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We show that any family of sets uniformly definable in an ominimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula.
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula i...
We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if n...
Universal cycles for combinatorial structures
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
Abstract: We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine funct...
Abstract: One of the benefit properties implied by the extensionality axiom of Hilbert's epsilon calculus is that the calculus becomes complete with respect to the choice structures as semantics. Anot...
The new concept of multilevel network is introduced in order to em-body some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classic...
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the prob...
We use the supergeometric formalism, more precisely, the so-called “big bracket”(for which brackets and anchors are encoded by functions on some graded symplectic manifold) to address the theory of Ja...
Let $S$ be a closed orientable surface of genus at least two, and let $C$ and $C'$ be complex projective structures on $S$ with the same holonomy and orientation. We show that, if, via Thurston's coor...
We construct toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are moduli spaces of log mixed Hodge structures with polarized grad...
We present an axiomatic framework for the residue structures induced by Prufer extensions with a stress upon the intimate connection between their arithmetic and arboreal theoretic properties. The ma...
In this note, we describe motivic cell structures arising from the Bia lynicki-Birula decomposition. This provides a description of stable A1-homotopy types of smooth projective Gm-varieties where the...

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