Events - Page 2

Note the non-standard start time!

 
Abstract: We consider mirror pairs of Calabi-Yau hypersurfaces X and X’ in toric varieties associated to dual reflexive polytopes. We will give a proof through tropical geometry that the Hodge numbers of X and X’ are mirror symmetric. The proof goes by considering tropical homology, and works over the ring of integer numbers. In particular, we can use our spectral sequence with Kris Shaw to explore the connections between the topology of the real part of X and cohomological operations on X’.

This is based on joint work with Diego Matessi. 

Doctoral candidate Viktor Balch Barth at the Department of Mathematics will be defending the thesis Endomorphisms of ℙ¹ and 𝔸ⁿ. Motivic homotopy classes and open images for the degree of Philosophiae Doctor.

C*-algebra seminar by Sergey Neshveyev.

Structural equation models are simultaneous equation regression models, whose variables are latent, and measured via a confirmatory factor model (that is, with measurement error and repeated measurements). When the functional form of the simultaneous equation system is unknown, it has previously been observed in simulations that factor scores inputted into non-parametric regression methods approximate the true functional form. Factor scores estimate the latent variables (per person), and several types exist. We provide a theoretical (though population-based) analysis of this procedure, and provide assumptions under which it is theoretically justified in using Bartlett factor scores, which are simple linear transformations of the data. In simulations, we compare this suggestion to an already available though understudied non-linear and computationally heavy procedure, and observe that the simple Bartlett approach appears to work better.

his talk discusses a nonparametric inference framework for occupation time curves derived from wearable device data. Such curves provide the total time a subject maintains activity above a given level as a function of that level. Taking advantage of the monotonicity and smoothness properties of these curves, we develop a likelihood ratio approach to construct confidence bands for mean occupation time curves.  An extension to fitting concurrent functional regression models is also developed. Application to wearable device data from an ongoing study of an experimental gene therapy for mitochondrial DNA depletion syndrome will be discussed. Based on joint work with Hsin-Wen Chang (Academia Sinica).

During this cold winter in Oslo, we certainly all have experienced the unsteady nature of friction and the sudden loss of stress bearing capacity that initiates catastrophic sliding. A similar kind of frictional rupture arises at the onset of a wide variety of natural disasters that includes earthquakes, landslides, as well as snow avalanches. In this talk, I will focus on the incipient stage of these catastrophic events that is characterized by the local nucleation of failure and its rapid propagation towards intact regions of the material. I will discuss how the analogy to fracture mechanics can be exploited to describe the dynamics of these rupture fronts and develop quantitative models to characterize the onset of failure in geomaterials.

Donaldson-Thomas and Pandharipande-Thomas theory are two approaches to counting curves on projective threefolds in terms of their moduli spaces of sheaves. An important special case in understanding the DT/PT correspondence the equivariant geometry of affine three-space with the natural coordinate action of the rank 3 torus. I will show how one can use new wall-crossing techniques to prove the equivariant K-theoretic DT/PT correspondence in this situation, which was previously known only in the Calabi-Yau limit.

This is part of an ongoing project with Felix Thimm and Henry Liu in which we aim to prove wall-crossing for virtual enumerative invariants associated to equivariant CY3 geometries by extending a vertex algebra formalism for wall-crossing developed by Joyce.

University of Oslo and University of Gothenburg invite to an informal workshop within machine learning with a focus on statistical aspects related to Machine Learning.

Bone stress injuries affect athletic populations who undertake activities in which bones are repeatedly loaded. In order to understand and reduce the risk of bone stress injuries, we need to quantify the loading experienced by the bones during activities such as running. Bone loading is difficult to quantify as the magnitudes of stress are influenced to a large extent by the magnitude of muscular forces acting on the bone. Musculoskeletal modelling, ranging from very simple to very complex approaches, can be used to estimate the internal loading experienced by the bone during running. This has allowed us to explore factors such as speed, slope and step length and their influence on bone loading during running. However, in order to truly understand risk of stress injuries this needs to be taken out of the lab and in-field. This talk will consider what we know and the limitations to current understanding.

Gromov—Witten invariants are virtual counts of curves with prescribed conditions in a given algebraic variety. One of the main techniques to study Gromov—Witten invariants is degeneration. The degeneration formula expresses absolute Gromov—Witten invariants in terms of relative Gromov—Witten invariants of algebraic varieties with tangency conditions along boundary divisors.

