Thursday, February 13, 2020
02/13/2020 - 3:00pm
One of the grand challenges in biomedical science is to develop effective methods for optical imaging. I will review recent work on related inverse problems for partial differential equations and applications to image reconstruction. This talk is intended for a general mathematical audience.
02/13/2020 - 4:00pm
Complex networks are said to exhibit four key properties: large scale, evolving over time, small world properties, and power law degree distribution. The Preferential Attachment Model (Barab´asi–Albert, 1999) and the ACL Preferential Attachment Model (Aiello, Chung, Lu, 2001) for random networks, evolve over time and rely on the structure of the graph at the previous time step. Further models of complex networks include: the Iterated Local Transitivity Model (Bonato, Hadi, Horn, Pralat, Wang, 2011) and the Iterated Local Anti-Transitivity Model (Bonato, Infeld, Pokhrel, Pralat, 2017). In this talk, we will define and discuss the Iterated Local Model. This is a generalization of the ILT and ILAT models, where at each time step edges are added deterministically according to the structure of the graph at the previous time step
02/13/2020 - 4:15pm
During the 1970s and 80s, Schmid and others analyzed in great detail how a polarized variation of Hodge structure degenerates near a normal crossing divisor. All subsequent applications of Hodge theory in algebraic geometry rely to some extent on their work. In the talk, I am going to outline a simplified proof for most of Schmid's results; I hope this will clarify the meaning of the "limiting mixed Hodge structure", the Hodge norm estimates, and other things.