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Guest lectures and seminars - Page 45

Time and place: , Online
Time and place: , NHA B1120
Hilbert schemes of points for a surface are a well studied subject with many famous results like Göttsche’s formula for its Betti numbers. A natural generalization comes from studying Grothendieck’s Quot-schemes and the associated enumerative invariants. Unlike the former, punctual Quot-schemes are smooth only virtually admitting perfect obstruction theories and virtual fundamental classes. This has recently been used to study invariants counting zero-dimensional quotients of trivial vector bundles by multiple authors who used virtual localization and therefore could not treat the case of a general vector bundle. We rely on other techniques which use a general wall-crossing framework of D. Joyce to study these. Our methods rely on existence of a Lie algebra coming from vertex algebras constructed out of topological data. I will explain how these arise naturally in the Quot-scheme setting and how one can obtain explicit invariants and study their symmetries.
Time and place: , Erling Svedrups plass (Niels Henrik Abel Hus, 8th floor) & ZOOM

Super-resolution is a hot topic in current day Machine Learning.  The origin of the methodology dates back to applications in seismic imaging. I discuss the evolution from the early days and highlight some papers which have given new theoretical insights along the way. I illustrate the bridge between traditional convex optimization and current day convolutional neural nets. Along the way I show some examples where we have used this for current day applications in seismic imaging.

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract: Transport and mixing in multiphase flow through porous media plays a key role in a range of biological, geological, and engineered systems. Here, we use numerical simulations to investigate the effect of intermittent multiphase flow on fluid stretching and folding, a fundamental mechanism driving solute mixing and reaction in porous media. We show that, in contrast to steady single-phase flows, the concurrent flow of two immiscible phases induces chaotic mixing, characterized by exponential stretching in the pore space. The stretching rate is found to decay with increasing capillary number, implying that the increasing flow intermittency observed at lower capillary numbers enhances the mixing efficiency. We propose a mechanistic model to link the basic multiphase flow properties to the chaotic mixing rate, opening new perspectives to understand mixing and reaction in multiphase porous media flows. The results presented here form part of the background for the recently started RCN-funded project M4: Mixing in Multiphase flow through Microporous Media, which will also be introduced.

This talk is part of the Mechanics Lunch Seminar series. Bring-your-own-lunch and lots of questions.

Time and place: , Niels Henrik Abels hus, 9th floor, seminar room 919

Abstract:  The cerebral circulation must ensure continuous blood perfusion of the brain which is the biggest oxygen consumer in the human body. It must also provide mechanisms for adaptability to changing oxygen demand as well as resilience to local blockages. We will look at such mechanisms at the level of the microcirculation where the mechanics of blood flow is dominated by red blood cells. We will find that red blood cells do not only play the role of oxygen carriers, but that they are an important element of blood flow regulation itself. To this end, we will compare results from in vitro studies in microfluidic chips to theoretical and computational models and to in vivo data from mice. We will derive local auto-regulation mechanisms for blood flow and will study how local modifications in the vascular network can modify the global hematocrit distribution. These results will emphasize the relevance of red blood cell mechanics and microvascular network geometry in cerebral blood perfusion.

This talk is part of the Mechanics Lunch Seminar series. Bring-your-own-lunch and lots of questions.