Talks

Fermi surfaces have a number of fascinating properties, including a continuum of gapless excitations, a landscape of possible collective modes, universal super-area law entanglement, and relevant deformations that can produce non-Fermi liquid quantum critical metals. Their extreme gaplessness makes them difficult to tame with the conventional tools of QFT. Bosonization provides a potential nonperturbative approach by describing Fermi surface dynamics through a collective field living on a part of phase space. However, while such a field is sensible semiclassically, the challenge of treating it quantum mechanically has prevented bosonization from providing as powerful a tool as in one dimension. I will show that general Fermi surfaces can be exactly described by a particular large N limit of a U(N)_1 WZW model, with a tower of irrelevant corrections. This matrix-valued description encodes the noncommutative nature of phase space, and its (solvable) strongly coupled dynamics resolves the naive overcounting of degrees of freedom in the collective field without the need to cut the Fermi surface into patches. 

Discs are among the simplest manifolds, but their groups of diffeomorphisms can be very complicated. I will describe the techniques from geometry, topology, and dynamics that were used to understand these groups in low dimensions, the relationship of these groups to stable homotopy theory and number theory in high dimensions, and recent breakthroughs in understanding their rational homotopy type. This talk will be aimed at a broader audience.

The Kawai–Lewellen–Tye (KLT) relations are a striking example of how string theory can reveal hidden structures and connect a web of, in principle, very different theories. Originally, they state that (tree-level) closed-string amplitudes can be expressed as quadratic combinations of open-string amplitudes. In the field theory limit, this gives rise to the celebrated double-copy between gluons and gravitons. In this talk, I will discuss how much of this elegant structure survives away from flat space, focusing on AdS. As a first step, I will propose the fundamental building blocks of tree-level string amplitudes in AdS and then show how they are related via an AdS version of the KLT relations, whose kernel can be computed exactly. This structure not only significantly simplifies explicit calculations but also points to deeper algebraic and geometric structures to be uncovered.

This talk will be a brief and interactive introduction to my current research and the cosmological concepts that go along with it. I will assume limited prior knowledge of GR and cosmology so that even students in unrelated fields can learn something interesting.

When dealing with QFTs or with quantum mechanical systems in the thermodynamic limit, one encounters uncountable Hilbert spaces. These are mathematically wilder and physically less realistic than their countable counterparts. In this talk, we will explore how vacua encode a choice to reduce the Hilbert Space in size. In spite of the mathematically sounding intro, we’ll see this has interesting physical implications.