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Research Interests: My general research interests lie in the areas of geometric group theory, geometric and algebraic topology, discrete geometry, and algebraic combinatorics. My specific research interests lie in the topics of L^2-(co)homology, CAT(0) geometry and group boundaries, Coxeter Groups, the (weighted) Singer Conjecture, the Strong Atiyah Conjecture, discrete Four-Vertex Theorems, growth series, and exploring new Hilbert-type series for graded rings.
Papers:
Survey: W. J. Mogilski, The Four-Vertex Theorem, The Evolute, and The Decomposition of Polygons, Arxiv 0906.2388 (2009).
W. J. Mogilski, Polygon Vertex Extremality and Decomposition of Polygons, Discrete Mathematics 310 (2010) 2231-2237.
W.J. Mogilski, The fattened Davis complex and weighted L^2-(co)homology of Coxeter groups, Algebraic & Geometric Topology 16-4 (2016), 2067--2105. DOI 10.2140/agt.2016.16.2067.
This is a merge of two separate papers that can be found on the arXiv (you may find these to be more accessible):
The weighted Singer conjecture for Coxeter groups in dimensions three and four, arXiv:1503.02518 [math.AT]
The fattened Davis complex and weighted L^2-(co)homology of Coxeter groups, arXiv:1502.07783 [math.AT]
W.J. Mogilski and K. Schreve, The Atiyah Conjecture and L^2-cohomology Computations, Geometriae Dedicata (2017). DOI 10.1007/s10711-017-0293-2.
W. Mogilski and Z. Hurdle, The Impact of Prerequisites for Undergraduate Calculus I Performance, International Electronic Journal of Mathematics Education 17.3 (2022): em0696.
W. Mogilski and K. Grant, A Discrete Four-Vertex Theorem for Hyperbolic Polygons, Discrete Mathematics, Volume 346, Issue 7 (2023). DOI 10.1016/j.disc.2023.113371.
W. Mogilski and Z. Hurdle, An Alternative Chip Model for Operations on Integers, Utah Mathematics Teacher, Volume 16, Winter 2024 (2024).
W. Mogilski, A. Parry, Reflective Homework System Environment in Calculus Courses, Journal of Mathematics Education at Teachers College, 16(1), 58--68 (2025).
W.J. Mogilski and W.A. Johnson, The e-vector of a simplicial complex, under review, arXiv:1806.05239 [math.CO] (2025) .
W. Mogilski and S. Oliver, Factors Impacting Undergraduate Calculus Performance, under review (2025).
W. Mogilski, D. Havens, A. Parry, J. Simons, Analysis Paralysis, in preparation.
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