Welcome to my website

My name is Lucas Fabian Hackl and I am a Postdoc at the School of Mathematics and Statistics & School of Physics at the University of Melbourne. My research program focuses on understanding questions about quantum matter and spacetime using tools from quantum information theory, Lie groups and differential geometry.

Previously, I was postdoc at the Villum Centre of Excellence for the Mathematics of Quantum Theory at the University of Copenhagen and at the Max Planck Harvard Research Center for Quantum Optics.

I completed my PhD under the supervision of Eugenio Bianchi at the Institute for Gravitation and the Cosmos of the Pennsylvania State University. I completed my Master’s at the Perimeter Institute, after which I was a teaching fellow at the African Institute for Mathematical Sciences in Sénégal and interned with the Global Public Policy Institute (GPPi) in Berlin. Beside my academic interests I have been involved in social projects, public policy, science policy and video productions.

On this website, you can learn more about me (including CV) and what I am working on: You can find information on my activities, my research and my teaching experience. Feel free to contact me if you are interested in my work.

Learn more about my fields of interest:

» Mathematical Physics

I am interested into mathematical physics with applications to fundamental theories, such as gravity and quantum field theories. I like to use and develop elegant mathematical methods, motivated by strong physical guiding principles.

  • Geometry of variational manifolds and generalized Gaussian states
    As an MPHQ Fellow, I am working with Ignacio Cirac on the geometry of variational manifolds with focus on generalized Gaussian states.
  • Circuit complexity in quantum field theory (arXiv:1803.10638, arXiv:1810.05151)
    As Visiting Graduate Fellow at Perimeter Institute, I am interested in understanding complexity of circuits and states in quantum field theory.
  • Entanglement production (arXiv:1709.00427, arXiv:1710.04279)
    My main PhD project focused on the time evolution of the entanglement entropy in bosonic systems. I found a novel relationship between entanglement and chaos: the entanglement entropy in classically unstable systems grows linearly with a rate given by a sum over the Lyapunov exponents of the system.
  • Entanglement typicality (arXiv:1703.02979, 1808.08963)
    In the study of quantum matter, I investigated simple translationally invariant fermion models and showed that the entanglement entropy of typical energy eigenstates dramatically differs from typical states in the Hilbert space.
  • Bosonic and fermionic Gaussian states from Kähler structures
    In the context of studying entanglement in various systems, I developed unifying mathematical framework that is particularly suitable to study entanglement and time evolution of bosonic and fermion Gaussian states. It uses a triple of mathematical objects known from Kähler geometry (metric, symplectic form and linear complex structure).
  • Semi-classical quantum geometries (arXiv:1605.05356, arXiv:1609.02219)
    In quantum gravity, I developed methods to describe quantum geometries with spacetime correlations that match the semi-classical limit studied in perturbative quantum gravity. The area law of the entanglement entropy plays an important role.
  • Entanglement in quantum fields on a lattice (arXiv:1507.01567, arXiv:1512.08959)
    During my second year, I worked on entanglement in quantum field theory on a lattice and introduced the notion of entanglement time.
  • Horizon complimentarity (arXiv:1409.6753)
    During my first year at Penn State I looked at horizon complimentarity in elliptic de Sitter space where we performed an observer dependent quantization and provided a translation recipe.
  • Shape dynamics
    For my Master’s thesis, I was working on shape dynamics, a reformulation of general relativity.
  • Amplitudes in massless QCD (arXiv:1206.2381)
    For my Bachelor’s thesis I worked with analytic expressions for tree-level amplitudes in massless QCD and their efficient implementation.
  • Tensorial spacetime geometries
    During an internship at the Max Planck Institute for Gravitational Physics I worked on new spacetime geometries.

» Public Policy

I want that my work helps people. I believe in education as important engine for development, and my experiences in Senegal made me very curious about the future of this more and more shining continent.

» Media

I enjoy working with different media and especially film excites me. Since highschool, I have worked in several projects covering a wide range of media including film, print, sound and web.