Sommerfeld Lecture Series (ASC)

Populations and communities rarely evolve in static environments; their fitness landscapes fluctuate across space and time, forming what may be called a noisy seascape. This talk examines how such variability modifies classical models of population dynamics and community stability. Beginning from the logistic equation, I will show how spatiotemporal fluctuations in fitness lead naturally to power-law population statistics and, under certain conditions, to the empirical (fractional) Richards growth law. Extending these ideas to interacting species reveals that the combined effects of dispersal and environmental noise can stabilize large, diverse communities despite strong competitive interactions. The resulting framework connects extinction, growth, and coexistence within a unified view of life on a noisy seascape.

Active systems are driven out of equilibrium by exchanging energy and momentum with their environment. This endows them with anomalous mechanical properties which leads to rich phenomena when active fluids are in contact with boundaries, inclusions, or disordered potentials. Indeed, studies of the mechanical pressure of active fluids and of the dynamics of passive tracers have shown that active systems impact their environment in non-trivial ways, for example, by propelling and rotating anisotropic inclusions. Conversely, the long-ranged density and current modulations induced by localized obstacles show how the environment can have a far-reaching impact on active fluids. This is best exemplified by the propensity of bulk and boundary disorder to destroy bulk phase separation in active matter, showing active systems to be much more sensitive to their surroundings than passive ones.

Quantum physics teaches us that even the emptiest vacuum is teeming with fluctuations of electromagnetic fields. When these fluctuations are confined between objects, they produce measurable forces: the Casimir effect describes an attraction between uncharged conductors arising solely from the confinement of the quantum void. In this talk, I will explore how this subtle quantum phenomenon connects to ideas of attraction, repulsion, and mechanical work. After introducing the origin and measurement of the Casimir force, I will discuss whether it can be made repulsive, and why true levitation remains elusive in equilibrium. Extending these ideas beyond equilibrium reveals new possibilities: radiation pressure from heat, nonreciprocal materials that generate motion and work without contact, and rotating bodies that spontaneously emit light. Together, these examples show how the restless quantum vacuum continues to surprise us.

Euclidean gravity on a sphere (euclidean de-Sitter) gives rise to some phase factors. We discuss how these phase factors change when we include an observer. We also discuss situations involving products of spheres.

We start by describing the geometrical notions central to Einstein's theory of gravity. We then discuss current ideas for how spacetime geometry could emerge in a quantum theory of gravity. We will see that quantum entanglement plays a crucial role.

I will show how a new set of twisted materials based on the M point rather than the K point can realize a series of exotic phases of matter, including quantum spin liquids and charge glasses. These materials, which have been exfoliated and twisted experimentally, will be at the forefront of new moire discoveries.

We will review the beginning of experimental and theoretical studies of moire systems and their evolution up to present. This type of systems represent a new way of “growing” materials, and has tremendous potential both for fundamental physics as well as for applications. Two dimensional periodic crystals, whose separation between atoms is of order angstroms, can be twisted controllably with respect to each other such that they form new “periodicities”, called moire periodicities. In the new “unit cell” we find thousands of atoms of the original crystal. These atoms behave in ways that are incredibly counterintuitive. We show how the controlled twisting of graphene and MoTe2 layers has led to a slew of states of matter not possible in bulk conventional materials. We will show how the collective behavior of thousands of p orbitals in a moire unit cell of graphene can create single Heavy fermion at moire scale, and how the interaction between such fermions can lead to a perfect quantum simulator of an Anderson model. We will then present a catalogue of possible twistable materials and show how a huge variety of strongly interacting models can be realized in twisted homo and hetero twisted bilayers and multilayers of these materials.