Welcome to Omar Saldarriaga`s Personal site
Teaching
- Spring 2022
Mathematics department
Highpoint University.
Instructor record of: Applied calculus for business.
- Fall 2007 to fall 2021
Department of Mathematics.
Universidad de Antioquia
Instructor Record of: Differential Geometry (graduate and under-gradutate), Theory of Lie groups (graduate and under-gradutate), Lie algebras (graduate and under-gradutate), Multi-linear algebra (graduate and under-gradutate), Hiperbolic geometry, Euclidean Geometry, Abstract algebra, Linear algebra, Calculus in several variables, Integral calculus, Differential calculus, Discrete Mathematics, Pre-calculus, Basic algebra, Mathematics for non math majors.
Online courses: Topics of arithmetic (Elementary number theory and Discrete math).
- Fall 2004 to spring 2007
Department of Mathematical Sciences
William Paterson University
Instructor of record for: Contemporary Mathematics, Algebra & geometry with applications, Calculus I and II, Pre-calculus, Math for high-school instructors, Linear algebra, Mathematics for Business, Mathematical logic and Euclidean Geometry
- Fall 1998 -- spring 2004
Department of Mathematical Sciences
SUNY Binghamton
Instructor of record for: Pre-calculus, Calculus I, Calculus II, Calculus III, Linear Algebra, Discrete Mathematics.
Teaching assistant for: Elementary Statistics, Calculus I, Complex Analysis.
E.O.P. Summer instructor for Pre-calculus and Calculus . Summer 1999 to 2003
- Fall 1993- Spring 1998
Department of Mathematical Sciences
Universidad de Antioquia
Teaching assistant for Pre-calculus
Adjunct faculty for Algebra for high school students.
Instructor of Vector Geometry.
Papers
Omar Saldarriaga, Alexander Flórez. On the group of affine transformations of flat affine homogeneous spaces. Available at Group of affine Transformations of flat affine homogeneous spaces.
Alberto Medina, Omar Saldarriaga, Andres Villabon. Flat Affine Manifolds And Their Transformations. Manuscripta Math 2020. Available at FlatAffineManifoldsandtheirTransformations DOI doi.org/10.1007/s00229-020-01262-7.
Omar Saldrriaga, Alexander Flórez. Transformation groups of certain flat affine manifolds. Sao Paulo Journal of Mathematics 2020. Available online at: https://doi.org/10.1007/s40863-021-00223-6
Alberto Medina, Omar Saldarriaga, Hernán Giraldo, Flat Affine or Projective Geometries on Lie groups, Journal of algebra, 445 (2016) 183--208.
Hernán Giraldo, Agustín Moreno Cañadas and Omar Saldarriaga. Some equivalences between homotopy and derived categories. Far East Journal of Mathematics, Vol 98 number 1, (2015) 1-14
Omar Saldarriaga, A particular case of the level increasing property for fusion algebras, JP Journal of algebra and combinatorics, 27 2012, no 2. 193--201
Omar Saldarriaga, Type A fusion rules, Integración, December 2009
Omar Saldarriaga, Fusion algebras, symmetric polynomials, and S_k-orbits of Z_N^k Journal of algebra, 312 (2007), no. 1, 257--293
Books
Omar Saldarriaga, Hernán Giraldo. Algebra Lineal con el uso del MatLab. Editorial Universidad de Antioquia. (2018) 391 pags. See cover.
Omar Saldarriaga. Tensor and Multilinear Algebra. In preparation. Available at Álgebra Multilineal y Tensorial
Omar Saldarriaga. Euclidean and hyperbolic geometry. In preparation. Available at Geometría, Capítulo 4, Capítulo 5, Capítulo 6, Capítulo 7, Capítulo 8, Capítulo 9
Student Advising
PhD Students
Affine or Symplectic Geometry on Homogeneous spaces. Andrés Villabón, 2017. (Awarded with Magna Cum Laude).
Group of Affine Transformations of Homogeneous Spaces. William Alexander Flórez. In progress.
Master students
Invariant metrics on homogeneous G-spaces. Carlos Alejandro Espinal, In progress.
Some Remarks about flat affine symplectic manifolds. Fabricio Valencia, Master Thesis, 2019. (Awarded with Magna Cum Laude). Available at Master thesis .
Infinitesimal Affine transformations. William Alexander Florez. 2015.
Flat Affine and flat projective structures on 3 and 4-dimensional Lie groups, Diego Espinal, Master thesis 2014.
Undergraduate students
Riemannian, Lorentzian and Hyperbolic mectrics on Lie groups of dimensions 2, 3 and 4. Juan Felipe Buitrago
Symplectic Geometry and Hess Connection. Juan Sebastian Herrera. 2017 (Awarded special mention).
Classification of Riemmanian and pseudo-Riemannian metrics on 3-dimensional Lie groups. Fabricio Valencia. 2017 (Awarded special mention).
Clasificación de las álgebras de Lie simples y semisimples finito dimensionales, William Alexander Flórez, 2013.
Grupos de Lie Matriciales y Geometría Afín sobre la Recta, Sebastián Álvarez, 2013.
Polinomios simétricos y tableros de Young, Luz Elena Domínguez, 2012.
Polinomios simétricos y el algoritmo de Racah-Speiser para calcular el producto tensorial para álgebras de Lie, Paola Andrea Avendaño, 2011.
Los teoremas de Lie y de Engel, Johani Bolaño, 2011.
Supersolids, Julio Borgoño, 2007.
Using conics to find solutions to quadratic and cubic equations, Margaret O'Keefe, 2007.
Infinity and Beyond, Lea Kelly, 2007.
DNA computations, Kenneth Ellsworth, 2007.
Symmetric Polynomials, Lindita Kurtishi, 2006.
Mathematical visualizations with Geometer's Scketchpad, Monika Bartnik, 2006.
Fibonacci numbers, puzzles and applications, Ennely Cid, 2005.
Parametrizing and finding rational points on linear, quadratic, and cubic polynomials, Giuseppe Tesauro, 2005.