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A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…
We prove that within a natural class of E_3-algebras, the graded Tor group induced by a span of E_3-algebra maps carries a graded algebra structure generalizing the classical structure when the algebras are genuine commutative differential…
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on…
We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…
We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…
We apply results of Harada, Holm and Henriques to prove that the Atiyah-Segal equivariant complex $K$-theory ring of a divisive weighted projective space (which is singular for nontrivial weights) is isomorphic to the ring of integral…
We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…
We consider the ring I_n of polynomial invariants over weighted graphs on n vertices. Our primary interest is the use of this ring to define and explore algebraic versions of isomorphism problems of graphs, such as Ulam's reconstruction…
We study the cohomology with modular coefficients of Deligne-Lusztig varieties associated to Coxeter elements. Under some torsion-free assumption on the cohomology we derive several results on the principal l-block of a finite reductive…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…
We prove that each isometric isomorphism, between the monoids of all nonegative 1-Lipschitz maps defined on invariant metric groups and equiped with the inf-convolution law, is given canonically from an isometric isomorphism between their…
An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. In this paper, we lay the groundwork for the study of isovariant stable homotopy theory. We prove an isovariant Blakers--Massey theorem and…
We give an elementary proof of the Eilenberg-Mac Lane trace isomorphism between the third 2-abelian cohomology group and quadratic forms. Our approach yields explicit constructions and we characterize when quadratic forms can be expressed…
The total homology of the loop space of the configuration space of ordered distinct n points in R^m has a structure of a Hopf algebra defined by the 4-term relations if m>2. We describe a relation of between the cohomology of this loop…
Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces it has to be redesigned when applied to other…
In the literature, the standard approach to finding bases of spaces of modular forms is via modular symbols and the homology of modular curves. By using the Eichler-Shimura isomorphism, a work by Wang shows how one can use a cohomological…
We prove continuous-valued analogues of the basic fact that Murray-von Neumann subequivalence of projections in II$_1$ factors is completely determined by tracial evaluations. We moreover use this result to solve the so-called trace problem…
We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism),…
We contribute to the program of extending computable structure theory to the realm of metric structures by investigating lowness for isometric isomorphism of metric structures. We show that lowness for isomorphism coincides with lowness for…