The starting point of the talk will be the identification of structure common
to tree-like combinatorial objects, exemplifying the situation with abstract
syntax trees~(as used in formal languages) and with opetopes (as used in
higher-dimensional algebra).  The emerging mathematical structure will be then
formalized in a categorical setting, unifying the algebraic aspects of the
theory of abstract syntax of [2,3] and the theory of opetopes of [5].  This
realization conceptually allows one to transport viewpoints between these, now
bridged, mathematical theories and I will explore it here in the direction of
higher-dimensional algebra, giving an algebraic combinatorial framework for a
generalisation of the slice construction of [1] for generating opetopes.  The
technical work will involve setting up a microcosm principle for
near-semirings and subsequently exploiting it in the cartesian closed
bicategory of generalised species of structures of [4].  Connections to
(cartesian and symmetric monoidal) equational theories, lambda calculus, and
algebraic combinatorics will be mentioned in passing.

[1] J.Baez and J.Dolan.  Higher-Dimensional Algebra III.  n-Categories and the
Algebra of Opetopes.  Advances in Mathematics 135, pages 145-206, 1998.

[2] M.Fiore, G.Plotkin and D.Turi.  Abstract syntax and variable binding.  
In 14th Logic in Computer Science Conf. (LICS'99), pages 193-202.  IEEE,
Computer Society Press, 1999.

[3] M.Fiore.  Second-order and dependently-sorted abstract syntax.  In Logic
in Computer Science Conf. (LICS'08), pages 57--68.  IEEE, Computer Society
Press, 2008. 

[4] M.Fiore, N.Gambino, M.Hyland, and G.Winskel.  The cartesian closed
bicategory of generalised species of structures.  In J. London Math. Soc.}, 
77:203-220, 2008. 

[5] S.Szawiel and M.Zawadowski.  The web monoid and opetopic sets.  In
arXiv:1011.2374 [math.CT], 2010.