Ivan Contreras
Contact Info
Address:
31 Quadrangle Drive
Amherst MA
Office:
502 Seeley Mudd Building
Phone number:
(413) 5425749
Email:
icontreraspalacios at amherst dot edu
Office Hours:
Mon: 1112, 13, Wed: 1112, Thu: 1112, Fri: 1112
Teaching
Courses
Amherst College
Spring 2021 MATH 102/PHYS 102: Geometry and Relativity.
Spring 2021 MATH 220: Mathematical Reasoning and Proof.
Fall 2020 MATH 255: Geometry (Sections 01 and 02 ).
Spring 2020 MATH 271: Linear Algebra.
Sprig 2020 MATH 221: Multivariable Calculus.
Fall 2019 MATH 280: Graph Theory.
Fall 2019 MATH 11101: Introduction to the Calculus.
Spring 2019 MATH 220: Mathematical Reasoning and Proof.
Spring 2019 MATH 405: Lie Groups and Lie Algebras.
Fall 2018 MATH 220: Mathematical Reasoning and Proof.
Fall 2018 MATH 11101: Introduction to the Calculus.
Previous Courses
University of Illinois, UrbanaChampaign
Spring 2018 MATH 415: Applied Linear Algebra.
Summer 2017 MATH 415: Applied Linear Algebra.
Fall 2016 MATH 415: Applied Linear Algebra.
Spring 2016 MATH 416: Abstract Linear Algebra.
University of California, Berkeley
Fall 2015 MATH 113: Abstract Algebra.
Summer 2015 MATH 16B: Calculus and analytic geometry.
Research
Research Interests
 Mathematical Physics
 Differential Geometry
 Lie Groups and Lie Algebras
 Poisson and Symplectic Geometry
Accepted Papers
Split Lagrangian Relations, with A.S. Cattaneo, to appear in Annales Henri lebesgue (2020).
Gluing of Graph Laplacians and Their Spectra, with M. Toriyama and C. Yu, Linear and Multilinear Algebra, Vol. 68, No 4 (2020).
Genus Integration, Abelianization and Extended Monodromy, with R.L. Fernandes, International Mathematics Research Notices, No. 7 (2019).
The graph Laplacian and Morse inequalities , with B. Xu, Pacific Journal of Mathematics, Vol. 300, No 2 (2019).
PolyPoisson sigma models and their relational polysymplectic groupoids , with N. Martinez Alba, Journal of Mathematical Physics, Vol. 59, Issue 7 (2018).
A functorial construction for quantum subtheories , with A. Duman, Entropy 19 (5) 220 (2017).
Geometric quantization and epistemically restricted theories , with A. Duman, Proceedings of Quantum Physics and Logic (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. 723767 (2015).
Groupoids, Frobenius algebras and Poisson sigma models,
in Mathematical Aspects of Quantum Field Theories, Mathematical Physical Studies, Springer, Part III, pp. 413427 (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. 315330 (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. 322339 (2013).
Relative Frobenius algebras are groupoids, with A.S. Cattaneo and C. Heunen, Journal of Pure and Applied Algebra 217, pp. 114124 (2012).
Selected Talks
 Dec. 2020: Geometry and Topology Seminar, UPenn
 Sep. 2020: Colloquium Talk, Amherst College
 Jun. 2020: Virtual Conference "A Gauge Summer with BV"
 Jun. 2020: Virtual REU Seminar, University of Connecticut
 May. 2020: Virtual Conference "Gone Fishing Poisson Geometry"
 Oct. 2019: Geometry Seminar, Dartmouth College
 Sep. 2019: Colloquium Talk, Amherst College
 Sep. 2019: Differential Geometry, Geometric Analysis and Mathematical Physics Session, Union College Mathematics Conference
 Aug. 2019: Colloquium Talk, Yale University
 Aug. 2019: SURF Faculty Presentation, Amherst College
 May 2019: Gong Talk, String Field Theory, Conference: String field theory, BV quantization, and moduli spaces, Simons Center for Geometry and Physics, Stony Brook
 Feb. 2019: Colloquium Talk, Smith College
 Jan. 2019: Colloquium Talk, Bucknell University
 Jan. 2019: Colloquium Talk, Mount Holyoke College
 Jan. 2019: Colloquium Talk, Rutgers University, Newark
 Jan. 2019: AMS Special Session on Latinx in Mathematics,
Joint Mathematical Meetings, Baltimore MD
 Dec. 2018: Colloquium Talk, University of Hartford
 Oct. 2018: AMS Special Session on Cluster Algebra, Poisson Geometry,
and Related Topics, AMS Sectional Meeting, Ann Arbor MI
 Oct. 2018: AMS Special Session on Aspects of Geometric Mechanics
and Dynamics, AMS Sectional Meeting, Ann Arbor MI
 Sep. 2018: Geometry and Topology Seminar, UMass Amherst.
