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Events - Page 13

Time and place: , Zoom

Professor Dan Crisan, Imperial College London, author of several books on filtering is now holding an intensive course.

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

Abstract: Mixed-dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimensions. Such mixed-dimensional PDEs naturally arise in a wide range of fields including geology, biomedicine, and fracture mechanics. We introduce an automated framework dedicated to mixed-dimensional problems as part of the FEniCS library. This talk gives an overview of the abstractions and algorithms involved. The introduced tools will be illustrated by concrete examples of applications in biomedicine (see below for more detailed context).

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

Time and place: , Rest area, 10th floor, NH Abels Hus
Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

The talk is elementary and discusses empirical modelling of single variables with insurance losses as example. There are in such cases little or no theory to go on, and the amount of data is many situation quite scarce. Why do we so often limit ourselves to fit two-parameter families? It will be suggested that it may be a good idea to work with more flexible models with three or four parameters and that this may provide a nice framework for automating the entire procedure for the computer to work alone. Sure, with little data the parameters may be unstably estimated, but that may not apply equally to the distributions they define. Many-parameter families suitable for insurance losses will be reviewed with some simple asymptotics in an example allowing this and with Monte Carlo to throw light on the issue in other cases.

Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

In this talk I will discuss the variational form of Bayes theorem by Zellner (1988). This result is the rationale behind the variational (approximate) inference scheme, although it is not always that clear in modern presentations. I will discuss two applications of this results. First, I will show how to do a low-rank mean correction within the INLA framework (with amazing results), which is essential for the next generation of the R-INLA software currently in development. In the second one, I will introduce the Bayesian   learning rule, which unify many machine-learning algorithms from fields such as optimization, deep learning, and graphical models. This includes classical algorithms such as ridge regression, Newton's method, and Kalman filter, as well as modern deep-learning algorithms such as stochastic-gradient descent, RMSprop, and Dropout.

The first part of the talk is based on our recent research at KAUST, while the second part is based upon \texttt{arxiv.org/abs/2107.04562} with Dr. Mohammad Emtiyaz Khan, RIKEN Center for AI Project, Tokyo.

Time and place: , Niels Henrik Abels hus, 12th floor, Abels utsikt

Abstract: The concept of symmetry breaking is well-known in physics, for instance in condensed matter, where it results from interactions in a many-body system — e.g., phase transition in a spin system. Yet, as physicists, we tend not to think of the patterned structures seen in living, many-body systems in terms of broken symmetries. Whether it is the spacing of knuckles on our hand, the collective alignment of hairs on an insect wing, or more globally the transformation of a homogeneous, isotropic embryo into a developed organism, symmetry breaking abounds in biology. What new insights can a physicist bring to understand the origin of these complex phenomena? (Click title to read full abstract below...)

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

Abstract: Elimination of substances from the brain is believed to occur by a combination of convection and diffusion. In previous work, transport along perivascular spaces around blood vessels have been explicitly meshed and modeled, and also 1D-3D models have been used to model the interaction between blood and brain tissue. A problem with both these approaches is that it requires spatial information of all blood vessels within the brain and in addition may result in a computationally expensive system to solve. In this talk, I will introduce a homogenized model of transport in the brain, also taking into account transfer between different compartments (like blood and brain tissue) within the brain. Fluid flow in and between compartments are modeled with the mulitple-porosity elasticity theory (MPET), while transport within and between compartments are modeled with convection-diffusion equations. I will further show preliminary results from our model and compare with experimental data obtained in a glioma (brain tumor) patient, where transport between blood and brain is typically altered.

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

Time and place: , NHA B1120
Planar polypols - “polygons with curved sides” - were proposed by Eugene Wachspress as generalized algebraic finite elements. In order to define barycentric coordinates for polypols, he introduced the adjoint curve of a rational polypol. In recent work by physicists, positive geometries are defined as certain semialgebraic sets together with a meromorphic differential form called the canonical form. We show that a rational regular polypol gives a positive geometry and give an explicit expression for its canonical form in terms of the adjoint and boundary curves of the polypol. In the special case that the polypol is a convex polygon, we show that the adjoint curve is hyperbolic and describe its nested ovals. 
 
