Colloquium

One of the major themes of the modern condensed matter physics is the study of materials with nontrivial electronic structure topology. Particularly significant progress in this field has happened within the last decade, due to the discovery of topologically nontrivial states of matter, that have a gap in their energy spectrum, namely Topological Insulators and Topological Superconductors.

Across science, women continue to be underrepresented.  The gender gap is considerable in physics and persists at all levels, from students through to senior physicists.  Recent research analyzed physics publications from around the world, reporting that 13% of authors in the senior author position are women, and this is changing by only 0.1% per year.  Despite the glaring lack of gender diversity, this issue is often not openly discussed in the day-to-day life of a physics department.

There is a rich interplay between higher algebra (category theory, algebraic topology) and condensed matter. I will describe recent mathematical results in the classification of gapped topological phases of matter. These results allow powerful techniques from stable homotopy theory and higher categories to be employed in the classification. In one direction, these techniques allow for complete a priori classifications in spacetime dimensions ≤6. In the other direction, they suggest fascinating and surprising statements in mathematics.

Cooling atomic gases to ultracold temperatures revolutionized the field of atomic physics, connecting with and impacting many other areas in physics. Advances in producing ultracold molecules suggest similarly dramatic discoveries are on the horizon. First, I will review the physics of ultracold molecules, including our work bringing a new class of molecules to nanokelvin temperatures. Chemistry at these temperatures has a very different character than at room temperature. One striking effect is our recent result using spin states of reactants to control chemical reaction pathways.