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

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.

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.

- A functorial construction for quantum subtheories , with A. Duman, Entropy 19 (5) 220, DOI: 10.3390/e19050220, 2017.

- Geometric quantization and epistemically restricted theories , with A. Duman, Proceedings of Quantum Physics and Logic, DOI: 10.4204/EPTCS.236, ISSN: 2075-2180, 2017.

- On the geometry of mixed states and the Fisher information tensor , with E. Ercolessi and M. Schiavina, Journal of Mathematical Physics, Vol. 57, Issue 6,062209, 2016.

- Relational symplectic groupoids , with A.S. Cattaneo, Letters in Mathematical Physics, Vol. 105, Issue 5, pp. 723-767, 2015.

- Groupoids, Frobenius algebras and Poisson sigma models, in Mathematical Aspects of Quantum Field Theories, Mathematical Physical Studies, Springer, Part III, pp. 413-427, 2015.

- Groupoids and Poisson sigma models with boundary, with A.S. Cattaneo, in Geometric and Topological Methods for Quantum Field Theory, Proceedings of the 2011 Villa de Leyva Summer School, Cambridge University Press, pp. 315-330, 2013.

- Models for formal groupoids, in Geometric and Topological Methods for Quantum Field Theory, Proceedings of the 2009 Villa de Leyva Summer School, Cambridge University Press, pp. 322-339, 2013.

- Relative Frobenius algebras are groupoids, with A.S. Cattaneo and C. Heunen, Journal of Pure and Applied Algebra 217, pp. 114-124, 2012.

- Genus Integration, Abelianization and Extended Monodromy, with R.L. Fernandes, submitted, 2018.

- Gluing of Graph Laplacians and Their Spectra, with M. Toriyama and C. Yu, preprint, 2018.

- Poly-Poisson Sigma Models and Their Relational Poly-Symplectic Groupoids , with N. Martinez Alba, submitted, 2017.

- Hyperwalk Formulae for Even and Odd Laplacians in Finite CW-Hypergraphs , with S. Loeb and C. Yu, submitted, 2017.

- The graph Laplacian and Morse inequalities , with B. Xu, submitted, 2017.

- Relational symplectic groupoids and Poisson sigma models with boundary, PhD Thesis, 2013.

- Geometric and Topological Methods for Quantum Field Theory, with A. Cardona and A. Reyes-Lega, Proceedings of the 2009 Villa de Leyva Summer School, Cambridge University Press, June 2013

- Un recorrido por el algebra, with J. Madronero, Universidad Antonio Narino, June 2006.

- Jun. 23, 2018: Poisson sigma models and poly-symplectic geometry, Great Lakes Mathematical Physcis Meeting, Michigan State University.

- Mar. 12, 2018: Colloquium talk, Union College.

- Jan. 23, 2018: Colloquium talk, Amherst College.

- Feb. 1, 2018: Integration of poly-Poisson structures, Mathematical Physics Seminar, Purdue University.

- Dec. 2, 2017: Integration of poly-Poisson structures, Joint UIUC-WUSL Seminar, Washington University in Saint Louis.

- Nov. 29, 2017: Integration of poly-Poisson structures, Representation Theory and Mathematical Physics Seminar, University of California Berkeley.

- Aug. 9, 2017: Graph Theory in Quantum Mechanics and Thermodynamics, Beling Lectures, Illinois Wesleyan University. Slides here and Video here .

- Jun. 9, 2017:Poisson sigma models and the symplectic category, Higher structures and Field Theories BIRS Conference, Oaxaca, Mexico. Lecture notes here.

- May. 4, 2017: Poisson sigma models and surfaces with genus, Gone Fishing Poisson Geometry Conference, University of Notre Dame, Indiana.

- Mar. 1, 2017: Quotient spaces, Lie theory and quantization, Doob Colloquium, University of Illinois at Urbana-Champaign. Handwritten notes here.

- Nov. 29, 2016: Mecanica Cuantica y Teoria de Grafos (Quantum Mechanics and Graph Theory), Mathematics for Students Conference, Universidad de Los Andes, Colombia. Handwritten notes (in Spanish) here.

