Sam Smith

Professor and Chair

Ph.D.

B.S.

Offices: Barbelin 228 x1559

Wednesday 10:00-1:00 or by appointment

Chance, Strategy, and Choice: An Introduction to the Mathematics of Games and Elections,

**Cambridge University Press**, 2015

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

**Articles**

Realizing spaces as classifying spaces,

**Proceedings of the American Mathematical Society, **vol. 144, no. 8, (2016), 3619-3633 with Gregory Lupton

Gottlieb groups of function spaces,

**Mathematical Proceedings of the Cambridge Philosophical Society, **vol 159, no. 1, (2015), 61-77 with Gregory Lupton

The effect of cell-attachment on the group of self-equivalences of an R-localized space,

**Journal of Homotopy and Related Structures**, vol. 10, no. 3, (2015), 549-564 with Mahmoud Benkhalifa

Rational homotopy type of the classifying space for fibrewise self-equivalences,

**Proceedings of the American Mathematical Society**, vol.141 (2013), 2153-2167 with Urtzi Buijs

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 Felix and Gregory Lupton

From rational homotopy theory to K-theory for continuous trace algebras,

*Superstrings, geometry, topology, and **C***-algebras, ***Proceedings of Symposia in Pure Math. **vol 81 (2010), 165-171 with John Klein and Claude Schochet

Homotopy theory of function spaces and related topics,

**Contemporary Mathematics**, vol 519 (2010), editor with Yves Felix and Gregory Lupton

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

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)

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 Felix, John Oprea and Daniel Tanre, Oxford University Press, 2008

**Journal** **of Geometry and Symmetry in Physics**, vol 13 (2008) 93-97

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

*Two Realization Problems for Self-Equivalences in Rational Homotopy Theory, *

Deformation Theory Seminar, University of Pennsylvania, August 2016

*Function Spaces and Classifying Spaces for Fibrations,*

Summer School on Rational Homotopy Theory, Rabat, Morocco, July, 2016

*Open Problems in Rational Homotopy Theory,*

Temple University, Philadelphia, PA, April 2013

*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 Felix 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

Last Updated 3/15