University of Regina

My research is in algebraic topology and homotopy theory, with a focus on realization problems. My interests include homotopy operations (such as Π-algebras), algebraic models for homotopy n-types, cohomology operations, power operations, and examples from chromatic and motivic homotopy theory.

I am also interested in obstruction theory, Quillen cohomology, simplicial methods, and tools from homological and homotopical algebra.

Here is my research statement.

- (with Ioannis Dokas and Sacha Ikonicoff) Quillen (co)homology of divided power algebras over an operad. Preprint.
- (with Sebastian Martensen and Marius Thaule) Toda brackets in n-angulated categories. Preprint.
- (with Don Stanley) Multiparameter persistence modules in the large scale. Preprint.
- (with Dan Christensen) On good morphisms of exact triangles.
*J. Pure Appl. Algebra*(2021), doi:10.1016/j.jpaa.2021.106846. Preprint. - (with Hans-Joachim Baues) The DG-category of secondary cohomology operations.
*Appl. Categ. Structures*28 (2020), no. 6, 877-905. Preprint. - (with Markus Spitzweck) Towards the dual motivic Steenrod algebra in positive characteristic. Preprint.
- (with Hans-Joachim Baues) Eilenberg-MacLane mapping algebras and higher distributivity up to homotopy.
*New York J. Math.*23 (2017), 1539-1580. Preprint. - (with Dan Christensen) Higher Toda brackets and the Adams spectral sequence in triangulated categories.
*Algebr. Geom. Topol.*17-5 (2017), 2687-2735. Preprint. - (with Hans-Joachim Baues) 2-track algebras and the Adams spectral sequence.
*J. Homotopy Relat. Struct.*11 (2016), no. 4, 679-713. Preprint. - (with Tobias Barthel) Completed power operations for Morava E-theory.
*Algebr. Geom. Topol.*15-4 (2015), 2065-2131. Preprint. - Behavior of Quillen (co)homology with respect to adjunctions.
*Homology Homotopy Appl.*17 (2015), no. 1, 67-109. Preprint. - (with Hans-Joachim Baues) The realizability of operations on homotopy groups concentrated in two degrees.
*J. Homotopy Relat. Struct.*10 (2015), no. 4, 843-873. Preprint. - Moduli spaces of 2-stage Postnikov systems.
*Topology Appl.*158 (2011), 1296-1306. Preprint. - Théorème de Künneth en homologie de Morse.
*Ann. Sci. Math. Québec*31 (2007), no. 1, 31-39.

Here is my list of publications as a pdf file.

- Is calculus secretly algebraic topology? Presentation for Pi Day.
- Cohomology of the Hawaiian earring. A short survey.
- A user's guide: Completed power operations for Morava E-theory. A behind-the-scenes look at the paper.
- 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.

- Alberta Topology Seminar, July 8, 2023.

- University of Haifa Topology and Geometry Seminar, December 20, 2022.

Slides: Multiparameter persistence modules in the large scale. - Canadian Geometry-Topology Seminar, UQAM, November 13, 2022.

Slides: Multiparameter persistence modules in the large scale. - NTNU Trondheim Topology Seminar, October 10, 2022.

Slides: Multiparameter persistence modules in the large scale. - Foundational Methods in Computer Science Workshop, University of Calgary, June 26, 2022.

Slides: Modules over bialgebroids and Beck modules. - CMS Summer Meeting, Memorial University, June 4, 2022.

Slides: Modules over bialgebroids and Beck modules.
Multiparameter persistence modules in the large scale.
- New Directions in Group Theory and Triangulated Categories, May 3, 2022.

Slides: On good morphisms of exact triangles. - Mathematical Congress of the Americas, July 21, 2021.

Slides: The homotopy theory of simplicial Beck modules. - Princeton University Algebraic Topology Seminar, March 25, 2021.

Slides: The monoidal fibered category of Beck modules. - University of Calgary Peripatetic Seminar, March 19, 2021.

