Talks

In these lectures, I discuss how GWs are produced by cosmological phase transitions. We start by a short recap of gravitational waves and then move to early attempts using pairs of bubbles and the envelope approximation. Next we cover the energy budget of phase transitions and the impact of sound waves. Finally I comment on recent developments.

The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example, when $c=1$, they are related to tau functions of integrable systems of Painlev\'{e} equations. They are also closely related to non-perturbative completions in the topological string theories. I will first explain what Virasoro conformal blocks are. Then I will describe a new way to construct Virasoro blocks at $c=1$ on $C$ by using the "abelian" Heisenberg conformal blocks on a branched double cover of C. The main new idea in our work is to use a spectral network and I will show the advantages of this construction. This nonabelianization construction enables us to compute the harder-to-get Virasoro blocks using the simpler abelian objects. It is closely related to the idea of nonabelianization of the flat connections in the work of Gaiotto-Moore-Neitzke and Neitzke-Hollands. This is based on a joint work with Andrew Neitzke.

Gravitational forces from the largest structures in the Universe leave a detectable imprint on galaxies and their local environment. I will present a new approach to tracing the tidal field using these correlations: the intrinsic alignment of small groups of galaxies, or "multipelts". Multiplets mostly consist of 2-4 galaxies within 1 Mpc/h of each other, and we measure their orientations relative to the galaxy-traced tidal field. Using spectroscopic redshfits from the DESI Y1 survey, we detect intrinsic alignment out to projected separations of 100 Mpc/h and beyond redshift 1. We find a simillar signal regardless of galaxy luminosity or color, which could make multiplet alignment a useful tool for mapping the direction of the tidal field and any cosmological effects which impact it. Our detection demonstrates that galaxy clustering in the non-linear regime of structure formation preserves an interpretable memory of the large-scale tidal field. 

This class is an introduction to the 2-species competitive Lotka-Volterra model. We will cover three canonical outcomes--coexistence, dominance and bistability-- for the pairwise competition between species. We will also use the model to predict co-culture's responses to different perturbations, and see how these predictions were experimentally verified in microcosms.

In these lectures, I discuss how GWs are produced by cosmological phase transitions. We start by a short recap of gravitational waves and then move to early attempts using pairs of bubbles and the envelope approximation. Next we cover the energy budget of phase transitions and the impact of sound waves. Finally I comment on recent developments.