TITLES and ABSTRACTS

Let X be a pure-dimensional, possibly non-reduced, analytic space. We describe how one can define smooth forms, currents, and the dbar-operator on X . We introduce fine sheaves AqX of (0, q)-currents with the following properties: They coincide with the sheaves of smooth forms where the underlying reduced space is smooth and the structure sheaf OX is Cohen-Macaulay, and the complex AX , ∂̄ is a (fine) resolution of OX . This is a joint work with R Lärkäng. Tien-Cuong Dinh: Large deviation theorem for zeros of polynomials and random matrices Abstract: We give abstract versions of the large deviation theorem for the distribution of zeros of polynomials and apply them to the characteristic polynomials of random Hermitian matrices. We obtain new estimates related to the local semi-circular law for the empirical spectral distribution of these matrices when the 4th moments of their entries are controlled. A similar result will be given for random covariance matrices. This talk is based on my paper submitted for a volume in memory of Gennadi Henkin and a forthcoming paper with Duc-Viet VU. We give abstract versions of the large deviation theorem for the distribution of zeros of polynomials and apply them to the characteristic polynomials of random Hermitian matrices. We obtain new estimates related to the local semi-circular law for the empirical spectral distribution of these matrices when the 4th moments of their entries are controlled. A similar result will be given for random covariance matrices. This talk is based on my paper submitted for a volume in memory of Gennadi Henkin and a forthcoming paper with Duc-Viet VU. Maciej Dunajski: Conics and Twistors Abstract: I shall describe the range of the Radon transform on the space of conics in CP, and show that for any function F in this range, the zero locus of F is a four–manifold admitting a scalar–flat Kahler metric which can be constructed explicitly. This is a joint work with Paul Tod. I shall describe the range of the Radon transform on the space of conics in CP, and show that for any function F in this range, the zero locus of F is a four–manifold admitting a scalar–flat Kahler metric which can be constructed explicitly. This is a joint work with Paul Tod. Michael Eastwood: Complex methods in real integral geometry Abstract: There are well-known analogies between holomorphic integral transforms such as the Penrose transform and real integral transforms such as the Radon, Funk, and John transforms. In fact, one can make a precise connection between them and hence use complex methods, as exemplified in the work of Gennadi Henkin, to establish results in the real setting. There are well-known analogies between holomorphic integral transforms such as the Penrose transform and real integral transforms such as the Radon, Funk, and John transforms. In fact, one can make a precise connection between them and hence use complex methods, as exemplified in the work of Gennadi Henkin, to establish results in the real setting. Charles Epstein: Geometry of the Phase Retrieval Problem. Abstract: Phase retrieval is a problem that arises in a wide range of imaging applications, including x-ray crystallography, x-ray diffraction imaging and ptychography. The data in the phase retrieval problem are samples of the modulus of the Fourier transform of an unknown function. To reconstruct this function one must use auxiliary information to determine the unmeasured Fourier transform phases. There are many algorithms to accomplish task, but none work very well. In this talk we present an analysis of the geometry that underlies these failures and points to new approaches for solving this class of problems. Phase retrieval is a problem that arises in a wide range of imaging applications, including x-ray crystallography, x-ray diffraction imaging and ptychography. The data in the phase retrieval problem are samples of the modulus of the Fourier transform of an unknown function. To reconstruct this function one must use auxiliary information to determine the unmeasured Fourier transform phases. There are many algorithms to accomplish task, but none work very well. In this talk we present an analysis of the geometry that underlies these failures and points to new approaches for solving this class of problems. Jürgen Leiterer: On the similarity of holomorphic matrices 1