Research

 
 
 

My research lies in the area of algebraic topology, specifically in the branch called stable homotopy theory.  In the past, I have been interested in calculating central powers of self-maps of finite p-local spectra.  Currently, I am interested in studying the ring of stably invertible modules over sub-Hopf algebras of the Steenrod Algebra, with the ultimate goal of understanding \( BP \langle n \rangle \wedge BP \langle n \rangle \) and the Tate spectrum of \( BP \langle n \rangle \) for all n.

 
 
 

Publications

 
 
 
  1. MR3220290 Bailey, S.M., Barrientos, C. Operations with mean graphs. Cong. Numer. 217 (2013), 5--19. 

     

  2. MR3220297 Bailey, S., Barrientos, C., Dancs, M., Driscoll, K., Krop, E., Raridan, C., Williams, D. Some new bounds for edge-magic graphs. Congr. Numer. 217 (2013), 101--106.

  3. MR2558747 (2010i:55011) Bailey, Scott M. On the spectrum \( b\mathrm{o}\wedge\mathrm{tmf}\), J. Pure Appl. Algebra 214 (2010), no. 4, 392--401.

    M. Mahowald, in his work on \(b\mathrm{o}\)-resolutions, constructed a \(b\rm{o}\)-module splitting of the spectrum \(b\mathrm{o}\wedge b\mathrm{o}\) into a wedge of summands related to integral Brown-Gitler spectra.  In this paper, a similar splitting of \(b\mathrm{o} \wedge \mathrm{tmf}\) is constructed.  This splitting is then used to understand the \(b\mathrm{o}_*\)-algebra structure of \(b\mathrm{o}_* \mathrm{tmf}\) and allows for a description of \(b\mathrm{o}^* \mathrm{tmf}\).

  4. MR1927621 (2003f:28011) Bailey, Scott M.; Kim, Theodore; Strichartz, Robert S. Inside the Levy Dragon, Amer. Math. Monthly 109 (2002), 689--703.

    We explore the interior of the fractal, and give a (conjectured) classification of its components.
 
 
 

Submitted

 
 
 
  1. arXiv:0904.3687 Bailey, S.M., Ricka, N. On the Tate spectrum of tmf at the prime 2. Submitted to Mathematische Zeitschrift.
 
 
 
 

Preprints & Drafts

 
 
 
  1. Bailey, S.M. and Ricka, N. On the Tate spectrum of tmf af the prime 2.
  2. MR2711440 Bailey, Scott Michael. Topological splittings of spectra related to tmf
  3. Graph Jacobians and Mackey functors
  4. Central power of the v_1 self map of the mod-p Moore spectrum
 
 
 

Presentations

 
 
 

  1. Modules and Splittings. University of Louisiana/Lafayette Topology Seminar. Lafayette, LA. April 2015.
  2. Modules and Splittings. Penn State University/Altoona Topology Seminar. Altoona, PA. November 2013.
  3. Modules and Splittings. University of Kentucky Topology Seminar. Lexington, KY. October 2013.
  4. Operations with Mean Graphs. 44th Southeastern International Conference on Combinatorics, Graph Theory, and Computing. Florida Atlantic University, Boca Raton, FL. March 2013.
  5. How to Tame a Dragon. Southern Polytechnic State University Math Colloquium. Marietta, GA. October 2012.
  6. Toward a splitting of the Tate spectrum of tmf. Wayne State University Topology Seminar. Detroit, MI. October 2012.
  7. Calculating, Dalton State College, Math and Snacks. April 2012.
  8. How to Tame a Dragon. Clayton State University, Math Club Invited Lecture Series.  August 2011 (Watch: PC/Mac, iPad, iPhone).
  9. On the Tate specturm of tmf at the prime 2. 1052nd AMS Meeting of the Eastern Section. University Park, PA - Special Session on Homotopy Theory, I. October 2009.
  10. The connective real K -theory of tmf . Penn State/Altoona Geometry-Topology Seminar. December 2008.
  11. On the Tate spectrum of tmf at the prime 2.  University of Rochester Topology Seminar.
  12. On the Tate spectrum of tmf at the prime 2. 1044th AMS Meeting of the Southeast Section. Huntsville, AL - Special Session on Homotopy Theory and Algebraic Topology, III. October 2008.
  13. On the Tate spectrum of tmf at the prime 2. 1043rd AMS Meeting of the Central Section. Kalamazoo, MI - Special Session on Homotopy Theory, II. October 2008.
  14. The splitting of botmf . 1033rd AMS Meeting of the Southeast Section.  Murfreesboro, TN - Special Session on Recent Advances in Algebraic Topology. November 2007.
  15. Inside the Levy Dragon fractal. 969th AMS Meeting of the Central Section. Columbus, OH - Special Session on Fractals. September 2001.
 
 
 
 
 
 
 
 
 
 
 
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