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These notes are based on lectures given at Zhejiang University, July 14–20, 2008. My goal was to present some analytic techniques that can be used to study the action of the mapping class group on the...
We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2, C) connections on a closed Riemann surface. We show that the trivial part of the action contains t...
ACTION OF THE JOHNSON-TORELLI GROUP ON REPRESENTATION VARIETIES     JOHNSON-TORELLI  mapping class group       font style='font-size:12px;'> 2015/9/29
Let Σ be a compact orientable surface with genus g and n boundary components B = (B1,...,Bn). Let c = (c1,...,cn) ∈ [−2,2]n. Then the mapping class group MCG of Σ acts on the relative SU(2)-cha...
AN ERGODIC ACTION OF THE OUTER AUTOMORPHISM GROUP OF A FREE GROUP     OUTER AUTOMORPHISM  ERGODIC ACTION       font style='font-size:12px;'> 2015/9/29
For n > 2, the action of the outer automorphism group of the rank n free group Fn on Hom(Fn, SU(2))/SU(2) is ergodic with respect to the Lebesgue measure class.
The modular group action on real SL(2){characters of a one-holed torus     one-holed torus  group action       font style='font-size:12px;'> 2015/9/29
The action of Γ preserves a Poisson structure de ning a Γ{invariant area form on each −1(t)\ R3. For t < 2, the action of Γ is properly discontinuous on the four contractible components of &...
The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle al...
Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, ρE : Gal(k/k) → GL2(Z b). For a fixed number field k, we describe the ima...
To each Drinfeld module of generic characteristic defined over a finitely generated field, one can associate a Galois representation arising from the Galois action on its torsion points. Recent work o...
We gives an explicit genus 3 curve over Q such that the Galois action on the torsion points of its Jacobian is a large as possible. That such curves exist is a consequence of a theorem of D. Zureick-B...
We will demonstrate that if M is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from M to U(1) on a separable probability algebra which pr...
A Chern-Simons action for noncommutative spaces     Chern-Simons action  noncommutative spaces  Operator Algebras       font style='font-size:12px;'> 2012/4/18
Witten constructed a topological quantum field theory with the Chern-Simons action as Lagrangian. We define a proper noncommutative generalization of the Chern-Simons action. "Proper", in this context...
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.
Inspired by a recent result of Cho-Kim-Park, we consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound ...
Abstract: We study the action of Luzin area operator on BErgman classes on the unit ball,providing some direct generalizations of recent results of Z.Wu.
Abstract: We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component syste...

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