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Gjesteforelesninger og seminarer - Side 2

Tid og sted: , Niels Henrik Abels hus, 9th floor

Protein condensates inside human cells are liquid-like droplets composed of protein and RNA. These condensates interact with the heterogeneous, active and dense environment of the cytoplasm, crossed by various cytoskeletal filaments such as microtubules and actin. Wetting interactions with the cytoskeleton lead to stereotypical positioning of such protein droplets inside the cell. Using statistical physics approaches, we identified complementary functions of filamentous actin and microtubules: protein droplets couple to actin’s native dynamics in the cell through steric interactions leading to directional motion towards the cell center. Microtubules (and their molecular building-blocks), on the other hand, act as Pickering agents and engage in energetically favorable wetting interactions that lead to a robust localization of protein condensates in microtubule-rich regions of the cell. These interactions are non-specific and ultimately arise from different affinities (contact angles) between condensate and filament, suggesting that similar mechanisms may govern localization of other liquid-like phases within the cell.

 
Tid og sted: , NHA 723 and Online
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C*-algebra seminar by Mathias Palmstrøm (Norwegian University of Science and Technology)

Tid og sted: , Niels Henrik Abels hus, 9th floor

What happens if we paint a steel box and put a water drop on it before it gets dry? The arcane curiosity arises: Will the paint remain the same or get destroyed? The answer is that it depends on the interaction between the surfaces and the length scale involved. My doctoral work was to study the stability of thin liquid films under aqueous drops. Slippery surfaces were used as a model system because they provide a frictionless surface with low contact angle hysteresis (<2°). We found that thin liquid films are stable on hydrophobic surfaces, while on hydrophilic surfaces, they rupture and dewet into droplets. We observed different dewetting patterns depending on the film thickness and slip. However, films on hydrophobic surfaces are stable but can be destabilized using external perturbations like an electric field. Due to the electric field, capillary waves are generated, and their evolution matches very well with a linear stability analysis. The reversible dewetting behavior with the applied field is an interesting observation of our work. With the applied frequency, the wavelength of the capillary waves does not follow the classical linear stability analysis; we modified the stability analysis, which agrees with our experimental findings. Finally, the coalescence of dewetted droplets and anomalous diffusive behavior with the applied external field will be discussed

Tid og sted: , NHA 108

Phase tropical surfaces can appear as a limit of a 1-parameter family of smooth complex algebraic surfaces. A phase tropical surface admits a stratified fibration over a smooth tropical surface. We study the real structures compatible with this fibration and give a description in terms of tropical cohomology. As an application, we deduce combinatorial criteria for the type of a real structure of a phase tropical surface.

 

Tid og sted: , NHA 108

Phase tropical surfaces can appear as a limit of a 1-parameter family of smooth complex algebraic surfaces. A phase tropical surface admits a stratified fibration over a smooth tropical surface. We study the real structures compatible with this fibration and give a description in terms of tropical cohomology. As an application, we deduce combinatorial criteria for the type of a real structure of a phase tropical surface.

 

Tid og sted: , Niels Henrik Abels hus, 9th floor

Physics of internal microstructure fluid flows plays important role both due to their applications as well as their more general research field. In most occasions this type of fluid flow problems are treated with discrete models that are both computational costly as well as unable to shed light into the more general physics of the problem. In this sense a continuous model in the Eulerian frame is adopted here that consists a generalization of the incompressible Navier-Stokes equation. The present model introduces an extra tensor in the governing equations that accounts for the angular velocity of the internal microstructure, namely the micropolar model.

 

Tid og sted: , NHA 108

In 1962 Ehrhart proved that the number of lattice points in integer dilates of a lattice polytope is given by a polynomial — the Ehrhart polynomial of the polytope. Since then Ehrhart theory has developed into a very active area of research at the intersection of combinatorics, geometry and algebra.

