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In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
In 2007, Andrews introduced the odd rank of odd Durfee symbols. Let N^0 (m,n) denote the number of odd Durfee symbols of n with odd rank m, and N^0 (r,m;n) be the number of odd Durfee symbols of n wit...
In this talk, I will introduce our recent result on Heintze Karcher type inequalities for capillary hypersurfaces supported on different types of umbilical hypersurfaces in hyperbolic space. I will in...
We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order 2s ∈ (0,2]. Our main motivation is the pricing of European or Amer...
Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain Ω ⊂ Rd with a continuous piecewise smooth obstacle. ...
In this paper we apply our results on the geometry of polygons in infinitesimal symmetric spaces, symmetric spaces and buildings, [KLM1, KLM2], to four problems in algebraic group theory. Two of these...
We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function.
This paper develops bounds on the rate of decay of powers of Markov kernels on finite state spaces. These are combined with eigenvalue estimates to give good bounds on the rate of convergence to sta...
Let M be a cg-connected manifold. Let L be a second-order differential operator with real cg(R) coefficients on M and such that L1 0 (i.e., L has no zero-order term). Assume that there exists a posi...
This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic So...
We present a simple and direct proof of the equivalence of various functional inequalities such as Sobolev or Nash inequalities. This proof applies in the context of Riemannian or sub-elliptic geome...
Most smoothing procedures are via averaging. Pseudo-Poincar¶e in- equalities give a basic Lp-norm control of such smoothing procedures in terms of the gradient of the function involved. When av...
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if ∆(L) is the order complex of a rank (r +1) geometric lattice L, then the for all i ≤ r...
We study soft threshold estimates of the non-centrality parameter ξ of a non-central χ2 d(ξ) distribution, of interest, for example, in estimation of the squared length of the mean of a Gaussian ve...
A wide variety of problems in system and control theory can be formulated (or reformulated) as convex optimization problems involving linear matrix inequalities, that is, constraints requiring an affi...

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