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
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.
See also Google Scholar.
- 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.
- 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 .
- 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.
- Oct. 16, 2015: Abelian BF theory and topological insulators, Representation Theory and Geometry Seminar, UC Berkeley. Handwritten notes
- 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
- Dec. 1, 2014: Lagrangian correspondences and extensions of the Poisson sigma model, Northern California Symplectic Geometry Seminar. Handwritten notes
- Nov. 9, 2014: Integration of Poisson manifolds and canonical relations,
Gone Fishing Meeting, UC Berkeley. Handwritten notes
- 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.
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.
Sarah Loeb (Graduate Team Leader)
Sarah Loeb (Graduate Team Leader)
Sai Aishwarya Korukanti
Oscar Rodrigo Araiza
Leonardo Javier Rodriguez
- 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.