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Sam Smith

Professor and Chair

Department of Mathematics

Saint Joseph's University

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

Courses

Spring 2013

Math 418 Topology of Point Sets

Office Hours

Offices: Barbelin 228 x1559

Monday, Wednesday 3:00-4:00, Tuesday 1:00-2:00 or by appointment

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Research

I am working on various collaborative projects studying rational homotopy theory and function spaces.

Edited Book

Homotopy theory of function spaces and related topics,
Contemporary Mathematics, vol 519 (2010), editor with Yves Félix and Gregory Lupton

Articles

In Press

Rational homotopy type of the classifying space for fibrewise self-equivalences,
to appear in Proceedings of the American Mathematical Society, with Urtzi Buijs

In Print

Fibrewise rational H-spaces
Algebraic & Geometric Topology, vol. 12, no. 3 (2012), 1667-1694 with Gregory Lupton
Rational homotopy type of the space of homotopy self-equivalences of a fibration
Homotopy, Homology and Applications, vol. 12, no. 2 (2010), 371-400 with Yves Félix and Gregory Lupton
From rational homotopy to K-theory for continuous trace algebras,
Proceedings of Symposia in Pure Mathematics, vol. 81, (2010), 165-171 with John Klein and Claude Schochet
The homotopy theory of function spaces: A survey,
Homotopy theory of function spaces and related topics, Contemporary Mathematics, vol 519 (2010), 3-39
Localization of grouplike function and section spaces with compact domain,
Homotopy theory of function spaces and related topics, Contemporary Mathematics, vol 519 (2010), 189-202 with Claude Schochet
Whitehead products in function spaces: Quillen model formulae,
Journal of the Mathematical Society of Japan vol 62 (2010), 49-81 with Gregory Lupton
Continuous trace C*-algebras, gauge groups and rationalization,
Journal of Topology and Analysis vol 1 (2009) 261-288 with John Klein and Claude Schochet
Banach algebras and rational homotopy theory,
Transactions of the American Mathematical Society vol. 361 (2009) 267-295 with Gregory Lupton, Christopher Phillips, Claude Schochet
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
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
The evaluation subgroup of a fibre inclusion,
Topology and its Applications, vol 154 (2007) 1107-1118 with Gregory Lupton,
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,
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,
Cyclic maps in rational homotopy theory
Mathematische Zeitschrift, vol 249 (2005) 113-124, with Gregory Lupton,
Rational homotopy type of classifying spaces for fibrations,
Groups of homotopy self-equivalences and related topics, Contemporary Mathematics vol 274 (2001) pg 299-307
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
Rational L.S. category of function space components for F_0-spaces,
Bulletin of the Belgian Mathematical Society, vol 6 (1999) pg 295-304
Rational classification of simple function space components for flag-manifolds,
Canadian Journal of Mathematics, vol 49 (1997) pg 855-866
A based Federer spectral sequence and the rational homotopy of function space components,
Manuscripta Mathematica, vol. 93 (1997) pg 59-66
Rational evaluation subgroups,
Mathematische Zeitschrift, vol. 221 (1996) pg 387-400
Postnikov sections of formal and hyperformal spaces,
Proceedings of the American Mathematical Society, vol. 122 (1994) 893-903.
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 Publications

Homotopy theory of function spaces and related topics, Mathematisches Forschungsinstitut Oberwolfach, Report 19/2009
Book review: Algebraic Models in Geometry, by Yves Félix, John Oprea and Daniel Tanré, Oxford University Press, 2008
Journal of Geometry and Symmetry in Physics, vol 13 (2008) 93-97
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 (undergraduate math major)
Innovative possibilities for undergraduate topology,
Mathematics Association of America Notes Series, vol 67 (2005) 81-88
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

Some Recent Lectures

· Fibrewise rational H-spaces,

Chinese Academy of Sciences, Beijing, China, June, 2012

· Derivations and function spaces,

Nankai University Mathematics Seminar, Tianjin, China, June 2012

· Fibrewise rational homotopy theory,

Yves Félix Festschrift, Ottawa, Canada, May 2012

· A Quillen model for the classifying space for fibrewise self-equivalences

Deformation Theory Seminar, University of Pennsylvania, Philadelphia, PA January 2012

· Algebraic models for function spaces

Drexel University Mathematics Colloquium, Philadelphia, PA March 2010

· 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