Related papers: Cobham-Semenov theorem and $\NN^d$-subshifts
Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects…
We discuss twisted cohomology, not just for ordinary cohomology but also for $K$-theory and other exceptional cohomology theories, and discuss several of the applications of these in mathematical physics. Our list of applications is by no…
We present in this continuation paper a new axiomatic derivation of the Schr\"odinger equation from three basic postulates. This new derivation sheds some light on the thermodynamic character of the quantum formalism. We also show the…
We prove the classical Riemann-Roch theorems for the Adams operations $\,\psi^j\,$ on $K$-theory: a statement with coefficients on $\mathbb{Z}[j^{-1}]$, that holds for arbitrary projective morphisms, as well as another one with integral…
We show that in supersymmetric theories, knowing the soft theorem for a single particle in a supermultiplet allows one to immediately determine soft theorems for the remainder of the supermultiplet. While soft theorems in supersymmetric…
Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor V |--> emb(V,N) from the poset O of open subsets of M…
In classical phenomenological thermodynamics the first and second laws can be regarded as independent statements. Statistical mechanics provides a microscopic substratum that explains thermodynamics in probabilistic terms via a microstate…
Since its first use by Behrend, Bryan, and Szendr\H{o}i in the computation of motivic Donaldson-Thomas (DT) invariants of $\mathbb{A}_{\mathbb{C}}^3$, dimensional reduction has proved to be an important tool in motivic and cohomological DT…
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
We shall prove a new non-vanishing theorem for the stable cohomotopy Seiberg-Witten invariant of connected sums of 4-manifolds with positive first Betti number. The non-vanishing theorem enables us to find many new examples of 4-manifolds…
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
We revisit and clarify some aspects of perturbative renormalization in pure Chern-Simons theory by means of a localization principle associated with an underlying supersymmetry. This perspective allows the otherwise perturbative one-loop…
In this work, on the one hand, we survey and amplify old results concerning tame dynamical systems and, on the other, prove some new results and exhibit new examples of such systems. In particular, we study tame symbolic systems and…
We introduce a theory of Clifford semialgebra systems, with application to representation theory via Hasse-Schmidt derivations on exterior semialgebras. Our main result, after the construction of the Clifford semialgebra, is a formula…
The $\mathrm{U}(1)$ Chern-Simons theory can be extended to a topological $\mathrm{U}(1)^n$ theory by taking a combination of Chern-Simons and BF actions, the mixing being achieved with the help of a collection of integer coupling constants.…
Coherently with the principle of analogy suggested by Dirac, we describe a general setting for reducing a classical dynamics, and the role of the Noether theorem -- connecting symmetries with constants of the motion -- within a reduction.…
We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences of numbers in {-1,0,1}, and introduce several natural generalizations. We study the relationships between these properties and…
We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…
The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. We show that this…