The Ehrhart polynomial encodes important information about the polytope such as its volume and the dimension. An important tool to study Ehrhart polynomials is the h*-polynomial, a linear transform of the Ehrhart polynomial which is given by the numerator of the generating series. By a famous theorem of Stanley the coefficients of the h*-polynomial are always nonnegative integers. In this talk, we discuss generalizations of this result to weighted lattice point enumeration in rational polytopes where the weight function is given by a polynomial. In particular, we show that Stanley’s Nonnegativity Theorem continues to hold if the weight is a sum of products of linear forms that a nonnegative over the polytope. This is joint work with Esme Bajo, Robert Davis, Jesús De Loera, Alexey Garber, Sofía Garzón Mora and Josephine Yu.

 

 

Tid og sted: , NHA 108

In 1962 Ehrhart proved that the number of lattice points in integer dilates of a lattice polytope is given by a polynomial — the Ehrhart polynomial of the polytope. Since then Ehrhart theory has developed into a very active area of research at the intersection of combinatorics, geometry and algebra.

The Ehrhart polynomial encodes important information about the polytope such as its volume and the dimension. An important tool to study Ehrhart polynomials is the h*-polynomial, a linear transform of the Ehrhart polynomial which is given by the numerator of the generating series. By a famous theorem of Stanley the coefficients of the h*-polynomial are always nonnegative integers. In this talk, we discuss generalizations of this result to weighted lattice point enumeration in rational polytopes where the weight function is given by a polynomial. In particular, we show that Stanley’s Nonnegativity Theorem continues to hold if the weight is a sum of products of linear forms that a nonnegative over the polytope. This is joint work with Esme Bajo, Robert Davis, Jesús De Loera, Alexey Garber, Sofía Garzón Mora and Josephine Yu.

 

 

Tid og sted: , NHA 108 University of Oslo
Tid og sted: , NHA 108

In this talk we define a new category of matroids, by working on matroid polytopes and rank preserving weak maps. This lets us introduce the concept of categorical valuativity for functors, which can be seen as a categorification of the ordinary valuativity for matroid invariants.

 

We also show that this new theory agrees with what we know about valuative polynomials: several known valuative polynomials can be seen as a Hilbert series of some graded vector space and we prove that these graded vector spaces let us define a valuative functor in the new sense. 

 

Lastly, we sketch how to categorify a Theorem by Ardila and Sanchez, which states that the convolution of two valuative invariants (respectively, valuative functors) is again valuative.

 

This is based on a joint ongoing project with Ben Elias, Dane Miyata and Nicholas Proudfoot.

Tid og sted: , NHA 108

In this talk we define a new category of matroids, by working on matroid polytopes and rank preserving weak maps. This lets us introduce the concept of categorical valuativity for functors, which can be seen as a categorification of the ordinary valuativity for matroid invariants.

 

We also show that this new theory agrees with what we know about valuative polynomials: several known valuative polynomials can be seen as a Hilbert series of some graded vector space and we prove that these graded vector spaces let us define a valuative functor in the new sense. 

 

Lastly, we sketch how to categorify a Theorem by Ardila and Sanchez, which states that the convolution of two valuative invariants (respectively, valuative functors) is again valuative.

 

This is based on a joint ongoing project with Ben Elias, Dane Miyata and Nicholas Proudfoot.

Tid:

C*-algebra seminar by Ali Miller (Southern University of Denmark)

Tid og sted: , NHA108

C*-algebra seminar by Emilie Elkiær (University of Oslo)

Tid og sted: , University of Oslo, Vilhelm Bjerknes Hus, Auditorium 1

Oslo Stability and Enumerative Geometry Workshop 2023

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C*-algebra seminar by Gaute Schwartz (University of Oslo)

