I am a graduate student at The Ohio State University working toward a Ph.D. in Mathematics, which I expect to complete in May 2018, under thesis advisor John E. Harper. I received a BA in Mathematics from Boston College in 2008.
Research Interests
My research interests lie mainly in homotopy theory and algebraic topology. I enjoy (co)-simplicial techniques in homotopy theory. In recent work I have developed estimates for strong convergence of completion of structured ring spectra with respect to the Freudenthal suspension map. I have also worked on completion of spaces with respect to stable homotopy, and their finite analogs, that recasts some of the earlier results in this area into the framework of a derived equivalence comparison with coalgebraic objects. A lot of the arguments developed use some neat Goodwillie calculus ideas, and their analogs in structured ring spectra, to work out some key connectivity estimates. I'm also working on a side project involving pro-structured ring spectra on developing some analogs of earlier ideas of Goerss and Isaksen for homological completion of spaces.
The Ohio State University
Ph.D. in Mathematics, May 2018 (expected)
Thesis advisor: John E. Harper
Boston College
B.A. in Mathematics, May 2012, Summa Cum Laude
Publications and Preprints
De-looping and de-suspending structured ring spectra.
In preparation.
Ring spectra, abelianization, and the density argument.
(with J. E. Harper and C. Ogle). In progress.
Suspension spectra and higher stabilization.
(with J. E. Harper). Submitted for publication (18 pages), 2016. pdf / arXiv
Iterated suspension and higher Freudenthal suspension.
(with J. E. Harper). This paper is being consolidated into an appendix of the stabilization paper above. (17 pages), 2016. pdf / arXiv
Integral chains and Bousfield-Kan completion.
(with J. E. Harper). Submitted for publication (25 pages), 2016. pdf / arXiv
Teaching
Math 1161: Accelerated Calculus I, Fall 2016, The Ohio State University, Columbus. Teaching assistant.
Math 1152: Calculus II, Fall 2015, The Ohio State University, Columbus. Teaching assistant.
Math 1152: Calculus II, Fall 2014, The Ohio State University, Columbus. Teaching assistant.
Math 1148: College Algebra, Spring 2014, The Ohio State University, Columbus. Teaching assistant.
Math 1151: Calculus I, Fall 2013, The Ohio State University, Columbus. Teaching assistant.
Invited and Contributed Talks
Michigan State University, Graduate Student Topology and Geometry Conference, April 9, 2017: "On an integral analog of Quillen's rational homotopy theorem".
Penn State Altoona, Topology Seminar, March 24, 2017: "On an integral analog of Quillen's rational homotopy theorem".
École Polytechnique Fédérale de Lausanne, Topology Seminar, February 21, 2017: "On an integral analog of Quillen's rational homotopy theorem".
Max Planck Institute, Conference for Young Researchers in Homotopy Theory and Categorical Structures, February 15, 2017: "On an integral analog of Quillen's rational homotopy theorem".
The Ohio State University, Topology Seminar, September 13, 2016: "On an integral analog of Quillen's rational homotopy theorem".
Indiana University Bloomington, Graduate Student Topology and Geometry conference, April 3, 2016: "Derived Koszul duality of Spaces".
Informal Talks
The Ohio State University, Infinity Seminar, Spring 2017: "Localization and rational and p-adic homotopy theory".
The Ohio State University, Graduate Student Seminar, Spring 2016: "Model categories and derived functors".
The Ohio State University, Higher Topos Theory Seminar, Fall 2014: "Model categories and the small object argument".
The Ohio State University, Topics in Algebraic Geometry, Spring 2014: "The unstable motivic homotopy category and some nice motivic spectra".
The Ohio State University, Algebra II, Spring 2013: "Construction of the Grothendiek spectral sequence".
Conference Participation
Graduate Student Topology and Geometry Conference, April 2017, organized by M. Hedden, L. Abbrescia, W. Chen, H. Gakhar, S. Klanderman, A. Mallick, M. Ozsarfati, and U. Yildirim, at Michigan State University.
Conference for Young Researchers in Homotopy Theory and Categorical Structures, February 2017, organized by V. Ozornova and C. Scheimbauer, at the Max Planck Institute.
Midwest Topology Seminar, May 2016, organized by J. Fowler, J.E. Harper, N. Johnson, J.F. Lafont, C. Ogle, N. Rao, G. Valenzuela, and D. Yau, at The Ohio State University.
Graduate Student Topology and Geometry Conference, April 2016, organized by H. Horton, A. Cohen, N. Coleman, E. Fischer, P. Haggerty, D. Kutluay, D. Lee, A. Lightfoot, Z. Lindsey, D. Martinez-Granado, M. Scott, K. Sozer, and C. Woo, at Indiana University Bloomington.
Homotopy Theory, Manifolds, and Field Theories Introductory School, May 2015, organized by S. Galatius, H. Miller, S. Schwede, and P. Teichner, at The Hausdorff Research Institute for Mathematics.
Midwest Topology Seminar, February 2015, organized by B. Antieau, at the University of Illinois at Chicago.
Young Topologists Meeting, July 2014, organized by M. Gomez, M. Grey, A. Høgenhaven, I. Laude, K. Moi, I. Patchkoria, T. Prytula, and M. Ungheretti, at the University of Copenhagen.
MIT Talbot Workshop, March 2014, organized by S. Glasman, G. Heuts, and D. Wilson, in Pigeon Forge, Tennessee.