Aaron has been a member of the Geneseo faculty since 2007. He received the Dr. Spencer J. Roemer Supported Professorship in 2019, and he was awarded the SUNY Chancellor's Award for Excellence in Teaching in 2011.
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"The essence of mathematics is not to make simple things complicated, but to make complicated things simple."
- Stan Gudder
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Math Links
Knot Mosaic Space - ProofSpace
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College Links
College Course List - College Calendar - Undergraduate Bulletin - Personal Web Page
Curriculum Vitae
Official CV
Click here to view my complete CV. (Updated January 2025)
Education
- B.S., Texas Christian University; 1998
- Ph.D., Rice University; 2004
Research Interests
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)
- Tabulating Knot Mosaics: Crossing Number 10 or Less,
Honors and Awards:
- 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)
Employment
- 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
List of courses I have taught:
- INTD 288 - Introduction to 3D Modeling and Printing
- Math 221 - Calculus I
- Math 222 - Calculus II
- Math 223 - Calculus III
- Math 233 - Linear Algebra I
- Math 239 - Introduction to Mathematical Proof
- Math 326 - Differential Equations
- Math 330 - Abstract Algebra
- Math 333 - Linear Algebra II
- Math 338 - Topology
- Math 348 - Oral Presentation and Research Seminar
- Math 380 - Low-Dimensional Topology 2018
- Math 380 - Low-Dimensional Topology 2009
- Math 380 - Algebraic Topology
- Math 388 - Honors Linear Algebra
- Math 388 - Tied up in Knots