Colloquium

By a celebrated theorem of Jacob Lurie, an extended TQFT is entirely determined by what it assigns to a point. It is natural to ask whether this theorem applies to TQFTs of physical interest. And, if yes, what do these theories assign to a point? In this talk, I will propose an answer for the case of 3-dimensional Chern-Simons theory. I will then
explore the relation to line defects in chiral WZW models, and boundary conditions for full WZW models. At last, I will present a conjectural classification of the above mentioned line defects and boundary conditions.

Laser-cooled trapped ions are among the most versatile experimental platforms for exploring quantum information. In this talk, I will give a brief overview of this system and its capabilities to simulate non-trivial interacting quantum models. Internal states of these ions, such as hyperfine states, constitute well isolated qubit (or spin-1/2) states, with quantum coherence demonstrated up to fifteen minutes. Individual qubits states can be detected by laser beams with near perfection. Quantum logic gates and interacting spin Hamiltonians are engineered by coupling internal states of multiple ions to their collective vibrational modes using optical forces. By suitably tailoring these spin-phonon couplings, interactions between ion-spins can be tuned in magnitude, range, and sign. The laboratory for Quantum Information with Trapped Ions at IQC aims to build a highly flexible quantum simulator with dozens of spins, and explore problems in quantum information and many-body physics in a regime that is intractable with classical computers.

The discovery of the Higgs boson at the LHC in 2012 was a watershed in particle physics. Its existence focuses attention on the outstanding questions about physics beyond the Standard Model: is `empty' space unstable? what is the dark matter? what is the origin of matter? what is the explanation for the small masses of the neutrinos? how is the hierarchy of mass scales in physics established and stabilized? what drove inflation? how to quantize gravity Many of these issues will be addressed by future runs of the LHC, e.g., by studies of the Higgs boson, and also motivate possible future colliders.

Black holes of 1 million to 20 billion solar masses have been found at the centers of galaxies.

New observational data and improved orbit models in the past several years have substantially expanded the sample of black holes with dynamically measured masses.  I will describe recent progress in discovering a new population of ultra-massive black holes and its impact on our understanding of the symbiotic relationships between black holes and galaxies.  I will discuss the implications for the ongoing pulsar timing array experiments searching for nano-Hertz gravitational waves from merging supermassive black hole binaries.

Conformal Field Theory (CFT) describes the long-distance
dynamics of numerous quantum and statistical many-body systems. The
long-distance limit of a many-body system is often so complicated that
it is hard to do precise calculations. However, powerful new
techniques for understanding CFTs have emerged in the last few years,
based on the idea of the Conformal Bootstrap. I will explain how the
Bootstrap lets us calculate critical exponents in the 3d Ising Model
to world-record precision, how it explains striking relations between
magnets and boiling water, and how it can be applied to questions
across theoretical physics.

In this talk, I will focus on cosmologies that replace the big bang with a big bounce. I will explain how, in these scenarios, the large-scale structure of the universe is determined during a contracting phase before the bounce and will describe the recent development of the first well-behaved classical (non-singular) cosmological bounce solutions.

 Non-Fermi liquids are exotic metallic states which do not support well defined quasiparticles. Due to strong quantum fluctuations and the presence of extensive gapless modes near the Fermi surface, it has been difficult to understand universal low energy properties of non-Fermi liquids reliably.  In this talk, we will discuss recent progress made on field theories for non-Fermi liquids. Based on a dimensional regularization scheme which tunes the number of co-dimensions of Fermi surface, critical exponents that control scaling behaviors of physical observables can be computed in controlled ways. The systematic expansion also provides important insight into strongly interacting metals. This allows us find the non-perturbative solution for the strange metal realized at the antiferromagnetic quantum critical point in 2+1 dimensions and predict the exact critical exponents.

In recent years, precise cosmological measurements have provided strong evidence for new physics beyond the Standard Model, occurring both in the very early universe and also today.  In the near future, large-scale galaxy surveys will open another window on many different areas of physics, including tests of gravity, probes of dark energy, and cosmic inflation.  However, interpreting galaxy surveys presents new challenges, because galaxies are sensitive to astrophysics that are unimportant for the cosmic microwave background.  I will discuss how galaxies may be used to study cosmology, and will argue that the messy astrophysics in galaxies actually offers entirely new probes of fundamental physics.  I will illustrate this with 3 examples, related to inflation, neutrino masses, and the properties of dark matter.

I will argue that the standard model contains a rather strong hint that -- instead of being simply an ordinary continuous 4D manifold -- spacetime is actually the product of a 4D manifold and a certain discrete/finite 6D space (i.e. there are 6D discrete/finite "extra dimensions").  I will introduce this idea and the evidence for it in simple way, and then discuss various outstanding puzzles and future directions.

Tensor networks offer an efficient representation of many-body wave-functions in an exponentially large Hilbert space by exploiting the area law of ground state quantum entanglement. I will start with a gentle introduction to the tensor network formalism. Then I will describe its application to realizing Wilson's renormalization group directly on quantum lattice models (e.g. quantum spin chains), with emphasis on the RG fixed points corresponding to conformal field theories. We will see how to define both global and local scale transformations on the lattice in such a way that, intriguingly, conformal invariance can be tested (and conformal data extracted) right at the UV cut-off scale.

Scale invariant transfer matrices and Hamiltonians Abstract We investigate the possibility of strictly scale invariant transfer matrices in quantum spin chains based on a certain planar algebra, both as operators and as quadratic forms.

Recent explorations of the space of quantum field theories have provided novel topological and geometric information about this space. This voyage has resulted in the solution of some long-standing questions:  the computation of sought-after topological invariants (Gromov-Witten invariants) by a new physics-based approach, the first instance of exact correlation functions in a four-dimensional QFT and the unearthing of the action of dualities on the basic observables of three dimensional gauge theories.