## Areas of Expertise

Representation theory of Lie groups and Lie algebras.

Matrix analysis.

## Education

Ph.D. Mathematics

Baylor University

2012

M.S. Mathematics

Baylor University

2008

## Biography

## Awards

Outstanding Mathematics Graduate Teaching Award, Baylor University (2010-2011).

Academic Excellence Award, Universidad de San Carlos (2002).

## Grants and Contracts Awarded

Faculty Development Research Grant, UNF, (Summer 2013).

## Publications & Presentations

**Published:**

(19) Some geometric properties of matrix means with respect to different distance functions, joint with Dumitru, R. and Dinh, T. Hoa (to appear in *Positivity*)

(18) On the Matrix Heron Means and Renyi Divergences, joint with Dumitru R. and Dinh T.H. (to appear in *Linear Multilinear Algebra*)

(17) Generalized Hellinger Metrics and Audenaert's In-Betweenness, joint with Dumitru R., *Linear Algebra Appl., 585, *(2020), 191-198, https://doi.org/10.1016/j.laa.2019.10.003

(16) Fundamental Theorems of Summability Theory for a New Type of Subsequences of Double Sequences, joint with Dumitru, R., *Journal of Classical Analysis, 15(1), (2019), 23–33.*

(15) Some trace inequalities for operator monotone and operator convex functions, joint with Dumitru, R. and Dinh, T. Hoa (to appear in *Math. Inequal. Appl.*)

(14) Non-Linear Interpolation of the Harmonic-Geometric-Arithmetic Matrix Means, joint with Dumitru, R. and Dinh, T. Hoa, *Lobachevskii Journal of Mathematics*, 40(1), (2019), 101-106.

(13) The Matrix Power Means and Interpolation, *Adv. Oper. Theory, https://doi.org/10.15352/aot.1801-1288,* (2018), joint with Dumitru, R. and Dinh, T. Hoa.

(12) On a q-Analogue of Hilbert's Inequality, joint with Dumitru, R., *Electronic Journal of Mathematical Analysis and Applications*, 6(2), (2018), pp. 279-287.

(11) New Characterizations of Operator Monotone Functions, joint with Dumitru, R. and Dinh, T. Hoa, *Linear Algebra Appl., 546, *(2018), 169-186, https://doi.org/10.1016/j.laa.2018.02.004

(10) On a conjecture of Bhatia, Lim, and Yamazaki, joint with Dumitru, R. and Dinh, T. Hoa, *Linear Algebra and its Applications*, 531, (2017), 140-145.

(9) On the monotonicity of weighted power means of matrices, joint with Dumitru, R and Dinh, T. Hoa., *Linear Algebra and its Applications*, 527, (2017), 128-140.

(8) Global Actions of the Lie Symmetries of the Nonlinear Filtration Equation, *Electronic Journal of Mathematical Analysis and Applications*, Vol. 5(1) Jan. 2017, pp. 208-218.

(7) Arithmagons and a Special Class of Multigraphs, Acta Math. Univ. Com., Vol. LXXXV, 1 (2016), pp. 87-95, *joint with Champion J, Lyons J*

(6) Globalization of the Actions of the Lie Symmetries of the Nonlinear Wave Equations with Dissipation, *European Journal of Mathematics, *(2015), Volume 1, Issue 2, pp 329-336*.*

(5) Global Representations of the Conformal Group and Eigenspaces of the Yamabe Operator on S1xSn, Pacific Journal of Mathematics 275-2 (2015), 463--480. DOI 10.2140/pjm.2015.275.463, joint with Sepanski, M.

(4) Global representations of the Heat and Schrodinger equation with singular potential, Electron. J. Diff. Equ., Vol. 2013 (2013), No. 154, pp. 1-16. (joint with Sepanski, M.)

(3) On the n-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group, SIGMA 9 (2013), 011.

(2) Global SL(2,R) representations of the Schrodinger equation with singular potential, Cent. Eur. J. Math. 10 (2012), 927-941, arXiv:1104.3508.

(1) Diseño de un simulador por computadora de procesos de evaporación en una línea de evaporadores de múltiple efecto JA Franco - Boletín electrónico de la Facultad de Ingeniería de la …, (2006)

**In Progress:**

Regular Methods of Summability and the Banach-Saks Property for Double Sequences, joint with Dumitru, R. and Patterson, R. (in preparation)

The Tricomi Equation and Complementary Series Representations of SL(2;R), joint with Hunziker, M. (in preparation)

Matrix Means and Uncertainty Principle Functions, joint with Dumitru R. and Zhang F. (submitted)

On the Uniform Convexity of the q-Analogues of L^p spaces and the q-Clarkson Inequalities, joint with Dumitru, R and Morales, P. (accepted for publication)

On a New Type of Permutation Invariant Spectral Metrics on Simple Graphs, joint with Nikolas Blain (submitted)