Events for 11/13/2009 from all calendars
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:40PM
Location: BLOC 627
Speaker: Andrew Comech, Texas A&M
Title: Operator version of the van der Corput lemma and Cotlar-Stein almost orthogonality lemma
Abstract: Operator version of the van der Corput lemma and Cotlar-Stein almost orthogonality lemma are two techniques often used in research on oscillatory integral operators. We will discuss how these results apply for the estimates on singular oscillatory integral operators in 1D and on nonsingular oscillatory integral operators in higher dimensions. No new results will be presented.
Algebra and Combinatorics Seminar
Time: 3:00PM - 3:50PM
Location: MILN 317
Speaker: Ke Ye, Texas A&M University
Title: The stabilizer of immanants
Abstract: Immanants are polynomials of degree n in n2 variables associated irreducible representations of the symmetric group on n elements Sn. We describe immanants as trivial Sn modules and showed that any homogeneous polynomial of degree n on the space of n×n matrices preserved up to scalar by left and right action by diagonal matrices and conjugation by permutation matrices is a linear combination of immanants. M. Antónia Duffner found equations that determine the stabilizer of immanants (except determinant and permanent) in the group GL(E⊗F). We solve these equations and give the explicit description of the stabilizer.
Several Complex Variables Seminar
Time: 3:05PM - 3:55PM
Location: MILN 313
Speaker: Alex Tumanov, Univ. of Illinois
Title: "Regularization of almost complex structures and gluing holomorphic discs to tori" (with A. Sukhov)
Geometry Seminar
Time: 4:00PM - 5:00PM
Location: MILN 216
Speaker: Gavin Brown, University of Kent at Canterbury
Title: Gorenstein models of complex 3-folds of general type.
Abstract: A (minimal) complex algebraic manifold is of general type if its canonical class (the determinant line bundle of the cotangent bundle) is positive. This is the typical behaviour, often interpreted loosely as being the hyperbolic case. Such manifolds have canonical embeddings into (weighted) projective space, simplifying questions of isomorphism and classification. Given equations of a manifold in some embedding, it is possible to compute the canonical embedding using various computer algebra packages. The images of these embeddings are defined by Gorenstein systems of equations. The easiest cases of this are when the image is cut out by one or two independent equations. Such complete intersection 3-folds of general type have been the subject of lists (by Reid and Fletcher in the 1980s) that were recently shown to be complete (by Chen-Chen-Chen). Turning the question around, I consider more complicated systems of Gorenstein equations, and construct analogous classifications of orbifold 3-folds in higher codimension.
Linear Analysis Seminar
Time: 4:00PM - 5:00PM
Location: MILN 317
Speaker: Mihai Putinar, UC Santa Barbara
Title: Mathematical aspects of elliptic growth
Abstract: A 2D boundary dynamics, obtained as the idealization of a fluid flow between two narrow plates, or electrodeposition, or bacterial growth leads to a simple mathematical idealization: the boundary velocity is proportional to the normal derivative of the Green function of the domain surrounded by the moving interface. Remarkably, this highly non-linear, non-equilibrium dynamical system admits many close solutions and an array of specific qualitative features which were repeatedly and independently been discovered during the last half-century. The lecture will be centered on three different linearizations of this growth process, all revealing complementary aspects: complete integrability of a 2D Toda lattice type, a statistical/quantum interpretation involving random normal matrices and a potential theoretic one having a natural Hilbert space operator realization.