Ph.D. University of Zürich, Switzerland (2013)
M.Sc. University of Utrecht, the Netherlands (2009)
B.A. Universidad de los Andes, Colombia (2004)
My research lies at the intersection of geometry, topology and mathematical physics. There are two different ways to understand physical systems. One is called classical, the analysis of phenomena at a macroscopic level, and the other one is called quantum, which deals with the physics at the subatomic scale. My focus is on understanding and connecting these two different approaches by using tools of differential geometry like Lie groups, Lie algebras and Poisson structures. I am also interested in undergraduate research, in particular the applications of some of these techniques to network theory and information theory.
I enjoy teaching courses with a wide range of topics and levels, from Introductory Calculus and Linear Algebra to more advanced ones, such as Lie Groups and Lie Algebras, Differential Geometry and Graph Theory. I encourage active participation and discussions during the lectures, and I emphasize connections with other branches of science and knowledge. I have mentored several research projects with both undergraduate and high school students, on topics which involve pure mathematics and applications to physics and network theory.
B. Casiday, I. Contreras, T. Meyer, S. Mi, E. Spingarn, Laplace and Dirac Operators on Graphs, Linear and Multilinear Algebra (2022) (41 pages).
I. Contreras, M. Keller and R. Mehta, Frobenius Objects in the Category of Spans, Reviews in Mathematical Physics, Vol. 34, No. 10 (2022) 2250036 (34 pages).
I. Contreras and M. Schiavina, Kähler Fibrations in Quantum Information Theory, Manuscripta Mathematica 168, 325–349 (2022).
I. Contreras, N. Moshayedi and K. Wernli, Convolution Algebras for Relational Groupoids and Reduction, Pacific Journal of Mathematics, Vol. 313, No. 1 (2021), pp. 75-105.
I. Contreras and R. Fernandes, Genus Integration, Abelianization and Extended Monodromy, International Mathematics Research Notices (IMRN), Issue 14 (2021), pp 10798-10840.
I. Contreras and N. Martinez Alba, Poly-symplectic Geometry and the AKSZ Formalism, Reviews in Mathematical Physics, Vol. 33, No. 9 (2021) 2150030 (14 pages).
A. Cattaneo and I. Contreras, Split Canonical Relations, Annales Henri Lebesgue, Vol. 4 (2021), pp 155-185.
I. Contreras, M. Toriyama and C. Yu, Gluing of Graph Laplacians and Their Spectra, Linear and Multilinear Algebra, Vol. 68, No 4 (2020), pp 710-749.
I. Contreras, B. Xu, The Graph Laplacian and Morse Inequalities, Pacific Journal of Mathematics, Vol. 300 (2019), No. 2, pp 331-345.
I. Contreras and N. Martinez Alba, Poly-Poisson Sigma Models and their Relational Poly-Symplectic Groupoids, Journal of Mathematical Physics, Vol. 59, Issue 7 (2018), (23 pages).
The whole list of publications can be found here
Since 2022, I am an Editor at Quantum Journal , an open journal for quantum sciences (Verein zur Förderung des Open
Access Publizierens in den Quantenwissenschaften, ISSN 2521-327X, Austria)
I co-edited (with Alexander Cardona and Andrés Reyes-Lega) the book "Geometric and Topological Methods for Quantum Field Theory: Proceedings of the 2009 Villa de Leyva Summer School". Cambridge University Press (2013)
You can see my personal website