## 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:**

(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:**

On Renyi Divergences and Matrix Means, joint with Dumitru R. and Dinh T.H. (in preparation)

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

Fundamental Theorems of Summability Theory for a New Type of Subsequences of Double Sequences, joint with Dumitru R. (submitted)

Generalized Hellinger Metrics and Audenaert's In-Betweenness, joint with Dumitru R. (submitted)

Some geometric properties of matrix means in different distance functions, joint with Dumitru, R. and Dinh, T. Hoa (submitted)

Some trace inequalities for operator monotone and operator convex functions, joint with Dumitru, R. and Dinh, T. Hoa (submitted)

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)

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**Office Hours**

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