Calendar

The mechanical properties of biomolecular assemblies play pivotal roles in many biological and pathological processes. In this talk, I’ll focus on two different self-assembled structures in cells: 1) the plasma membrane, which defines the boundary of a cell; and 2) protein condensates, which arise from liquid-liquid phase separation (LLPS) inside cells.
In the first part, I’ll discuss recent findings on how cell membranes respond to local mechanical perturbations. In most non-motile cells, local perturbations to membrane tension remain highly localized, leading to subcellular Ca2+ influx and vesicle fusion events. Membrane-cortex attachments are responsible for impeding the propagation of membrane tension. Exception to this rule can be found in the axon of neurons, where a rapid propagation of membrane tension coordinates the growth and branching of the axon.

In the second part, I’ll discuss the development of quantitative techniques to measure the surface tension and viscosity of liquid protein condensates. Our results highlight a common misconception about LLPS in biology: ‘oil droplets in water’ is often used to give an intuition about protein condensates in cells. However, oil droplets and protein condensates represent two extremes in the realm of liquid properties. The unique properties of protein condensates have important implications in achieving molecular and functional understanding of LLPS.

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Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of  W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behaviour of FQH systems.  Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.

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We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones.

References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx] Jing-Yuan Chen, [1902.06756].

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Condensed-matter theorists have discovered examples of physical systems with unusual behavior, such as pointlike excitations that behave neither as bosons nor as fermions, leading to the idea of topological phases of matter. Classifying the possible topological phases has been the focus of a lot of research in the last decade in condensed-matter theory and nearby areas of mathematics. In this talk, I’ll focus primarily on the special case of invertible phases, also called symmetry-protected topological (SPT) phases, whose classification uses techniques from homotopy theory. I will discuss two different approaches to this, due to Kitaev and Freed-Hopkins, followed by details of the homotopy-theoretic classifications. The latter includes work of Freed-Hopkins and of myself.

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I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

Based on 2102.09555 and 2106.03842

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