Aaron Heap

Click here to view my complete CV. (Updated 2025)

• B.S., Texas Christian University; 1998
• Ph.D., Rice University; 2004

Geometric and Algebraic Topology, including low-dimensional topology, mapping class groups, classical 3-manifold topology, bordism theory, and knot theory

Publications:

• Tabulating Knot Mosaics: Crossing Number 10 or Less,
        With co-authors D. Baldwin, J. Canning, G. Vinal;
        Involve: A Journal of Mathematics, Volume 18, Issue 1, January 2025.
• Knot Mosaics with Corner Connection Tiles,

        With co-authors U. Donovan, R. Grossman, N. Laine, C. McDermott, M. Paone, D. Southcott;
        Pi Mu Epsilon Journal of Mathematics, Volume 15, No. 9, Fall 2023.

• Space-Efficient Prime Knot 7-Mosaics,
        With co-author N. LaCourt;
        Symmetry, Volume 12, Issue 4, April 2020.
• Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6,
        With co-author D. Knowles;
        Involve: A Journal of Mathematics, Volume 12, Issue 5, May 2019.
• Tile number and space-efficient knot mosaics,
        With co-author D. Knowles;
        Journal of Knot Theory and Its Ramifications, Volume 27, Issue 6, May 2018.
• On the Andreadakis-Johnson Filtration of the Automorphism Group of a Free Group,
        With co-authors F. Cohen and A. Pettet;
        Journal of Algebra, Volume 329, Issue 1, March 2011, pp. 72-91.
• Bordism Invariants of the Mapping Class Group,
        Topology, Volume 45, Issue 5, September 2006, Pages 851-886.
• Bordism Invariants of the Mapping Class Group,
        PhD Thesis, Rice University (Completed 5/20/2004)

• Dr. Spencer J. Roemer Supported Professorship (2019-2022)
• Open SUNY Innovative Instruction Technology Grant (IITG, 2014-2015)
• Phi Eta Sigma Honorary Faculty Inductee (2013)
• SUNY Chancellor’s Award for Excellence in Teaching (2010-2011)
• Univeristy of Rochester Undergraduate Professor of the Year (2004-2005)
• Clay Mathematics Institute Liftoff Fellow (2004)

• Associate Professor: SUNY Geneseo, 2013-Present
• Assistant Professor: SUNY Geneseo, 2007-2013
• Visiting Assistant Professor: University of Rochester, 2004-2007
• Graduate Instructor and Teaching Assistant: Rice University, 1998-2004