6th meeting, 10th September 2018,
10 September 2018
Nelly Villamizar, Swansea University
13:00 - 13:40 Hamza Fawzi (University of Cambridge)
13:40 - 14:20 Dimitra Kosta (University of Glasgow)
14:20 - 14:40 Coffee break
14:40 - 15:20 Heidi Dahl (SINTEF, Norway)
15:20 - 16:00 Dante Kalise (Imperial College)
16:00 - 16:40 Samet Sarioglan (Hacettepe University)
Heidi Dahl: From Big Data to Smart Data: Geometric modelling for Big Data and Artificial Intelligence
Abstract: In ANALYST, a new research project funded by The Norwegian Research Council, we are combining geometric modelling with artificial intelligence to visualize and analyse big datasets from medical imaging and geospatial modelling. In this presentation we will show some early results, using volumetric Locally Refined (LR-) splines to model data from Magnetic Resonance Imaging (MRI) scans. Evaluating the LR-model at each level of the approximation, we investigate how the fit of the model evolves. In the next stage of the project, such LR-models will be the basis for advanced analytics such as segmentation and feature detection.
Dimitra Kosta: Log canonical thresholds in birational geometry and applications
Abstract: There has been a lot of current interest in log canonical thresholds in algebraic statistics due to the work of Watanabe connecting them to singular statistical models and model selection. In this talk I will talk about how one can compute log canonical thresholds for del Pezzo surfaces with Du Val singular points. Log canonical thresholds are also connected with the existence of Kahler-Einstein metrics on Fano varieties. As a consequence I will show that del Pezzo surfaces of degree 1 with Du Val singular points of type An with n less than or equal to 6 admit a Kahler-Einstein metric answering a question initiated by Tian and Yau.
Samet Sarıoğlan: Algebraic Structure of Generalized Splines
Abstract: Splines are piecewise polynomial functions over polyhedral complexes that agree up to a smoothness degree at the intersection of faces. They increase the power to control of the shape of a surface. Splines are used in several areas related with industry, computer based animations and geometric design. While splines are defined on polyhedral complexes, generalized splines are defined on edge labeled graphs with a base ring. The set of generalized splines on an edge labeled graph has ring and module (over the base ring) structure algebraically. We study the module structure of generalized splines.
In this talk, the motivation and basic definitions of generalized spline theory will be given. We also introduce some results related to the freeness and bases of generalized spline modules on arbitrary graphs and base rings. These results are obtained from joint work with Selma Altınok Bhupal.
There are directions to the university here http://www.swansea.ac.uk/the-university/location/directions/
The talks will be in room Faraday Tower 314 (building 8.2 on the campus map that you can find here).
If you arrive before, the Maths Department is located on the second floor of the Talbot Building (number 8.3 on the campus map). The best way to access the Talbot Building is via the Faraday Building. Note that the main entrance of the Faraday building is actually already on the first floor, so you only need to ascend one set of stairs.
We are grateful for the financial support from the Glasgow Mathematical Journal Learning and Research Support Fund, from the Edinburgh Mathematical Society, the London Mathematical Society.