Talks

A fundamental model for large-scale ocean flow is two-dimensional (2D) turbulence above topography and has been studied since the 1970s. Ocean observations show that long-lived vortices sit astride prominent topographic features. Using a suite of numerical experiments, we illustrate the phenomenology of random topographic turbulence. As in two-dimensional turbulence, the energy of the flow is transferred towards larger scales of motion; after some rotation periods, however, the process is halted as the flow pattern becomes aligned along the topographic contours. It is found that global energy decays faster as the roughness of topography increases due to more effective viscous dissipation. The quasi-steady state reached by the flow is characterized by the relationship between potential vorticity and stream function which is found using minimum enstrophy arguments.

Internal gravity waves pervade the oceans, profoundly shaping their dynamics. Their interactions with eddies and other waves govern energy transfers and can lead to wave breaking, and density mixing, thus influencing large-scale mean flows. Despite their significance, the relative importance of wave-mean flow interactions vis-à-vis wave-wave interactions remains elusive. We investigate internal gravity wave-mean flow interactions with the novel numerical Internal Wave Energy Model (IWEM) based on the six-dimensional radiative transfer equation. We simulate wave interactions with local coherent mesoscale eddies, to find a wave energy loss at the eddy rim akin to critical layer behavior. We investigate internal gravity wave-wave interactions by numerically evaluating the kinetic equation derived from weak interaction assumptions. Our findings unveil a predominantly forward energy cascade from wave-wave interactions

We focus on plane Poiseuille flow where an incompressible fluid is pushed between two parallel plates by maintaining a constant bulk velocity. Plane Poiseuille flow is a canonical wall-bounded shear flow where a subcritical transition to turbulence is observed. Assuming periodic boundary conditions in streamwise and spanwise directions, we classify invariant subspaces of the plane Poiseuille flow up to half-box shifts. Exploiting the interplay between symmetries and dynamics, we find new finite amplitude traveling wave solutions in some invariant subspaces, far below the linear stability threshold.

Planning and adapting to future coastal ocean conditions requires accurate coastal ocean predictions of the nutrient, pollutant, heat and sediment transport. As coastal ocean turbulence is often driven by relatively small scale processes such as high-frequency internal waves and submesocale eddies that are not captured in most regional ocean models turbulence parameterisation is challenging Using a combination of process-based field campaigns and long-term monitoring data we have characterised the relationship between diapycnal mixing and diverse external forcings and differing flow regimes on the Australian northwest shelf. We show that the overall diapycnal mixing is dominated by relatively rare but energetic mixing events. We observe that the semi-diurnal barotropic tide, the spring-neap tidal variability, and the seasonal variability in stratification all affect the magnitude of diapycnal mixing and its vertical distribution.

Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of matter arising from quantum scale symmetry can turn into constraints on the gravitational dynamics, both by exploring the asymptotically safe fixed-point structure, and by exploring resulting infrared physics.

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Given a semisimple group G and a smooth projective curve X over an algebraically closed field of arbitrary characteristic, let Bun_G(X) denote the moduli space of principal G-bundles over X. For a bundle P without infinitesimal symmetries, we describe the n^th order divided-power infinitesimal jet spaces of Bun_G(X) at P for each n. The description is in terms of differential forms on X^n with logarithmic singularities along the diagonals. Furthermore, we show the pullback of these differential forms to the Fulton-Macpherson compactification space is an isomorphism, thus illustrating a connection between infinitesimal jet spaces of Bun_G(X) and the Lie operad.

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Presented in collaboration with Navigating Quantum and AI Career Trajectories: A Beginner’s Mini-Course on Computational Methods and their Applications

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Deeptech or science-based innovations often spend more than a decade percolating within academic and government labs before their value is recognized (Park et al., 2022). This development lag time prior to venture formation is only partly due to technological development hurdles. Because science-based inventions are often generic in nature (Maine & Garnsey, 2006), meaning that they have broad applicability across many different markets, the problem of identifying a first application requires the confluence of deep technical understanding with expert knowledge of the practice of commercialization. This process of technology-market matching is a critical aspect of the translation of science-based research out of the lab (Pokrajak 2021, Gruber and Tal, 2017; Thomas et al, 2020, Maine et al, 2015) and is often delayed by a lack of capacity to identify, prioritize and protect market opportunities. Typically, deeptech innovations can take 10-15 years of development, and tens (or even hundreds) of millions of dollars of investment to de-risk before a first commercial application (Maine & Seegopaul, 2016). Academics seeking to commercialize such inventions face the daunting challenge of competing for investment dollars in markets that are ill suited to the uncertainty and timescales of deep tech development. The time-money uncertainty challenge faced by science-based innovators is compounded by the fact that most of the scientists and engineers with the world-leading technical skills required to develop science-based inventions, lack innovation skills training, and so cannot navigate the complexities of early and pre-commercialization development critical to venture success. Some researchers, having developed a mix of technical and business expertise, have demonstrated a long-term ability to serially spin out successful ventures (Thomas et al., 2020). Entrepreneurial capabilities, which can be learned, enable scientistentrepreneurs to play formative roles in commercialising lab-based scientific inventions through the formation of well-endowed university spin-offs. (Park et al, 2022; 2024). Commercialization postdocs, when supported by well designed training, stipends, and de-risking supports, can lead the mobilization of fundamental research along multiple commercialization pathways. Recommendations are provided for scholars, practitioners, and policymakers to more effectively commercialise deeptech inventions.

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Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively under-explored. We will give various definitions for replica topological order in mixed states. Similar to the replica trick, our definitions also involve n copies of density matrix of the mixed state. Within this framework, we categorize topological orders in mixed states as either quantum, classical, or trivial, depending on the type of information they encode.

For the case of the toric code model in the presence of decoherence, we associate for each phase a quantum channel and describes the structure of the code space. We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered. We accomplish this by describing the mixed state as a projected entangled pairs state (PEPS) and identifying the symmetry-protected topological order of its boundary state to the bulk topology.

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