 Jun. 2018: Great Lakes Mathematical Physics Meeting, Michigan State University.
 Mar. 2018: Colloquium talk, Union College.
 Jan. 2018: Colloquium talk, Amherst College.
 Feb. 2018: Mathematical Physics Seminar, Purdue University.
 Dec. 2017: Joint UIUCWUSL Seminar, Washington University in Saint Louis.
 Nov. 2017: Representation Theory and Mathematical Physics Seminar, University of California Berkeley.
 Aug. 2017: Beling Lectures, Illinois Wesleyan University. Slides here and Video here .
 Mar. 2017: Doob Colloquium, University of Illinois at UrbanaChampaign. Handwritten notes here.
 Oct. 2015: Representation Theory and Geometry Seminar, UC Berkeley. Handwritten notes
here.
 Sep. 14, 2015: Symplectic Geometry Seminar, UC Berkeley.
 May 21, 2015: Oberseminar, Max Planck Institute of Mathematics, Bonn. Handwritten notes
here.
 Feb. 6, 2015: Representation Theory, Geometry and Combinatorics Seminar, UC Berkeley.
 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.
 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.
Mentoring
In Summer 2020 I am the faculty mentor the SURF (Summer Undergraduate Research Fund)/Greg Call Project: Small World Networks and Dynamics on Graphs .
In Summer 2019 I was the faculty mentor the SURF (Summer Undergraduate Research Fund)/Greg Call Project: Quantum Entropy and Graph Theory .
In Summer 2018 I was the faculty mentor of the Uni High School Project Dynamics on Fractals .
In Spring 2018 I was the faculty mentor of the IGL Project Poisson geometry in low dimensions.
In Summer 2017 I was 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 CWcomplexes.
In Fall 2016 I was the faculty mentor of the first stage of the IGL Project Quantum mechanics for graphs and CWcomplexes.
Thesis Advising
Alexander Mangiafico (20192020): Topological Data Analysis and Persistent Homology
Andrew Tawfeek (20192020): Discrete Morse Theory (CoAdvisor: Alejandro Morales (UMass)
Advising: Undergraduate Research Projects
Summer 2020 (Remote)
Katie Lingen
Zhara Shah
Malaika Kironde (Smith College)
Leo Xu
Summer 2019
MariaCristiana Girjau
Andrew Moore
Andrew Rosevear
Matthew Sanders
Dawit Wachelo
Andrew Tawfeek
Spring 2018
Joel Villatoro (Graduate Team Leader)(Current position: postdoc at KU Leuven)
Oscar Rodrigo Araiza (Current position: PhD student, Harvard University)
Leonardo Javier Rodriguez (Current position: Msc. University of Illinois)
Jessica Bai
Summer 2017
Andrew Eberlein (Current position: PhD student, Texas A&M University)
Mateo Muro
Yunting Zhang
Schur Zhao
Spring 2017
Sarah Loeb (Graduate Team Leader)
Sai Aishwarya Korukanti
Zitong Chen
Oscar Rodrigo Araiza
Fall 2016
Sarah Loeb (Graduate Team Leader) (Current position: Assistant Professor at HampdenSydney College)
Zhe Hu (Current position: MsC. Cornell University)
Michael Toriyama (Current position: PhD student, Northwestern University)
Boyan Xu (Current position: PhD student, University of California, Berkeley)
Chengzheng Yu (Current position: PhD student, University of Illinois)
Service

In Fall 2020, I am the Amherst College Putnam Coordinator. If you are interested in joining the training sessions, click here
for further details.
 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 coorganizer 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.
Media

A profile in Lathisms, which recognizes contributions of Latinx and Hispanics in Mathematical Sciences.