Degrees

• Ph.D. University of Zürich, Switzerland (2013).
• M.Sc. University of Utrecht, the Netherlands (2009).
• B.A. Universidad de los Andes, Colombia (2004).

Research Interests

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 graph theory, topological combinatorics and information theory.

Teaching Interests

I enjoy teaching courses with a wide range of topics and levels, from Introductory Calculus and Linear Algebra to more advanced ones, including Graph Theory, Lie Theory and Differential Geometry. 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. 

Selected Publications and Preprints

• Ivan Contreras, Adele Long, Sophia Marx and Rajan Mehta, Examples and Classification of Frobenius Objects in Rel, to appear in Higher Structures in Geometry, Topology and Physics, Contemporary Mathematics, AMS (2024) (18 pages).
• Ivan Contreras and Andrew Tawfeek, On Discrete Gradient Vector Fields and Laplacians of Simplicial Complexes, Annals of Combinatorics, Vol. 28, Issue 1 (2024), pp 67–91.
• Beata Casiday, Ivan Contreras, Thomas Meyer, Sabrina Mi and Ethan Spingarn, Laplace and Dirac Operators on Graphs, Linear and Multilinear Algebra, Vol. 72:2 (2024), pp 325–365.
• Ivan Contreras, Rajan Mehta and Walker Stern, Frobenius and Commutative Pseudomonoids in the Bicategory of Spans ,  (Preprint) arXiv: 2311.15342 (2023) (46 pages).
• Ivan Contreras, Pavel Mnev and Konstantin Wernli, Combinatorial QFT on Graphs: First Quantization Formalism,  (Preprint) arXiv: 2308.07801 (2023) (72 pages).
• Ivan Contreras, Chris Elliott and Owen Gwilliam, Defects via Factorization Algebras, Letters in Mathematical Physics, Vol. 113: 46 (2023) (26 pages).
• Ivan Contreras, Molly Keller and Rajan Mehta, Frobenius Objects in the Category of Spans, Reviews in Mathematical Physics, Vol. 34, No. 10 (2022) 2250036 (34 pages).
• Ivan Contreras and Michele Schiavina, Kähler Fibrations in Quantum Information Theory,  Manuscripta Mathematica 168, pp. 325–349 (2022).

• Ivan Contreras, Nima Moshayedi and Konstantin Wernli, Convolution Algebras for Relational Groupoids and Reduction, Pacific Journal of Mathematics, Vol. 313, No. 1 (2021), pp 75-105.

• Ivan Contreras and Rui Fernandes, Genus Integration, Abelianization and Extended Monodromy, International Mathematics Research Notices (IMRN), Issue 14 (2021), pp 10798-10840.

• Ivan Contreras and Nicolas Martinez Alba, Poly-symplectic Geometry and the AKSZ Formalism, Reviews in Mathematical Physics, Vol. 33, No. 9 (2021) 2150030 (14 pages).

• Alberto Cattaneo and Ivan Contreras, Split Canonical Relations, Annales Henri Lebesgue, Vol. 4 (2021), pp 155-185.

• Ivan Contreras, Michael Toriyama and Chengzeng Yu, Gluing of Graph Laplacians and Their Spectra, Linear and Multilinear Algebra, Vol. 68, No 4 (2020), pp 710-749.

• Ivan Contreras and Boyan Xu, The Graph Laplacian and Morse Inequalities, Pacific Journal of Mathematics, Vol. 300 (2019), No. 2, pp 331-345.

• Ivan Contreras and Nicolas 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.

Editorial Work

• 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).

Activities

• I am one of the organizers of the Primer Encuentro Colombiano de Geometría y Topología, at Universidad Nacional de Colombia, Bogotá, in Summer 2024.
• In March 2023, I was one of the local organizers of the 9th Gone Fishing Conference in Poisson Geometry at Amherst College. The conference was centered on the theme “Poisson geometry and its derived, shifted, and higher variants”. The conference was partially supported by the NSF grant DMS-2232673. 
• Since February 2024 I am a member of the Selection Committee of the Award For Math Programs That Make A Difference, American Mathematical Society (AMS).
• Since February 2024 I am a member of the AMS-Simons Travel Grants Committee.

Personal Website

You can see my personal website