Sam Smith

Professor

Department of Mathematics and Computer Science

Saint Joseph's University

Ph.D. University of Minnesota, 1993
B.S. Bucknell University, 1988

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Courses

Fall 2009

• Honors 1483 Mathematics of Games and Politics

Game Theory Lecture Notes

• Math 1171 Topics in Contemporary Mathematics
• MED 4015 History of Mathematics

Office Hours

Offices: Barbelin 212 x1559

Tuesday  10:00-11:30, 1:00-2:00, Thursday 10:00-11:30 or by appointment

Research

My research interests are in rational homotopy theory. I am working on various collaborative projects studying the rational homotopy theory of function spaces.

In April, 2009, I co-organized (with Yves Félix and Gregory Lupton) an Oberwolfach workshop entitled “Homotopy theory of function spaces and related topics”.

Here is a link to some photographs from the conference. Here is the conference report.

Articles:

Submitted

• From rational homotopy to K-theory for continuous trace algebras ,
  with John Klein and Claude Schochet
• Localization of grouplike function and section spaces with compact domain,
  with Claude Schochet
• Rational homotopy type of the monoid of self-equivalences of a fibration
  with Yves Félix and Gregory Lupton

 In Print

1. Whitehead products in function spaces: Quillen model formulae,
   Journal of the Mathematical Society of Japan vol 62 (2010), 1-33 with Gregory Lupton
2. Continuous trace C*-algebras, gauge groups and rationalization,
   Journal of Topology and Analysis vol 1 (2009) 261-288 with John Klein and Claude Schochet
3. Banach algebras and rational homotopy theory,
   Transactions of the American Mathematical Society vol. 361 (2009) 267-295 with Gregory Lupton, Christopher Phillips, Claude Schochet
4. A criteria for components of a function space to be homotopy equivalent ,
   Mathematical Proceedings of the Cambridge Philosophical Society vol 145, (2008) 95--106 with Gregory Lupton
5. Cardinality of the set of real functions with a given continuity set,
   Pi Mu Epsilon Journal, vol 12, no. 8, (2008) 449-454 with Jiaming Chen
6. Rank of the fundamental group of any component of a function space,
   Proceedings of the American Mathematical Society vol 135 (2007) 2649-2659 with Gregory Lupton
7. The evaluation subgroup of a fibre inclusion, 
   Topology and its Applications, vol 154 (2007) 1107-1118 with Gregory Lupton,
8. Rationalized evaluation subgroups of a map II: Quillen models and adjoints,  
   Journal of Pure and Applied Algebra, vol 209 (2007), 173-188 with Gregory Lupton, 
9. Rationalized evaluation subgroups of a map I: Sullivan models, derivations and G-sequences
   Journal of Pure and Applied Algebra, vol 209 (2007), 159-171 with Gregory Lupton, 
10. Cyclic maps in rational homotopy theory
    Mathematische Zeitschrift, vol 249 (2005) 113-124, with Gregory Lupton,
11. Rational homotopy type of classifying spaces for fibrations,
    Contemporary Mathematics vol 274 (2001) pg 299-307
12. The rational homotopy Lie algebra of classifying spaces for formal, two-stage spaces,
    Journal of Pure and Applied Algebra vol 160 (2001) pg 333-343
13. Rational L.S. category of function space components for F_0-spaces,
    Bulletin of the Belgian Mathematical Society, vol 6 (1999) pg 295-304
14. Rational classification of simple function space components for flag-manifolds,
    Canadian Journal of Mathematics, vol 49 (1997) pg 855-866
15. A based Federer spectral sequence and the rational homotopy of function space components,
    Manuscripta Mathematica, vol. 93 (1997) pg 59-66
16. Rational evaluation subgroups,
    Mathematische Zeitschrift, vol. 221 (1996) pg 387-400
17. Postnikov sections of formal and hyperformal spaces,
    Proceedings of the American Mathematical Society, vol. 122 (1994) 893-903.
18. Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups,
    Transactions of the American Mathematical Society, vol. 342 (1994) 895-915.

Other Published Work

• Book review: Algebraic Models in Geometry, by Yves Félix, John Oprea and Daniel Tanré, Oxford University Press, 2008
  in Journal of Geometry and Symmetry in Physics, vol 13 (2008) 93-97
• Rationalization of the G-sequence for Gottlieb group,(published lecture)
  Proceedings of the International Conference on Homotopy Theory and Related Topics,
  Korea University  (2005), 87-97
• Innovative possibilities for undergraduate topology,
  Mathematics Association of America Notes Series, vol 67 (2005) 81-88

Recent Lectures

· Why gauge groups are rationally abelian,

Tetrahedral Topology and Geometry Seminar, Lancaster, PA April 2009

· Gauge groups and related objects in rational homotopy theory,

Special Session on Homotopy Theory, AMS Central Sectional Meeting, Kalamazoo, MI, October 2008

· Actions of the space of self-equivalences on the components of a function space,

International Conference on Self-Equivalences and Related Topics, Halifax, Canada, June 2008

· Rank of the fundamental group of any component of a function space,

Winter Meeting of the American Mathematical Society, New Orleans, January 2007

· Detecting C*-algebra invariants with  rational homotopy theory

The Deformation Theory Seminar, University of Pennsylvania, June, 2006

· Banach algebras and rational homotopy theory

The Deformation Theory Seminar, University of Pennsylvania, October, 2005

· Rationalized evaluation subgroups of a map and the rationalized G-sequence

International Conference on Homotopy Theory,  Korea University, Seoul, Korea, February 2005

· The evaluation subgroup of a fibre inclusion,

International Homotopy Theory Conference, Hannam University, Korea, January 2005

· Rational Lie derivations, adjoints and a question of Gottlieb

The Deformation Theory Seminar, University of Pennsylvania, March 2004

 Links

• The American Mathematical Society
• The Hopf Topology Archive
• The xxx Mathematics Archive
• Some pictures from home

• Send email to: smith@sju.edu

Last Updated 11/09