While in verb-initial Old Irish, topicalization was achieved via left dislocation and focalization was achieved through clefting, the older Continental Celtic languages achieved such pragmatic information structuring through movement into the left periphery of the clause (though the right edge of the clause could also be a target for such purpose).  This paper commences with an inspection of relative clause syntax in Continental Celtic while outlining what we can tell about other movement mechanisms in the clause and then goes on to explore the architecture of the left periphery in these languages.  This exploration provides some insight into the prehistoric development of verb-initial clausal configuration in Insular Celtic.  Some comparative attention is also paid to the architecture of the left periphery in other Indo-European languages and it is found that the Continental Celtic languages have a role to play in determining the degree of articulation to be reconstructed for the left periphery of proto-Indo-European itself.

Details to be announced.

Have you heard of M.C. Escher? Origami?

He is said to have created more mathematicians than any other person in history, through his numerous books and long-running recreational math column in Scientific American. Widely revered among mathematicians, Gardner passed away in 2010. However his influence and legacy continue to inspire us to approach seemingly intractable problems from unconventional angles.

Title:  The combinatorial structure behind the free Lie algebra

Abstract:  We explore a beautiful interaction between algebra and combinatorics in the heart of the free Lie algebra on n generators: The multilinear component of the free Lie algebra Lie(n) is isomorphic as a representation of the symmetric group to the top cohomology of the poset of partitions of an n-set tensored with the sign representation. Then we can understand the algebraic object Lie(n) by applying poset theoretic techniques to the poset of partitions whose description is purely combinatorial. We will show how this relation generalizes further in order to study  free Lie algebras with multiple compatible brackets.

Title:  Eilenberg-MacLane Spaces

Abstract:  A space X is a K(G,n)  if \pi_n(X)=G and \pi_i(X)=0 if i\neq n. An interesting aspect is that the homotopy type of a CW comples K(G,n) is uniquely determined by G and n. We will investigate the construction of K(G,1), otherwise known as BG, for an arbitrary (discrete) group G, the homology of K(G,1) spaces, and the infinite symmetric product SP(X).

Title:  Duals of Skew θ-Constacyclic Codes

Abstract:  We generalize cyclic codes to skew θ-constacyclic codes using skew polynomial rings. We provide a useful tool for exploring these codes: the circulant. In addition to presenting some properties of the circulant, we use it to re-examine a theorem giving the dual code of a skew θ- constacyclic code first presented by Boucher/Ulmer (2011). This talk includes work with Dr. Heide Gluesing-Luerssen.

Title:  Extremal functions in modules of systems of measures

Abstract:  We study Fuglede’s p-modules of systems of measures in condensers in the Euclidean spaces. First, we generalize the result by Rodin that provides a way to compute the extremal function and the 2-module of a family of curves in the plane to a variety of other settings. More specifically, in the Euclidean space we compute the p-module of images of families of connecting curves and families of separating sets with respect to the plates of a condenser under homeomorphisms with some assumed regularity. Then we calculate the module and find the extremal measures for the spherical ring domain on polarizable Carnot groups and extend Rodin’s theorem to the spherical ring domain on the Heisenberg group. Applications to special functions and examples will be provided. Joint work with Melkana Brakalova and Irina Markina.