Ivan Contreras

J.L Doob Research Assistant Professor
Department of Mathematics

University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801

Office: Altgeld Hall 107
E-mail: icontrer(at)illinois(dot)edu
Office Hours: By appointment


Spring 2018 (UIUC) MATH 415: Applied Linear Algebra.
Summer 2017 (UIUC) MATH 415: Applied Linear Algebra.
Fall 2016 (UIUC) MATH 415: Applied Linear Algebra.
Spring 2016 (UIUC) MATH 416: Abstract Linear Algebra.
Fall 2015 (UC Berkeley) MATH 113: Abstract Algebra.
Summer 2015 (UC Berkeley)MATH 16B: Calculus and analytic geometry.


I work in the Poisson/Symplectic geometry group, and my postdoctoral mentors are Rui Loja Fernandes and Eugene Lerman . Previously, I was a SNSF (Swiss National Science Foundation) postdoctoral fellow at University of California, Berkeley, in the group of Kolya Reshetikhin.
Here is my CV.

I am interested in geometric and algebraic aspects of mathematical physics, in particular problems relating symplectic and Poisson geometry with classical and quantum field theories. I am also interested in problems coming from groupoid theory and lately I have been trying to understand some links between field theories and derived geometry, as well as quantum information theory.
I wrote my PhD thesis under the guidance of Alberto Cattaneo in Zurich University. In there we describe a generalization of symplectic groupoids that extends to the case of non integrable Poisson manifolds, and is also compatible with the construction of the Poisson sigma model (PSM) as a Lagrangian field theory with boundary.

Together with Alberto and Chris Heunen we proved an equivalence between the category of an extended version Frobenius algebras and the category of groupoids, this gives an algebraic counterpart of the construction of symplectic groupoids and it might be useful for quantization.

With Elisa Ercolessi and Michele Schiavina we have studied the relationship between the geometry and topology of coadjoint orbits and quantum information theory. In particular, we have described the skew symmetric part of the Fisher tensor in terms of the Konstant-Kirilov-Souriau symplectic form for coadjoint orbits, by means of the construction of the symmetric logarithmic differential. This object results very useful while understanding quantum metrology for mixed and pure states of finite dimensional quantum systems.

Accepted papers

See also Google Scholar.



Selected Talks

Undergraduate Research Projects:

In Summer 2017 I am the faculty mentor of the IGL Project Graph theory and statistical quantum mechanics. You may find further information here.
In Spring 2017 I was the faculty mentor of the IGL Project Quantum mechanics for CW-complexes. If you are undergraduate or graduate student interested in joining the team, you may find further information here.

In Fall 2016 I was the faculty mentor of the first stage of the IGL Project Quantum mechanics for graphs and CW-complexes.


Fall 2016
  • Sarah Loeb (Graduate Team Leader)
  • Zhe Hu
  • Michael Toriyama
  • Boyan Xu
  • Chengzheng Yu
    Spring 2017
  • Sarah Loeb (Graduate Team Leader)
  • Sai Aishwarya Korukanti
  • Zitong Chen
  • Oscar Rodrigo Araiza
  • Leonardo Javier Rodriguez
    Summer 2017
  • Andrew Eberlein
  • Mateo Muro
  • Yunting Zhang
  • Schur Zhao