Guest lectures and seminars - Page 7
Gromov—Witten invariants are virtual counts of curves with prescribed conditions in a given algebraic variety. One of the main techniques to study Gromov—Witten invariants is degeneration. The degeneration formula expresses absolute Gromov—Witten invariants in terms of relative Gromov—Witten invariants of algebraic varieties with tangency conditions along boundary divisors.
Relative Gromov—Witten invariants with only one relative marking are relative invariants with maximal contacts along the unique relative marking. The local-relative correspondence proved by van Garrel—Graber—Ruddat states that genus zero relative invariants with maximal contacts are equal to local Gromov—Witten invariants of a line bundle. Local invariants are usually easier to compute. However, The degeneration formula usually involves relative invariants beyond maximal contacts (i.e. with several relative markings). I will explain a generalization of the local-relative correspondence beyond maximal contacts, hence determine all the genus zero relative invariants that appear in the degeneration formula.
This is based on joint work with Yu Wang.
Qombine seminar by Joakim Bergli, Department of Physics (UiO)
The climatic ocean wave spectrum serves as a pivotal tool in comprehending the long-term characteristics and variations of wave patterns across different regions of the world's oceans. The presentation explores the methodologies employed to derive wave spectra from observational data. Basically, consists of a statistical approach that provides a quantitative understanding of the variability and extremes of wave conditions. In essence, an ocean wave spectrum is a representation of the distribution of energy among different wave frequencies and wavelengths. So, engineers rely on this valuable information to mitigate risks and design solutions that can withstand the dynamic forces of ocean waves. However, it is necessary to present such information in a robust and practical mode to better comprehend the variations. In this way, a robust and resistant approach will be presented to define such variabilities, thus reducing uncertainties and representing the climatic wave spectrum in a compact and informative way.
Future robots need to be robust and adaptable, and new design approaches are needed for new production methods. I will talk about my research in using evolutionary algorithms and biologically inspired methods with the aim of having more intelligent, robust, and adaptive behavior in robots. I will give a short introduction to some of the algorithms and show how we apply them in our robotic platforms for exploring automatic design and adaptation.