Dr. Eduardo Martínez-Pedroza

Current research group members at Memorial

• Eric Pope, Undergraduate Honours student.
• Griffin Bartlett, MSc Student.
• Diana Belén Vizcaíno Torres, MSc Student.
• Matthew Brannock, PhD Student.
• Haoyang He, PhD Student.

Former PhD students

• Shivam Arora 2017-2022
  Thesis: On compactness properties of subgroups. Memorial University, 2022.
  S. Arora and E. Martínez-Pedroza. Topological groups with a compact open subgroup, Relative hyperbolicity and Coherence. (Submitted)
  S. Arora and E. Martínez-Pedroza. Fixed Point Sets in Diagrammatically Reducible Complexes. (Submitted)
  S. Arora, G. Corob Cook, I. Castellano and E. Martinez-Pedroza. Subgroups, Hyperbolicity and Cohomological Dimension for Totally Disconnected Locally Compact Groups. Journal of Topology and Analysis. (Online ready)
  S. Arora and E. Martínez-Pedroza. Subgroups of Word Hyperbolic Groups in Rational Dimension 2. Groups, Geometry, and Dynamics. (2021)

Former Master students

• Juan Felipe Rodriguez-Quinche, 2020-2022
  MSc Thesis: Cops and Robber Games on Graphs: An approach from Large Scale Geometry. Memorial University, 2022.
  Jonathan Lee, E. Martínez-Pedroza and Farhan Rashid Coarse geometry of the Cops and robber game.

• Farhan Feroz Ali Rashid, 2018-2020
  MSc Thesis: Hyperbolically Embedded Subgroups in terms of Fine graphs. Memorial University, 2020.
  E. Martínez-Pedroza and Farhan Rashid A Note on Hyperbolically Embedded Subgroups. Communications in Algebra. (In Press)

• Jonathan Lee, 2016-2019
  MSc Project report: Games of Cops and Robbers on Cayley Graphs, and Group Invariance. 2019.
  Jonathan Lee, E. Martínez-Pedroza and Farhan Rashid Coarse geometry of the Cops and robber game.

• Takehiko Yamaguchi, 2014-2016. Co-supervise with J.C Loredo-Osti.
  MSc Project report: Persistent Homology and its Use for Time Dependent Data. Memorial University, 2016.

• Muhan Yu, 2013-2015.
  MSc Project report: Persistent Homology and High Dimensional Data Analysis. Memorial University, 2015.

• Richard Gaelan Hanlon, 2012-2014.
  MSc Thesis: Isoperimetric functions of groups and their subgroups. Memorial University, 2014.
  G. Hanlon and E. Martínez-Pedroza. A Subgroup Theorem for Homological Dehn Functions. Groups, Geometry, and Dynamics. 10 (2016)
  G. Hanlon and E. Martínez-Pedroza. Lifting Group Actions, Equivariant Towers and Subgroups of Non-positively Curved Groups. Algebraic & Geometric Topology, 14 (2014)

Former Undergraduate students

During the Summer, I usually supervise undergraduate students under the SURA (Student Undegraduate Research Award) program at Memorial, and the USRA (Undergraduate Student Research Award) program of NSERC. I have supervised honours projects in Pure mathematics and Applied mathematics. Projects under my supervision, in general, involve some geometry, topology or group theory.

• Eric Pope. (SURA Summer 2024)

• Anders Christien Cornect. (USRA Summer 2023; Honours project 2023-2024; USRA Summer 2024)
  Honours project: The Lamplighter groups and Thompson's group F have infinite weak-cop number.
  Summer project: Gromov's Approximating Tree and the All-Pairs Bottleneck Paths Problem.

• Noah MacAuley (Honours project 2016-2017)
  Honours project: Isospectral Plane Domains, Transplantation, and Sunada's Method

• Joshua W. Fleming. (SURA Summer 2015 and 2016)
  J.W. Fleming and E. Martínez-Pedroza. Finiteness of Homological Filling Functions. Involve. (2018)

• Brandon Thorne. (Honours project 2015, co-supervised with Danny Dyer)
  Honours project: Coarse Geometry of the Firefighter Problem. 2015.
  D.Dyer, B.Thorne and E. Martínez-Pedroza. The Coarse Geometry of Hartnell's Firefighter Problem on Infinite Graphs. Discrete Mathematics. (2017)

• Adam Gardner. (USRA 2012; Honours project 2014, co-supervised with H. Kunduri)
  Honours project: A Combinatorial Riemannian Penrose Inequality. 2014

• Justin McGrath. (USRA, 2013; Honours project, 2014; USRA 2014)
  Honours project: Effective Coherence in Random Groups. 2014

• Jonathan Poulin. (MUCEP, 80 hours, 2013)