I particularly enjoy working on research projects with students.
Luis Rodriguez, Riemann, Lebesgue and Henstock-Kurzweil integrals: a comparative analysis, Spring23-Summer 23
Fadoua Chigr, Convergence spaces theory and applications in Topology, Fall 18-Fall 19
Naima Ouabourrane, On the concepts of limit and of infinitesimal, Fall17-Spring 18
Abdurhaman Pllana, elements of fixed point theory, Fall 16-Spring 17
Sofiane Boudib, on the development of the concept of group, Fall 15-Spring 16
Jose Pedraza: filters, grills and Ramsey Theory, Spring 15-Spring 16
Zineb Hassoune, concepts of integral, Fall 15-Fall 16
Ray Macchiarola: decomposition of continuity, Fall 14-Spring 15
William Trott, Elements of convergence approach space theory, May 2014 (See publications for two joint papers)
Nathan Farmer, Compact filters and the Arzelà-Ascoli Theorem, May 2012
In recent years I have been invited to participate to several PhD jury. I welcome it, as long as the work is presented in English, Spanish, or French. In some cases, I have collaborated with graduate students as a result.
Karen Van Opdenbosch, A study of topological properties in approach theory using monodical topology, Free University of Brussels and University of Antwerp,Belgium, February 2019
Emilio Angulo-Perkins, Algunas adjunciones a GConv, Benemétrica Universidad Autónoma de Puebla, Mexico, June 2021
Jesús González Sandoval, Levantamiento de estructuras, operadores límite y subcategorías coreflexivas en categorías topológicas, Benemétrica Universidad Autónoma de Puebla, Mexico, September 2021
Rayza Riofrio, why convergence of filters?, Summer 23
Sally Mangassa, Order and Spacetime, Summer 22
Rachael Mazzarella, Domain Theory and Topology, Summer 22
Daniel Esteva, Quaternions and their geometric interpretation, Summer 21
Jason Gonzaga, Spaces of ultrafilters and convergence spaces, Summer 20
Abdelrahman Bereka, Real Induction, Summer 19
Leonardo Moncada, Counting collisions, tracking beams of light, and Pi, Summer 19
Ammer Abdin, convergence, filters and ultrafilters, Summer 19 and Summer 20
Angel Madera, fractals and fractal dimension, Summer 18
Crystal Simon, a geometric approach to the Basel problem, Summer 18
Fadoua Chigr, elements of convergence theory, Summer 17 (presented at NJCU Research Symposium, April 18; at the STEM C2 Research Summit at Bergen Community College on April 13, 2018; at NYC Math Alliance Regional Conference, Kean University, September 15, 2018)
Fares Boutrous, decomposition of continuity, Summer 17 (presented at NJCU Research Symposium, Spring 18)
Particularly noteworthy is the peer-reviewed publication of the following paper as a result of Fadoua Chigr's project:
F. Chigr and F. Mynard, The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces, Mathematica Slovaca vol. 69, no. 1, 2019, pp. 185-198. https://doi.org/10.1515/ms-2017-0213
Jessee Nesmith, filters and compactifications, Spring and Fall 2008
Anh Tran, Structure of spaces of ultrafilters and combinatorial applications (Fall 2009 and Spring 2010: presented at Eagle Undergraduate Mathematics Conference in Spring 2010)
William Trott, Ultrafilter techniques in Ramsey Theory (Fall 2011 and Spring 2012: presented at Eagle Undergraduate Mathematics Conference and Kennesaw Mountain Undergraduate Mathematics Conference in Spring 2012)
Daniel Diaz Casanueva, quotient of metric spaces, Fall 12-Spring 13