Gavin J. Seal
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Mathematical Sciences
Georgia Southern University
Statesboro, GA 30460
Phone: (912) 478 5390
Fax: (912) 478 0654

gseal at georgiasouthern dot edu
Office: 3041

Brief CV

After obtaining my Master's Degree from the University of Geneva, in Switzerland, I received my Ph.D. in 2000 from the Université Libre de Bruxelles, while working as a teaching assistant at the Ecole Polytechnique Fédérale de Lausanne. In 2001, taking advantage of a grant awarded by the Swiss National Science Foundation, I spent 18 months at York University, in Toronto, pursuing my research with Walter Tholen. After returning to Switzerland in 2003, I took up a job as a mathematics teacher at the Collège de la Golette for one year. In 2004, I left for the math department at McGill University, in Montreal, where Michael Barr funded  me through his NSERC grant. A few months later, I switched to another grant from the Swiss National Science Foundation, and joined Prakash Panangaden's group. Finally, in 2007, I got hired as a temporary assistant professor at Georgia Southern University in the United States, where you can find me now.


For a more detailed CV, click here.

Research Interests

Although the main subject of my Ph.D. Thesis was in incidence geometry, the approach that my supervisor Claude-Alain Faure suggested was categorical in nature. This lead me to category theory and more specifically to categorical topology. In the early years of my doctoral studies, I also had the opportunity to tackle questions in functional analysis for my Master's Thesis, numerical analysis via a problem in dynamical systems, and differential geometry (this is in fact the subject of my Minor Thesis, which is a requirement for the Belgian doctorate).

Since my postdoctoral stay at York University, in Toronto, my interest in category theory and its applications in topology has grown to become my main area of research. Currently, I am contributing to the development of lax Eilenberg-Moore algebras, which allow for a convergence-theoretic approach of diverse structures in topology. In this regard, I am involved in the writing of a monograph on the subject with Maria Manuel Clementino, Eva Colebunders, Dirk Hofmann, Robert Lowen, Christoph Schubert, and Walter Tholen to present the state of research in the field. I am also collaborating with Frédéric Mynard on aspects of the theory, and am seeking developments in domain and homotopy theory.


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Publications

Research papers

  1. A Kleisli-based approach to lax algebras. Revised version to appear in Appl. Categ. Struct., 15 pages; pdf, dvi.
  2. Canonical and op-canonical lax algebras. Theory Appl. Categ. 14 (2005), 221-243; pdf, dvi.
  3. Cartesian closed topological categories and tensor products. Appl. Categ. Struct.13 (2005), 37-47; pdf, dvi.
  4. Free modules over cartesian closed topological categories. Appl. Categ. Struct.13 (2005), 181-187; pdf, dvi.
  5. Polar spaces embedded in projective spaces. Adv. Geom. 5 (2005), 353-361; pdf, dvi.
  6. Morphisms of polar spaces. In collaboration with Claude-Alain Faure. Beitr. Alg. Geom. 45 (2004), 169-181; pdf, dvi.
  7. Embeddings of polar spaces. J. Combin. Theory A 102 (2003), 194-200; pdf, dvi.

Preprints

  1. Phenotype spaces. In collaboration with Frédéric Mynard. 14 pages; pdf, dvi.
  2. Extensions in the theory of lax algebras. In collaboration with Christoph Schubert. 30 pages; pdf, dvi.
  3. The Chu construction for complete atomistic co-atomistic lattices. In collaboration with Boris Ischi. 19 pages; pdf, dvi.

PhD thesis

  • Morphisms of Polar Spaces and Related Structures. (2000), 106 pages; pdf, dvi.
 

Teaching

 
The content of personal and other unofficial home pages is not sanctioned by Georgia Southern University and does not represent official information or opinions of the University. The author of this page, Gavin J. Seal, is solely responsible for its contents. Last modified: 7th April, 2008.