Slides: The monoidal fibered category of Beck modules. - University of Melbourne Topology Seminar, October 27, 2020.

Slides: On good morphisms of exact triangles. - Fields Institute Toric Topology Seminar, May 7, 2020.

Slides: On good morphisms of exact triangles. - Ohio State University Homotopy Theory Seminar, February 20, 2020.

Slides: On good morphisms of exact triangles. - NTNU Trondheim Topology Seminar, November 7, 2019.

- Equivariant Topology and Derived Algebra, NTNU Trondheim, July 29, 2019.

Slides: On good morphisms of exact triangles. - Universität Osnabrück Oberseminar Topologie, July 24, 2019.

- Electronic Computational Homotopy Theory Seminar, February 28, 2019.

Slides: The DG-category of secondary cohomology operations. - University of Western Ontario Geometry & Topology Seminar, February 20, 2019.

- CMS Winter Meeting, Vancouver, December 9, 2018.

Slides: Towards the dual motivic Steenrod algebra in positive characteristic. - University of British Columbia Topology Seminar, December 6, 2018.

- University of Washington Topology Seminar, November 8, 2018.

- Adam Mickiewicz University in Poznań Geometry and Topology Seminar, July 3, 2018.

- Topology Meeting, University of Oslo, May 30, 2018.

- Workshop on Homotopy Theory, Universität Regensburg, May 5, 2018.

- University of North Carolina Wilmington, March 15, 2018.

- University of Louisiana at Lafayette Mathematics Colloquium, March 12, 2018.

- Georgia Southern University, March 9, 2018.

- University of Regina, March 6, 2018.

- EPFL Topology Seminar, October 17, 2017.

- Homotopy Theory: Tools and Applications, Urbana-Champaign, July 19, 2017.

Slides: Eilenberg-MacLane mapping algebras and higher distributivity up to homotopy. - Adam Mickiewicz University in Poznań Geometry and Topology Seminar, June 2, 2017.

Slides: Realization problems in algebraic topology. - Universität Regensburg Arbeitsgruppenseminar Prof. Bunke, December 1, 2016.
- Colloque du GDR "Topologie Algébrique et Applications", Amiens, October 14, 2016.
- Conference on Combinatorial Structures in Geometry, Osnabrück, August 12, 2016.
- University of Copenhagen Algebra/Topology Seminar, June 16, 2016.

- Operations in Highly Structured Homology Theories, Banff, May 26, 2016.

Slides: The mod p motivic Steenrod algebra in characteristic p. - Westfälische Wilhelms-Universität Münster Oberseminar Topologie, April 11, 2016.

- University of Edinburgh Topology Seminar, March 25, 2016.

Slides: Higher Toda brackets and the Adams spectral sequence. - Newcastle University Algebra & Geometry Seminar, March 22, 2016.
- 24th NRW Topology Meeting, Bochum, November 13, 2015.

Slides: The algebra of tertiary cohomology operations. - MPIM Oberseminar, October 8, 2015.
- Wayne State University Topology Seminar, November 4, 2014.
- Wayne State University Mathematics Colloquium, November 3, 2014.

Slides: Realization problems in algebraic topology. - Joint Mathematics Meetings, Baltimore, January 17, 2014.

Slides: Completed power operations for Morava E-theory. - 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.
- CMS Summer Meeting, University of Regina, June 2, 2012.

Slides: Non-realizable 2-stage Π-algebras. - Joint Mathematics Meetings, Boston, January 7, 2012.

Slides: Non-realizable 2-stage Π-algebras. - Ruhr-Universität Bochum Oberseminar Topologie, November 22, 2011.
- CMS Summer Meeting, University of Alberta, June 5, 2011.

Slides: Moduli spaces of 2-stage Postnikov systems. - 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.
- Penn State Altoona Homotopy Theory Mini Conference, October 23, 2009.

Slides: Quillen cohomology of Π-algebras.