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Physical Sciences and Mathematics Commons™
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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
On The Orders Of Periodic Diffeomorphisms Of 4-Manifolds, Wm Chen
On The Orders Of Periodic Diffeomorphisms Of 4-Manifolds, Wm Chen
Mathematics and Statistics Department Faculty Publication Series
This paper initiated an investigation on the following question: Suppose that a smooth 4 -manifold does not admit any smooth circle actions. Does there exist a constant C>0 such that the manifold supports no smooth Zp -actions of prime order for p>C ? We gave affirmative results to this question for the case of holomorphic and symplectic actions, with an interesting finding that the constant C in the holomorphic case is topological in nature, while in the symplectic case it involves also the smooth structure of the manifold.
Entropic Fluctuations In Statistical Mechanics: I. Classical Dynamical Systems, V Jakšić, C-A Pillet, L Rey-Bellet
Entropic Fluctuations In Statistical Mechanics: I. Classical Dynamical Systems, V Jakšić, C-A Pillet, L Rey-Bellet
Mathematics and Statistics Department Faculty Publication Series
Within the abstract framework of dynamical system theory we describe a general approach to the transient (or Evans–Searles) and steady state (or Gallavotti–Cohen) fluctuation theorems of non-equilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. In addition to its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.
Representations Of Semi-Simple Lie Algebras In Prime Characteristic And Noncommutative Springer Resolution, R Bezrukavnikov, I Mirkovic
Representations Of Semi-Simple Lie Algebras In Prime Characteristic And Noncommutative Springer Resolution, R Bezrukavnikov, I Mirkovic
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.
Symmetric Symplectic Homotopy K3 Surfaces, Wm Chen, S Kwasik
Symmetric Symplectic Homotopy K3 Surfaces, Wm Chen, S Kwasik
Mathematics and Statistics Department Faculty Publication Series
A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is shown that an effective action by various maximal symplectic K3 groups forces the corresponding homotopy K3 surface to be minimally exotic with respect to our measure. (However, the standard K3 is the only known example of such minimally exotic homotopy K3 surfaces.) The possible structure of a finite group …