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We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that...
The main result of this paper states that a symplectic s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary). Based on this theorem...
A study of symplectic actions of a finite group G on smooth 4-manifolds is initiated. The central new idea is the use of G-equivariant Seiberg–Witten–Taubes theory in studying the structure of the fix...
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and ...
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 supp...
Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associa...
Manifold learning has been successfully applied to a variety of medical imaging problems. Its use in real-time applications requires fast projection onto the low-dimensional space. To this end, out-of...
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the syste...
Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require ...
In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds.
In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the conv...
Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}...
In partially linear models the dependence of the response y on (xt, t) is modeled through the relationship y = xt +g(t)+" where " is independent of (xt, t). In this paper, estimators of g are constr...
A common belief in high-dimensional data analysis is that data are concentrated on a lowdimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide ...
In this paper, we prove, using Malliavin calculus, that under a global Hormander condition the law of a Riemannian manifold valued stochastic process, a solution of a stochastic differential equati...

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