This talk is based on joint work with K. Kohn, K. Ranestad, F. Rydell, B. Shapiro, R. Sinn,  M.-S. Sorea, and S. Telen.
Time and place: , Abels utsikt

Now it's time for the traditional Section 3 PhDs' & postdocs' gathering, which will take place in Abels Utsikt on October 12th, 2021, 09.30 - 16.30. All PhD students and postdocs have the opportunity to give a 15-minute talk on their research. In addition, Andrey Pilipenko (National Academy of Sciences of Ukraine/Igor Sikorsky Kyiv Polytechnic Institute) will give a talk on solving ODEs with non-Lipschitz coefficients by perturbation and Hao Tang (UiO) will introduce his research on stochastic fluid models. Welcome!

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

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.

Time and place: , NHA B1120

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.

Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

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.

Time and place: , NHA B1120

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.

Time and place: , Zoom

Doctoral candidate Trygve Kvåle Løken at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is  defending the thesis Experiments and new observation techniques related to wave-ice interactions for the degree of Philosophiae Doctor.

Time:

For the second talk, I will talk about how to relate relative Gromov--Witten invariants with relative periods via relative mirror symmetry and, given a degeneration, how relative periods and (absolute) periods are related on the mirror side.  

Time and place: , Zoom

Doctoral candidate Christian Pedersen at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is  defending the thesis Elastohydrodynamic and capillary thin film flows at small scales for the degree of Philosophiae Doctor.

Time and place: , NHA B1120
For the first talk, I will talk about the story of Gromov--Witten theory on the A-side. Relative Gromov--Witten invariants play a central role in computing Gromov--Witten invariants via the degeneration formula. I will give a summary of some recent progress of basic structures in relative Gromov--Witten theory.
Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

Template Model Builder (TMB) is an R-package that is well suited for performing fast inference with latent Gaussian models when the likelihood can be written as a three times differentiable function. TMB automatically differentiates the likelihood and utilizes Markov structures to efficiently integrate over latent variables with the Laplace approximation. In this seminar I will first introduce TMB and then elaborate a fish stock assessment model implemented with use of TMB that provides quota advice for approximately 25 different fish species in Europe.

Time and place: , NHA B1120

A cohomology class of a smooth complex variety of dimension n has coniveau ≥c if it vanishes in the complement of a closed subvariety of codimension ≥c, and has strong coniveau ≥c if it comes by proper pushforward from the cohomology of a smooth variety of dimension ≤n−c. We show that these two notions differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties. This is joint work with Olivier Benoist.

Time and place: , NHA B1120

A graded Artinian Gorenstein ring A is a quotient of a polynomial ring S with the apolar ideal of a homogeneous form. The Betti numbers of the resolution of A as an S-module are invariants to the homogeneous form. In joint work with Michal and Gregorz Kapustka, Hal Schenck, Mike Stillman and Beihui Yuan, we use these Betti numbers to describe a stratification of the space of quartics in four variables.

Time and place: , NHA B1120

Alberto Merici will present his paper (joint with Frederico Binda and Shuji Saito) "Derived log Albanese sheaves".

Time and place: , NHA B1119

Oliver Röndigs will give a one hour talk entitled "Homotopy of SLn and the relation between Milnor- and Quillen K-theory"

Time and place: , Zoom

Doctoral candidate Christian Agrell at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is  defending the thesis Probabilistic machine learning and phenomenological knowledge Developments for optimization under uncertainty in safety-critical systems for the degree of Philosophiae Doctor.

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

Abstract: It is known that a sessile drop subject to a forced vibration will vibrate in different shapes depending on the frequency of the forcing, the drop’s liquid properties and the liquid/solid/gas system. So the question then becomes, what can these vibrating drops help us understand? Here we find that we can use the motion of these drops to understand the constitutive law relating the drop’s apparent dynamic contact angle to its contact line velocity. We find we are able to extract mobility parameters like those described by the Davis-Hocking model, and that mobility parameters extracted in this fashion can be used in simulations of drop-drop coalescence to accurately predict post-coalescence dynamics.

This talk is part of the Mechanics Lunch Seminar series. That means 20min talks plus discussion in an informal setting and bring-your-own-lunch.

Time and place: , Zoom

Abstract: Efficient and parameter robust solvers for multiscale/multiphysics systems, where the coupling is enforced by the Lagrange multipliers, rely on operators in fractional Sobolev spaces defined over the interface. Arguably, this feature is not unexpected as there is explicit coupling/an interfacial variable in the system. However, in this talk we show that even for coupled problems free of Lagrange multipliers the fractional operators are a crucial component for constructing robust preconditioners. Stokes-Darcy/Biot systems will be discussed.

This talk is part of the Mechanics Lunch Seminar series. That means 20min talks plus discussion in an informal setting.

Zoom: To obtain the Zoom meeting details please contact Timo Koch (timokoch at math.uio.no).