We introduce a matrix model for SU(2)-gauge theory, and introduce its symmetries. We construct its gauge invariant partition function by projecting out colored states from the path integral, and simulate the theory on a lattice. We observe that the theory has two minima, one of which is metastable. We find phase transitions, and draw the phase diagram.

1. Combating human trafficking 2. Rehabilitation and empowerment of transitioning adults with intellectual disabilities and trafficked/at-risk individuals transitioning out of CNCP (Children in Need of Care and Protection) homes 3. Emphasising the impact of individual awareness sessions

A common envelope (CE) event occurs when a giant star, consisting of a dense core and bloated envelope, engulfs a much smaller binary companion. This leads to the core and companion inspiralling inside a shared envelope, to which they transfer orbital energy and angular momentum via gravitational drag (gas dynamical friction). This can result in a merger between the core and companion, which may produce a luminous red nova, or the ejection of the envelope, resulting in a stable short-period `post-CE' binary. Global three-dimensional hydrodynamical simulations can be used to better understand the key physical processes that govern CE evolution. We are currently focusing on evaluating the applicability of various drag force models from the literature by comparing their predictions with the drag force measured from the simulations. We find that certain analytic drag models can reproduce the simulation results with remarkable accuracy. Due to their much lower computational cost, one-dimensional spherically symmetric simulations may be better suited for certain science goals, but should reliably reproduce key outcomes of the 3D simulations. I will discuss our ongoing effort to develop global 1D hydrodynamical CE simulations, which involves deploying the analytic models mentioned above in the 1D simulations and comparing 1D and 3D simulations at each stage of model development.

A Landau–Siegel zero, or exceptional zero, is a potential counterexample to the generalized Riemann hypothesis for Dirichlet $L$-functions associated with quadratic number fields. Assuming the existence of a Landau-Siegel zero, we establish an explicit Deuring--Heilbronn zero repulsion phenomenon for Dirichlet $L$-functions modulo $q$. Our estimate is uniform in the entire critical strip. It is a joint work with Kubra Benli, Henry Twiss, and Asif Zaman.