Stefan Forcey     sf34 AT uakron DOT edu, (330) 972-6779

Department page.     Associahedra.     Research talks.     Papers.     Projects.     Polytopes.     Department seminar.     n-Lab .     My Akron.


News:
Recent special session on geometric and algebraic combinatorics.

Research:

Preprints on the arXiv


Current research projects


Publication abstracts


Publication reviews


CV


Google scholar











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Teaching:

- Fundamentals of Ad. Math: Math 307

- Advanced combinatorics: Math 636

Recent Courses:
- Calculus III: Math 223

- Combinatorics: Math 415/515.

- Ordinary Differential Equations: Math 335

- Advanced linear algebra: Math 410/510.

- Algebras and Geometric Combinatorics.

- Algebraic Topology.

- The Associahedron: Math 697.

- Structured Category Theory.



Papers:

Convex Polytopes from Nested Posets. (with S. L. Devadoss, S. Reisdorf, P. Showers)
    submitted, 2013. [ journal ]   [ arXiv ]   [ preprint ]

Recursive bijections for Catalan objects. (with M. Kafashan, M. Maleki and M. Strayer)
    Journal of Integer Sequences, 16, Article 13.5.3, pp 1-20, 2013. [ journal ]   [ arXiv ]   [ preprint ]

Cofree compositions of coalgebras. (with A. Lauve & F. Sottile)
    Annals of Combinatorics, 17(1), pp 105-130, 2013. [ journal ]   [ arXiv ]   [ preprint ]

When does compromise prevent more pollution?
    (with C. Clemons, J. Cossey, M. Ferrara, T. Norfolk, G. Obeng, D. Ricciardi, G. Young)
    Notices of the A.M.S, 59(9), pp 1223-1234, 2012. [ journal ]  [ arXiv (soon) ]   [ preprint ]

Extending the Tamari lattice to some compositions of species.
    Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift.,
    Progress in Mathematics, Vol. 299, pp 187-210, F. Müller-Hoissen, J. Pallo, J. Marcel, J. Stasheff (Eds.), 2012. [ book ]  [ arXiv ]   [ preprint ]  [ contents ]

Cofree compositions of coalgebras (extended abstract). (with A. Lauve & F. Sottile)
    DMTCS Proceedings, FPSAC 23, Reykjavik, Iceland. 363-374, 2011. [ journal ]  [ arXiv ]   [ preprint ]

Pseudograph associahedra. (with M. Carr & S. Devadoss)
    Journal of Combinatorial Theory, Series A 118(7), pp 2035-2055, 2011. [ journal ]   [ arXiv ]   [ preprint ]

Hopf structures on the multiplihedra. (with A. Lauve & F. Sottile)
    SIAM Journal on Discrete Mathematics, 24(4), pp 1250-1271, 2010. [ journal ]   [ arXiv ]   [ preprint ]

Geometric combinatorial algebras: cyclohedron and simplex. (with D. Springfield)
    Journal of Algebraic Combinatorics, 32, pp 597-627, 2010. [ journal ]   [ arXiv ]   [ preprint ]

New Hopf structures on binary trees. (with A. Lauve & F. Sottile)
    DMTCS Proceedings,21st Formal Power Series
    and Algebraic Combinatorics (Hagenberg, Austria),
pp 411-420 , 2009. [ journal ]   [ arXiv ]   [ preprint ]

Marked tubes and the graph multiplihedron. (with S.L. Devadoss)
    Algebraic and Geometric Topology, 8(4), pp 2081–2108, 2008. [ arXiv ]   [ journal ]

Convex Hull Realizations of the Multiplihedra
    Topology and its Applications, 156, 326-347, 2008. [ arXiv ]   [ journal ]

Quotients of the multiplihedron as categorified associahedra.
    Homotopy, Homology and Applications, vol. 10(2), pp 227–256, 2008. [ arXiv ]   [ journal ]

Operads in iterated monoidal categories (with J. Siehler, E. Seth Sowers)
    Journal of Homotopy and Related Structures, 2, pp 1-43, 2007. [ arXiv ]   [ journal ]

Classification of braids which give rise to interchange (with F. Humes)
    Algebraic and Geometric Topology, 7, pp 1233-1274, 2007. [ arXiv ]   [ journal ]

Vertically iterated classical enrichment
    Theory and Applications of Categories, 12, pp 299-325, 2004. [ arXiv ]   [ journal ]

Enrichment over iterated monoidal categories
    Algebraic and Geometric Topology, 4, pp 95-119, 2004. [ arXiv ]   [ journal ]
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Selected talks:

(see CV for chronology)

Akron Physics Club Mar. 2014
Seeing in 4 dimensions. [ slides]

Annual Greater Akron High School Mathematics Challenge Jan. 2013
Pattern. [ slides]    [ Plot Mandlebrot sequences in Excel ]

Coxeter Groups meet Convex Geometry: Workshop Aug. 2012
Tubings and polytope truncations. [ schedule ]

Species and Hopf Algebraic Combinatorics, AMS Eastern Sectional, Sept. 2011
Composing species and composing coalgebras. [ slides ]

REU at Kent State University, Applications and Ramifications of Linear Algebra, 2011
Polytopes, phylogenetics, puddles and fractals. [ slides ]

FPSAC (Formal Power Series and Algebraic Combinatorics) 2011, Reykjavik.
Compositions of cofree coalgebras: Trees and polytopes. [ slides ]

Session on physically inspired higher homotopy algebra, AMS Eastern Sectional, 2011.
Trees and polytopes. [ slides ]

SIAM conference on Discrete Math, 2010.
Composing and covering of coalgebras. [ slides ]

Algebras of polytopes based on network topology. [ slides ]

Advanced combinatorics, March 2011.
Shapes and Lattices: introduction for students. [ slides ]

Special Session on Homotopical Algebra with Applications to Mathematical Physics and selected talks.
Polytopes, positrons, and antipodes. [ slides ]

Texas A&M Algebra and Combinatorics seminar Fall 2008
Polytopes, positrons, and antipodes. [ slides ]

Williams College Colloquium
How to draw a multiplihedron.

Seminar on Categories and Applications IV
N-fold operads: braids, Young diagrams, and dendritic growth. [ slides ]

Recent Advances in Algebraic Topology (AMS)
Multiplihedra: polytopes, pasting, and parameterized enrichment. [ slides ]

University of Pennsylvania Deformation Theory Seminar
Operads in iterated monoidal categories, featuring Young diagrams.

Category Theory O6
A categorification of the associahedra. [ slides ]

Workshop on Categorification and Higher-Order Geometry
Enrichment and Delooping of Categories with Loop Space Nerves.

n-categories: summer workshop at the IMA
Varieties of iterated enrichment. [ slides ]

Topology & Group Theory Seminar Vanderbilt University Fall 2005
Higher categories and geometric combinatorics of free groups.

Streetfest: Categories in algebra, geometry, and mathematical physics
n-fold operads in iterated monoidal categories. [ slides ]

Union College Mathematics Conference
Loop spaces, enrichment, and n-categories. [ slides ]
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From the Cornell Chronicle :
In brane-world theory, the ends of strings are anchored in our brane, so the particles we see can only move within the brane. But the particles that carry the gravitational force, known as gravitons, are closed strings -- little Cheerios -- and can "leak" out of the brane. This explains why gravity is much weaker than the electromagnetic force and the strong and weak nuclear forces. It also offers a possible explanation for the "dark matter" that astronomers need to explain why the mass of the universe doesn't agree with the observed objects. Dark matter could be in an adjacent brane, with its gravitons leaking into ours.




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