Talks

Height models and random tiling are well-studied objects in classical statistical mechanics and combinatorics that lead to many interesting phenomena, such as arctic curve, limit shape and Kadar-Parisi-Zhang scaling. We introduce quantum dynamics to the classical hexagonal dimer, 6- and 19-vertex models to construct frustration-free Hamiltonians with unique ground state being a superposition of tiling configurations subject to a particular boundary configuration. The local Hilbert space is enlarged with a color degree of freedom to generate long range entanglement that makes area law violation of entanglement entropy possible. The scaling of entanglement entropy between half systems is analysed with the surface tension theory of random surfaces and under a q-deformation that weighs random surfaces in the ground state superposition by the volume below, it undergoes a phase transition from area law to volume scaling. At the critical point, the scaling is L logL due to the so-called "entropic repulsion” of Gaussian free fields conditioned to be positive. An exact holographic tensor network description of the ground state is proposed with one extra dimension perpendicular to the lattice. I will also discuss inhomogeneous deformations to obtain sub-volume intermediate scaling and possible generalisations to higher dimension.

Collective cell movement is critical to the emergent properties of many multicellular systems including microbial self-organization in biofilms, wound healing, and cancer metastasis. However, even the best-studied systems lack a complete picture of how diverse physical and chemical cues act upon individual cells to ensure coordinated multicellular behavior. Myxococcus xanthus is a model bacteria famous for its coordinated multicellular behavior resulting in dynamic patterns formation. For example, when starving millions of cells coordinate their movement to organize into fruiting bodies – aggregates containing tens of thousands of bacteria. Relating these complex self-organization patterns to the behavior of individual cells is a complex-reverse engineering problem that cannot be solved solely by experimental research. In collaboration with experimental colleagues, we use a combination of quantitative microscopy, image processing, agent-based modeling, and kinetic theory PDEs to uncover the mechanisms of emergent collective behaviors.

In any approach to quantum gravity, the quantum representation theory of the "algebra" of Cauchy hypersurface deformations plays a crucial role. Its faithful implementation is a key step towards constructing a valid theory of quantum gravity as it ensures quantum spacetime diffeomorphism covariance. Bergmann and Komar were the first to consider the possibilty of a corresponding quantum "group". Its construction is mathematically challenging in more than 1+1 spacetime dimensions because one leaves the realm of Lie algebras and Lie groups. After an introduction to these concepts, we show that the Bergmann Komar "group" can indeed be faithfully implemented in a weakly self-interacting truncation of 3+1 quantum gravity with two propagating polarisations. We then discuss possible implications for the actual, untruncated theory.

Zoom link:  https://pitp.zoom.us/j/91488383205?pwd=bkxGS0huMGNEYXc3Y2FJSGZHQ0pqQT09