Costel-Gabriel Bontea

Visiting Assistant Professor of Mathematics and Statistics
Colby College
Mayflower Hill Drive
Waterville, ME 04901

Office: Davis Science Center 330
Phone: 207-859-5843
E-mail: cgbontea@colby.edu
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About me

I completed my Ph.D. studies in 2017, at University of New Hampshire, under the supervision of Dmitri Nikshych. After graduation, I stayed for another year at the same institution as Lecturer. Now I am a Visiting Assistant Professor at Colby College where I am teaching introductory Statistics and Calculus courses.

My research area is in the field of tensor categories. These are mathematical constructions that arise in many areas of mathematics and also in mathematical physics (conformal field theory, quantum statistics) and theoretical computer science (quantum computation). My approach in studying these structures is through the lense of the more developed and better understood theory of Hopf algebras.

You can find a copy of my CV here and a link to my arXiv articles here.



Teaching

Below is a list of all the courses that I've taught.

As an instructor:

  • Series/Multi-Variable Calculus (Fall 2019)
  • Introduction to Statistics and Data Science (Fall 2018, Spring 2019, Fall 2019)
  • Multidimensional Calculus (Summer 2018, Spring 2017, Summer 2016)
  • Calculus I (Spring 2018, Spring 2019)
  • Calculus II (Fall 2017)
  • Calculus for Social Sciences (Fall 2017)

As a teaching assistant:

  • Differential Equations with Linear Algebra (Spring 2016)
  • Calculus for Social Sciences (Fall 2015)
  • Multidimensional Calculus (Spring 2015)
  • Calculus I (Fall 2014)



Research

Publications:

  1. Pointed braided finite tensor categories, with D. Nikshych, Tensor categories and Hopf algebras, 67-94, Contemp. Math., 728, Amer. Math. Soc., Providence, RI, 2019
  2. On the Brauer-Picard group of a finite symmetric tensor category, with D. Nikshych, Journal of Algebra 440 (2015), 187-218
  3. Classifying bicrossed products of two Sweedler's Hopf algebras, Czechoslovak Mathematical Journal 64 (139) (2014), no. 2, 419–431
  4. The classification of all crossed products H4 # k[Cn], with A.-L. Agore and G. Militaru, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 10 (2014), 049
  5. Classifying bicrossed products of Hopf algebras, with A.-L. Agore and G. Militaru, Algebras and Representation Theory 17 (2014), no. 1, 227–264
  6. Classifying coalgebra split extensions of Hopf algebras, with A.-L. Agore and G. Militaru, Journal of Algebra and Its Applications , Vol. 12, No. 5 (2013)

Presentations:

International conferences and workshops:

  1. Classifying pointed braided finite tensor categories, Mathematical Congress of the Americas, July 24-28, 2017, Montreal, Canada (invited talk at the "Hopf algebras and Tensor Categories" Session)
  2. Classification of non-semisimple pointed braided tensor categories and their Brauer-Picard groups, "Modular Categories - Their Representations, Classification, and Applications" workshop, Casa Matemática Oaxaca, Oaxaca, Mexico, August 14-19, 2016 (invited talk)
  3. The factorization problem for Hopf algebras, “Rings, Categories and Hopf algebras” workshop, dedicated to the 70th birthday of Professor Constantin Năstăsescu, University of Bucharest, Bucharest, Romania, May 18-19, 2013 (invited talk)
  4. Classifying bicrossed products of quantum groups, 8-th workshop on “Algebra, Geometry and Mathematical Physics” (AGMP-8), Brno University of Technology, Brno, Czech Republic, September 12-14, 2012.

National meetings:

  1. Classifying pointed braided finite tensor categories, AMS 2017 Fall Western Sectional Meeting, University of California - Riverside, Riverside, California, November 4-5, 2017 (invited talk at the “Special Session on Tensor Categories: Bridging Algebra, Topology, and Physics”)
  2. On the Brauer-Picard group of a finite symmetric tensor category, AMS 2016 Fall Eastern Sectional Meeting, Bowdoin College, Brunswick, Maine, September 24-25, 2016 (invited talk at the “Special Session on Topological Phases of Matter and Quantum Computation”)

Graduate conferences, seminars, etc.:

  1. Tensor categories and Hopf algebras, Colby College, May 1st, 2018
  2. Tensor categories and Hopf algebras, Seminar Series, University of Massachusetts Boston, April 25th, 2018
  3. Brauer groups of finite tensor categories, Algebra and Number Theory Seminar, Dartmouth College, May 18th, 2017
  4. A classification result for pointed braided finite tensor categories, "Hopf algebra representations and tensor categories" Scientific Seminar, Institute of Mathematics of the Romanian Academy, April 4th, 2017
  5. A classification result for a class of finite tensor categories, Graduate Research Conference, University of New Hampshire, April 10-11, 2017
  6. The Brauer-Picard group of some finite tensor categories, Binghamton University Graduate Conference in Algebra and Topology (BUGCAT), Binghamton University, November 14-15, 2015
  7. Modified supergroup algebras and the classification of finite dimensional triangular Hopf algebras, "Hopf algebra representations and tensor categories" Scientific Seminar, Institute of Mathematics of the Romanian Academy, January 16th, 2014