Talks

Compact, spinning, and horizonless spacetimes can develop an ergoregion, where massless negative-energy states are quasi-trapped and drive the ergoregion instability. I will briefly review the linear mechanism and then describe recent progress in understanding the nonlinear evolution. Nonlinear mode coupling can amplify high-frequency modes through a turbulent direct cascade inside the ergoregion. Gravitational backreaction leads to an enhancement of the unstable process, and ultimately, black hole formation. I will illustrate the relevant dynamics and discuss implications for strongly gravitating horizonless systems.

The Perimeter Institute has provided me with 16 years of interactions, engagement and stimulating discussion. I'll describe some of my happy times at Perimeter and focus on one research area of interest: ultralight axions as a cosmological component. I'll describe constraints from the cosmic microwave background and large scale clustering of matter, through to novel constraints from voids and future prospects from stellar streams.

In this talk I will discuss one of the frontiers of both theory and data analysis in gravitational wave astronomy - understanding the ringing of black holes and probing them from real data. I will review past efforts started from Chandrasekhar, Detweiler, et al in analyzing modes of black holes and explain what we currently understand in both linear and nonlinear wave properties, as well as the corresponding detection aspect. At last I will show a few pressing problems and where we will be heading.

I will discuss BBN and a new python-based tool (PRyMordial) which allows one to easily simulate it both in the context of a standard cosmological model as well as in various scenarios of physics beyond the Standard Model. I’ll discuss how BBN provides a unique probe of physics relevant for the ~ MeV scale, and how it constrains or hints at modifications to the standard picture.

Complete minimal surfaces in R^3 have been much studied but much less is known about R^4. I will recall the main tools in R^4 and give a couple of examples of minimal embeddings of the complex plane in R^4. Then I will focus on complete minimal tori of curvature -8π and one end: in R^3 there is a unique example (the Chen-Gackstetter square torus) but in R^4 we can construct examples on all the rectangular tori. I will discuss the strategy for the construction and indicate the many questions which remain open. Joint work with Marc Soret.

We discuss the topological realization problem for minimally embedding compact surfaces in round spheres and balls. In 1970, using the solution to the Plateau problem, Lawson constructed orientable minimal surfaces of each genus embedded in $S^3$. In recent work with Karpukhin, McGrath and Stern, using equivariant eigenvalue optimization methods and a priori eigenspace dimension bounds, we constructed orientable free boundary minimal surfaces in $B^3$ of any genus and (positive) number of boundary, components. Now we have extended our methods to handle the nonorientable case, constructing embedded minimal surfaces in $S^4$ diffeomorphic to the connect-sum of any number of real projective planes: these all have area (so Willmore bending energy) under $8\pi$ and enjoy other interesting geometric features. The analogous construction for nonorientable free boundary minimal surfaces embedded in $B^4$ looms on the horizon. Open problems and speculation about potential discretizations may be offered if time permits....