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Time and place: , NHA B1120


Abstract: 

In this joint work in progress with Helge Ruddat and Bernd Siebert, we employ a particular type of Log Smooth Degeneration (LSD) to study the Geometry of Enumerative Mirror Symmetry (GEMS).
 
Mirror Symmetry is a broad conjecture that predicts that symplectic invariants of a Kähler manifold correspond to algebro-geometric invariants of a mirror-dual complex algebraic variety. This is generally proven by computing both sides.
 
In this work, we take the first steps towards a full enumerative correspondence that canonically identifies the invariants of both sides. To do so, we employ the Intrinsic Mirror Construction of Gross-Siebert. Then the enumerative correspondence passes through an intermediary tropical manifold and tropical invariants thereof.
 
I will start by briefly describing the string theory origins of mirror symmetry (Candelas-de la Ossa-Green-Parkes) followed by a brief description of the computational solution to the physics prediction (Givental Mirror Symmetry). Then I will outline our program which puts the physics intuition on firm ground and takes the first steps towards showing that Enumerative Mirror Symmetry follows from the geometric dualities of the Intrinsic Mirror Construction.
Time and place: , Room 1020 NHA

The Section 4 seminar for the Spring 2024 will be held Thursdays 14:15–15:00 in room 1020

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

Our project partner Statkraft owns and operates several hydropower plants in Brazil and requires information about the future potential for hydropower production in this region. To provide inflow projections for the next several decades, we use climate model output in combination with a regression model that links meteorological variables such as precipitation and temperature to inflow over various catchments in the region. The relatively short time period for which observation data are available raises concerns about overfitting. We therefore explore an alternative model fitting approach that retains the original, easily interpretable regression model but estimates the regression coefficients within an artificial neural network (ANN) framework which permits spatial and temporal regularization and thus prevents overfitting. We show some examples of the inflow projections obtained with that methodology and discuss some caveats and limitations.

Time and place: , 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.

 
Time and place: , NHA 723 and Online
Time and place: , Abels Utsikt (NHA 1259)
Time:

C*-algebra seminar by Mathias Palmstrøm (Norwegian University of Science and Technology)

Time and place: , room 1259 (Abels Utsikt) - Niels Henrik Abels hus

Doctoral candidate Riccardo Parviero at the Department of Mathematics will be defending the thesis Statistical modelling of adoption processes on social graphs for the degree of Philosophiae Doctor.

Time and place: , 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

Time and place: , 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.

 

Time and place: , 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.

 

Time and place: , 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.

 

Time and place: , 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.

 

 

Time and place: , 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.

 

 

Time and place: , NHA 108 University of Oslo
Time and place: , 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.

Time and place: , 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.

Time:

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

Time and place: , Thon Hotel Opera

The workshop will bring together leading specialists in modeling roughness and long-range dependence in a cozy Nordic atmosphere in the center of Oslo close to the seafront.

Time and place: , NHA108

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

Time and place: , University of Oslo, Vilhelm Bjerknes Hus, Auditorium 1

Oslo Stability and Enumerative Geometry Workshop 2023

Time and place: , Niels Henrik Abels buidling, University of Oslo

SCV conference 2023, remembering Berit Stensønes. 

Time:

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

Time and place: , Abels Utsikt (NHA 1259)