Past

Some results of R.Harvey and B.Lawson on the Dirichlet problem for a class of fully nonlinear elliptic equations will be presented.

No background is required; the talk will be expository.

This is the first (of two) talks which will be given concerning the Birch--Swinnerton-Dyer Conjecture.

If a distribution, say F, has all moments finite, then either F is unique (M-determinate) in the sense that F is the only distribution with these moments, or F is non-unique (M-indeterminate).  In the latter case we suggest a method for constructing a Stieltjes class consisting of infinitely many distributions different from F and all having the same moments as F.  We present some shocking examples involving distributions such as N, LogN, Exp and explain what and why.  We analyse conditions which are sufficient for F to be M-determinate or M-indeterminate.  Then we deal with recent problems from the following areas:

(A)  Non-linear (Box-Cox) transformations of random data.

(B) Distributional properties of functionals of stochastic processes.

(C) Random sums of random variables.

If time permits, some open questions will be outlined.  The talk will be addressed to colleagues, including doctoral and master students, working or having interests in the area of probability/stochastic processes/statistics and their applications. 

I will discuss the so-called Lasso method for signal recovery for high-dimensional data and show applications in computational biology, machine learning and image analysis.

This talk will be based on a joint work with Professor Terry Lyons and Mr Gechun Liang (OMI). I will explain a new approach to define and to solve a class of backward dynamic systems including the well known examples of non-linear backward SDE. The new approach does not require any kind of martingale representation or any specific restriction on the probability base in question, and therefore can be applied to a much wider class of backward systems.

I will briefly describe a differential geometric construction of Hitchin's projectively flat connection in the Verlinde bundle, over Teichm\"uller space, formed by the Hilbert spaces arising from geometric quantization of the moduli space of flat connections on a Riemann surface. We will work on a general symplectic manifold sharing certain properties with the moduli space. Toeplitz operators enter the picture when quantizing classical observables, but they are also closely connected with the notion of deformation quantization. Furthermore, through an intimate relationship between Toeplitz operators, the Hitchin connection manifests itself in the world of deformation quantization as a connection on formal functions. As we shall see, this formal Hitchin connection can be used to construct a deformation quantization, which is independent of the Kähler polarization used for quantization. In the presence of a symmetry group, this deformation quantization can (under certain cohomological conditions) be constructed invariantly. The talk presents joint work with J. E. Andersen.