Ivan Contreras

Contact Info    Teaching     Research     Talks    Mentoring    Service    Media   

I am an Assistant Professor in the Mathematics and Statistics Department at Amherst College.
My research lies in the intersection of Differential Geometry, Topology and Mathematical Physics.
I earned my PhD degree in Mathematics at the University of Zurich, under the supervision of Professor Alberto Cattaneo.
After that I held postdoctoral positions at University of California, Berkeley and University of Illinois at Urbana-Champaign.

Here is my CV.

Contact Info


Address: 
Department of Mathematics and Statistics, Amherst College
31 Quadrangle Drive
Amherst MA

Office:
502 Seeley Mudd Building

Phone number: 
(413) 542-5749

E-mail: 
icontreraspalacios at amherst dot edu

Office Hours:
Mon: 11-12, 1-3, Wed: 11-12, Thu: 11-12, Fri: 11-12

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 111-01: 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 111-01: Introduction to the Calculus.

Previous Courses

University of Illinois, Urbana-Champaign

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

Accepted Papers

See also Google Scholar.

  • 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).
  • Poly-Poisson sigma models and their relational poly-symplectic 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. 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).

    • Preprints

  • Convolution algebras for Relational Groupoids and Reduction , with N. Moshayedi and K. Wernli (2020).
  • Graph De Rham Cohomology and the Automorphism Group, with A. Rosevear (2020).
  • Poly-Symplectic Geometry and the AKSZ Formalism, with N. Martinez Alba (2019).
  • Kahler fibrations in quantum information theory, with M. Schiavina  (2019).
  • Relational symplectic groupoids and Poisson sigma models with boundary, PhD Thesis (2013).

    • Editorial Work

    Selected Talks

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

    Thesis Advising

  • Alexander Mangiafico (2019-2020): Topological Data Analysis and Persistent Homology
  • Andrew Tawfeek (2019-2020): Discrete Morse Theory (Co-Advisor: Alejandro Morales (UMass)

    Advising: Undergraduate Research Projects

    Summer 2020 (Remote)
  • Katie Lingen
  • Zhara Shah
  • Malaika Kironde (Smith College)
  • Leo Xu
    Summer 2019
  • Maria-Cristiana 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 Hampden-Sydney 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

    Media