Relative Gromov—Witten invariants with only one relative marking are relative invariants with maximal contacts along the unique relative marking. The local-relative correspondence proved by van Garrel—Graber—Ruddat states that genus zero relative invariants with maximal contacts are equal to local Gromov—Witten invariants of a line bundle. Local invariants are usually easier to compute. However, The degeneration formula usually involves relative invariants beyond maximal contacts (i.e. with several relative markings). I will explain a generalization of the local-relative correspondence beyond maximal contacts, hence determine all the genus zero relative invariants that appear in the degeneration formula.

This is based on joint work with Yu Wang.

Qombine seminar by Joakim Bergli, Department of Physics (UiO)

The climatic ocean wave spectrum serves as a pivotal tool in comprehending the long-term characteristics and variations of wave patterns across different regions of the world's oceans. The presentation explores the methodologies employed to derive wave spectra from observational data. Basically, consists of a statistical approach that provides a quantitative understanding of the variability and extremes of wave conditions. In essence, an ocean wave spectrum is a representation of the distribution of energy among different wave frequencies and wavelengths. So, engineers rely on this valuable information to mitigate risks and design solutions that can withstand the dynamic forces of ocean waves. However, it is necessary to present such information in a robust and practical mode to better comprehend the variations. In this way, a robust and resistant approach will be presented to define such variabilities, thus reducing uncertainties and representing the climatic wave spectrum in a compact and informative way.

Future robots need to be robust and adaptable, and new design approaches are needed for new production methods. I will talk about my research in using evolutionary algorithms and biologically inspired methods with the aim of having more intelligent, robust, and adaptive behavior in robots. I will give a short introduction to some of the algorithms and show how we apply them in our robotic platforms for exploring automatic design and adaptation.

Doctoral candidate Edvard Aksnes at the Department of Mathematics will be defending the thesis Tropical homology manifolds for the degree of Philosophiae Doctor.

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

Engineering principles to develop advanced biomaterials and scaffolds. This study focuses on utilising engineering principles to facilitate new bone growth, specifically in designing and fabricating bone scaffolds. The core of our investigation lies in applying titanium dioxide (TiO2) scaffolds, which have emerged as promising candidates due to their osteoconductive properties and the potential for enhancing bone tissue engineering.

Our research aims to bridge the gap between engineering and biology by harnessing fluid mechanics and material science to create scaffolds that mimic the natural bone environment. By comparing TiO2 scaffolds with commercial porous calcium phosphate biomaterials under simulated perfusion culture conditions, we delve into the mechanical and fluidic stimuli that are crucial for bone regeneration. The study emphasises the role of fluid dynamics to make better “spare-parts” for the human body, highlighting the importance of permeability, mechanical load transfer and wall shear stress with a porous ceramic.

Furthermore, we validate our fluid mechanic simulations with the impact of dynamic seeding techniques. Our findings demonstrate the superiority of dynamic culture conditions in enhancing the expression of bone-related proteins and genes, thereby facilitating more effective bone regeneration. In addition, the study presents a clinical trial that shows that these porous bioceramic functions well in patients. The trial's outcomes confirm the potential of TiO2 scaffolds for in vivo bone formation and showcase the successful integration of engineering principles in the development of biomaterials for tissue engineering.

This research underscores the pivotal role of engineering in advancing tissue engineering and biomaterials science. By leveraging engineering principles to optimise scaffold design and functionality, we pave the way for innovative strategies in bone regeneration, offering new hope for patients requiring bone tissue reconstruction.

C*-algebra seminar by Corey Jones (North Carolina State University)

Controlling the spontaneous ruptures of nanoscale liquid thin films is crucial to various applications such as solar cell manufacturing. Over the past few decades, theoretical work based on the long-wave theory of thin liquid films has successfully identified a critical film height, below which the surface nanowaves become linearly unstable, leading to spontaneous rupture. This dewetting in the ‘spinodal regime’ has been repeatedly confirmed in experiments using atomic force microscopy on polymer films. However, ruptures are also observed for thicker films (linearly stable) in a different manner. It is believed that the random (Brownian) movement of particles is the cause of dewetting in this ‘thermal regime’ but the theoretical framework predicting the rupture is missing. In this talk, we present a theory to account for the rupture of a two dimensional linearly stable thin film by utilizing fluctuating hydrodynamics and rare events theory. By modelling the film dynamics with the stochastic thin-film equation (STF) and solving it numerically, we observe rupture in the linearly stable thermal regime and record the average waiting time for rupture. We show that the STF can be rearranged into the form of a gradient flow, which allows us to apply Kramer’s law from the rare events theory to obtain a theoretical prediction of the average waiting time. Molecular dynamics (MD) simulations are also performed and we find good agreements between the numerics, the prediction, and the MD.