurations, analytic results for the Casimir energy and force are obtai...
Article
Full-text available
We de?ne a special type of hypersurface varieties inside $\mathbb{P}_k^{n-1}$ arising from connected planar graphs and then find their equivalence classes inside the Gr\"othendieck ring of projective varieties. Then we find a characterization for graphs in order to de?ne irreducible hypersurfaces in general.
Article
Full-text available
We consider semitransparent pistons in the presence of extra dimensions. It is shown that the piston is always attracted to the closest wall irrespective of details of the geometry and topology of the extra dimensions and of the cross section of the piston. Furthermore, we evaluate the zeta regularized determinant for this configuration.
Article
Full-text available
In this article we consider a piston modelled by a potential in the presence of extra dimensions. We analyze the functional determinant and the Casimir effect for this configuration. In order to compute the determinant and Casimir force we employ the zeta function scheme. Essentially, the computation reduces to the analysis of the zeta function ass...
Chapter
Full-text available
We consider a piston modelled by a potential in the presence of extra dimensions. We analyze the functional determinant and the Casimir effect for this configuration. In order to compute the determinant and Casimir force, we employ the zeta function scheme. Essentially, the computation reduces to the analysis of the zeta function associated with a...
Conference Paper
We consider semitransparent pistons in the presence of extra dimensions. It is shown that the piston is always attracted to the closest wall irrespective of details of the geometry and topology of the extradimensions and of the cross section of the piston. Furthermore, we evaluate the zeta regularized determinant for this configuration.

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