Tid og sted: , Niels Henrik Abels hus, 9th floor

A peculiarity of nonlinear hyperbolic problems is that they must be interpreted as limits of second-order equations with vanishing viscosity. Despite not explicitly being present in the hyperbolic case, diffusion is needed, e. g., at discontinuities or to avoid the occurrence of nonphysical states. In the case of gas dynamics, for instance, dissipation corresponds to the production of thermodynamic entropy. To solve hyperbolic problems numerically, one needs to adapt these ideas to the discrete setting. Standard high-order methods, however, do not incorporate the appropriate amounts of artificial viscosity because these need to be chosen adaptively based on the solution. Among the high-resolution schemes capable of doing so are the recently proposed monolithic convex limiting (MCL) techniques [1] to be discussed in this talk. They offer a way to enforce physical admissibility, entropy stability, and discrete maximum principles for conservation laws. These methods can also be generalized to systems of balance laws in a well-balanced manner [2]. In addition to second-order finite element methods, extensions to high-order discontinuous Galerkin (DG) schemes shall also be presented [3]. Numerical examples for the so-called KPP problem, the nonconservative shallow water system, and the compressible Euler equations will be shown. An overview of MCL and other property-preserving methods can be found in our recently published book [4].

Tid og sted: , NHA 723 and Online
Tid og sted: , NHA B1120

We prove that (logarithmic, Nygaard completed) prismatic and (logarithmic) syntomic cohomology are representable in the category of logarithmic motives. As an application, we immediately obtain Gysin maps for prismatic and syntomic cohomology, and we precisely identify their cofibers. In the second part of the talk we develop a descent technique that we call saturated descent, inspired by the work of Niziol on log K-theory. Using this, we prove crystalline comparison theorems for log prismatic cohomology, log Segal conjectures and log analogues of the Breuil-Kisin prismatic cohomology, from which we get Gysin maps for the Ainf cohomology.

Tid og sted: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor
This paper considers hypothesis testing in semiparametric models which may be non – regular for certain values of a (potentially infinite dimensional) nuisance parameter. In such models no (locally) regular estimator of the parameter of interest exists. The situation for testing is somewhat different: I establish that C(α) – style test statistics achieve their limiting distributions in a (locally) regular manner under mild conditions, leading to tests with correct size in situations where standard tests fail to control size. Additionally, I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the case where the efficient information matrix is singular. This permits the generalisation of classical power bounds to the non – regular case. I provide appropriate statements of these bounds and give conditions under which they are attained by the proposed C(α) – style tests. Three examples are worked out in detail.
Tid og sted: , Niels Henrik Abels hus, 9th floor

We combine a pressure correction scheme with interior penalty discontinuous Galerkin (dG) discretisation to solve the time-dependent Navier–Stokes equations. We prove unconditional energy stability and a priori error estimates for the velocity. With duality arguments, optimal L2 error rates are obtained. Convergence of the discrete pressure is also established.  Further, we propose a splitting scheme,  integrating the pressure correction approach, for the Cahn–Hilliard–Navier–Stokes system  The numerical analysis of dG combined with this scheme is discussed. Namely, we show well--posedness, stability, and error estimates. Numerical results with manufactured solutions display our theoretical findings, and a spinodal decomposition example portrays the robustness of our approach.

Tid og sted: , Erling Svedrups plass and Zoom https://uio.zoom.us/j/64912028556?pwd=QmJpa1ZPS0hBNTFZUDhzWDlaMmJKQT09

Traditional quantile estimators are not well-suited for data streams because the memory and computational time increase with the volume of data received from the stream. Incremental quantile estimators refer to a class of methods designed to maintain quantile estimates for data streams. These methods operate by making small updates to the estimate every time a new observation is received from the stream. In this presentation, I will introduce some of the incremental quantile estimators we have developed.

Tid og sted: , Niels Henrik Abels hus, 9th floor

Your brain has its own waterscape: whether you are reading, thinking or sleeping, fluid flows through or around the brain tissue, clearing waste in the process. These biophysical processes are crucial for the well-being and function of the brain. In spite of their importance we understand them but little, and mathematical and computational modelling could play a crucial role in gaining new insight. In this talk, I will give an overview of mathematical, mechanical and numerical approaches to understand mechanisms underlying pulsatility, fluid flow and solute transport in the human brain. Topics include fluid-structure interactions, generalized poroelasticity, mixed finite element discretizations and preconditioning, uncertainty quantification, and optimal control.

Tid og sted: , NHA108

C*-algebra seminar by Jordy Timo van Velthoven (University of Vienna)