Guest lectures and seminars - Page 50

Abstract: My soft matter research group investigates the autonomous transformation of phospholipid agglomerates into membrane compartments through a sequence of topological changes on solid interfaces. This process is initiated by contact and wetting of artificially created as well as natural surfaces by the lipids, and proceeds via a network of interconnected lipid nanotubes to produce nearly uniform lipid bilayer compartments. Under minimal assumptions it is conceivable that such process could have occurred on the early Earth, where the autonomous formation of simple membrane compartments is presumed to have enabled encapsulation of nucleotides and prebiotic chemistry precursors. According to the currently accepted “bulk hypothesis”, such compartments have spontaneously formed under moderate environmental conditions from lipids suspended in bulk aqueous medium. Only very recently, surfaces have emerged as potential supporting structures for the self-assembly of prebiotic compartments. In my talk, I will report on new evidence for the involvement of surfaces in protocell nucleation and development. The talk will highlight the implications of the new findings for our understanding of possible origin of life processes, and argue that materials properties-driven autonomous processes on solid interfaces might have greater role in the development of life than currently considered.

Stable polynomials are a multivariate generalization of real-rooted univariate polynomials. This notion of stability for hypersurfaces can be extended to lower-dimensional varieties, giving rise to positively hyperbolic varieties. I will present results showing that tropicalizations of positively hyperbolic varieties are very special polyhedral complexes with a rich combinatorial structure. This, in particular, generalizes a result of P. Brändén showing that the support of a stable polynomial must be an M-convex set.

Marginal maximum likelihood estimation of longitudinal latent variable models for ordinal observed variables is challenging due to the high latent dimensionality required to accurately model residual dependencies for repeated measurements. We use second-order Laplace approximations to the high-dimensional integrals in the marginal likelihood function for longitudinal item response theory models and implement an efficient estimation method based on the approximations. The method is illustrated with items from the Montreal Cognitive Assessment, administered at four time points in a Hong Kong study of aging and well-being. We discuss the limitations of the proposed estimation method and outline a potential extension to the approach that uses a dimension-reduction technique.

In a famous paper, Geir Ellingsrud and Stein Arild Strømme use the Atiyah-Bott localization theorem in equivariant cohomology to compute the number of complex twisted cubics on a complete intersection. Motivated by results from A1-homotopy theory there is a new way of doing such enumerative counts which works over an arbitrary base field, not only the complex numbers. Recently, Marc Levine proved a version of Atiyah-Bott localization for this new way of counting.

In the talk I will recall the classical Atiyah-Bott localization theorem and explain how one can use it in enumerative geometry. Furthermore, I will explain how this new way of counting works and present some results about twisted cubics on complete intersections counted this way. This is based on joint work with Marc Levine.