Martin Frankland

Visiting Assistant Professor
Department of Mathematics
University of Illinois at Urbana-Champaign

Office: 247A Illini Hall
Email: franklan(at)illinois.edu
Phone: 217-244-1848

Mailing address:

Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green St
Urbana, IL 61801

Personal information

I am currently doing postdoctoral work under the supervision of Charles Rezk.

I completed my Ph.D. in algebraic topology in 2010; my advisor was Haynes Miller. Here is my thesis.

Here is my CV.

Research interests

I am interested in algebraic topology, homotopy theory, and other fields with a topological flavor. My interests include the realization of Π-algebras, Quillen cohomology, algebraic models for homotopy n-types, obstruction-theoretic methods, topological K-theory, p-completion of spectra, and some related questions in homological and homotopical algebra.

Here is my research statement.

Papers and notes

• (with Hans-Joachim Baues) The realizability of operations on homotopy groups concentrated in two degrees. Preprint.
• Moduli spaces of 2-stage Postnikov systems. Topology Appl. 158 (2011), 1296-1306. Preprint.
• Behavior of Quillen (co)homology with respect to adjunctions. Preprint.
• Equivalent statements of the telescope conjecture. Notes from a talk given in the UIUC topics seminar in algebraic topology.
• Fibered category of Beck modules. Notes from a talk given at the Graduate Student Topology and Geometry Conference 2010.
• Kervaire invariant and Whitehead square. Notes from a talk given in the summer seminar on the Kervaire invariant problem.
• Théorème de Künneth en homologie de Morse. Ann. Sci. Math. Québec 31 (2007), no 1, 31-39.

Presentations

• Ohio State University Topology Seminar, March 5, 2013.
• Purdue University Topology Seminar, November 29, 2012.
• Ruhr-Universität Bochum Oberseminar Topologie, November 20, 2012.
• University of Haifa Geometry and Topology Seminar, July 26, 2012.
• Updated slides. 2012 CMS Summer Meeting, University of Regina, June 2, 2012.
• Non-realizable 2-stage Π-algebras. 2012 Joint Mathematics Meetings, Boston, January 7, 2012.
• Ruhr-Universität Bochum Oberseminar Topologie, November 22, 2011.
• Moduli spaces of 2-stage Postnikov systems. 2011 CMS Summer Meeting, University of Alberta, Edmonton, June 5, 2011.
• Johns Hopkins University Topology Seminar, April 11, 2011.
• University of Georgia Topology Seminar, February 7, 2011.
• Ohio State University Topology Seminar, February 3, 2011.
• Northwestern University Topology Seminar, November 8, 2010.
• University of Chicago Algebraic Topology Seminar, October 19, 2010.
• UIUC Topology Seminar, September 7, 2010.
• Université Lille 1 Séminaire de topologie, March 26, 2010.
• Heinrich-Heine-Universität Düsseldorf Oberseminar Topologie, January 20, 2010.
• Ruhr-Universität Bochum Oberseminar Topologie, January 19, 2010.
• Wesleyan University Topology Seminar, December 9, 2009.
• University of Chicago Algebraic Topology Seminar, November 17, 2009.
• Northwestern University Topology Seminar, November 16, 2009.
• Quillen cohomology of Π-algebras. Penn State Altoona Homotopy Theory Mini Conference, October 23, 2009.

Teaching

• Spring 2013: Math 527 - Homotopy Theory
• Fall 2012: Math 535 - General Topology
• Spring 2012: Math 241 - Calculus III
• Fall 2011: Math 416 - Abstract Linear Algebra
• Spring 2011: Math 285 - Intro Differential Equations
• Fall 2010: Math 125 - Elementary Linear Algebra
• Fall 2010: Math 415 - Applied Linear Algebra

Some seminars I like & Useful links

• Winter 2013 Midwest Topology Seminar at UIUC
• UIUC Topology Seminar
• UIUC Topology Suminar 2011
• UIUC Topics seminar in algebraic topology
• Midwest Topology Seminar
• Midwest Topology Network
• List of conferences in algebraic topology
• MIT Topology Seminar