- Oct. 11, 2016: Poisson geometry and BV-BFV theories, Topology Seminar,University of Notre Dame, Indiana.

- Feb. 8, 2016: Split Lagrangian subspaces in field theories, Symplectic and Poisson Geometry Seminar, University of Illinois at Urbana-Champaign. Handwritten notes here.

- Oct. 16, 2015: Abelian BF theory and topological insulators, Representation Theory and Geometry Seminar, UC Berkeley. Handwritten notes here.

- Sep. 14, 2015: Symplectic and Lagrangian structures in field theories with boundary, Symplectic Geometry Seminar, UC Berkeley.

- May 21, 2015: Lie theory and topological field theories, Oberseminar, Max Planck Institute of Mathematics, Bonn. Handwritten notes here.

- Feb. 6, 2015 AKSZ formulation for two dimensional topological field theories, RTGC Seminar, UC Berkeley. Handwritten notes here.

- Dec. 1, 2014: Lagrangian correspondences and extensions of the Poisson sigma model, Northern California Symplectic Geometry Seminar. Handwritten notes here.

- Nov. 9, 2014: Integration of Poisson manifolds and canonical relations, Gone Fishing Meeting, UC Berkeley. Handwritten notes here.

- May 22, 2014: Lagrangian correspondences and extensions for the Poisson sigma models, Talks in Mathematical Physics, ETH, Zürich.

- April 22, 2014: Differential forms in derived Artin stacks, Derived (Symplectic) Geometry seminar, UC Berkeley. Handwritten notes here.

- April 16, 2014: Structured factorization algebras, Seminar on Factorization Algebras in Quantum Field Theory UC Berkeley. Handwritten notes here.

- March 21, 2014: Poisson sigma models, Lie's third theorem and Lagrangian correspondences, Geometry, Representation theory and Combinatorics seminar, UC Berkeley. Handwritten notes here.

- April 22, 2014: A (quick) introduction to stacks, Seminar on derived algebraic geometry, ETH Zurich. Handwritten notes here.

- July 20, 2013: Grupoides simplecticos en Teorias topologicas de campos (Symplectic groupoids in Topological field theories), Colombian Congress of Mathematics.

- June 7, 2013: Relational symplectic groupoids and Poisson sigma models with boundary, PhD dissertation, Zurich University.

- February 7, 2013: The extended symplectic category, Winter school in Mathematical Physics, Les Diablerets, Switzerland.

- February 19, 2013: What is a symplectic groupoid? Zurich Graduate Colloquium, Switzerland.

- October 30, 2012: Relational symplectic groupoids, Knot theory seminar, Geneva University, Switzerland.

- March 16, 2012: Lie algebroids and Poisson sigma models, Non commutative geometry seminar, Athens University, Greece.

- July 5, 2011: Symplectic groupoids and field theories with boundary, Summer School "Geometric, Algebraic and Topological Methods for Quantum Field Theory", Villa de Leyva, Colombia.

- July 14, 2009: Models for formal symplectic groupoids, Summer School "Geometric, Algebraic and Topological Methods for Quantum Field Theory", Villa de Leyva, Colombia.

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.

- Since Spring 2017, I am organizing the Symplectic and Poisson Geometry Seminar at UIUC. You may find the calendar of the seminar here.

- Since Spring 2017, I am co-organizing with Laura Escobar the Doob Colloquium at UIUC.

- In Spring 2015, I helped Alan Weinstein with the organization of the Freshman Seminar (MATH 24) on "Geometry, Relativity, and the Fourth Dimension" at UC Berkeley.

- I was co-organizer of the Zurich Graduate Colloquium, intended to be a "What is...? "-type of Colloquium, given by graduate students and postdocs, at UZH and ETH.

- Also in Zurich, during the Fall Semester 2013, I organized the seminar The moduli space of flat connections, for advanced undergraduate students, Master and PhD students. This is the program of the course. Notes of the special talks given by Victoria Hoskins for the seminar can be found here.