A particular population of galaxies have drawn much interest recently, whichare as faint as typical dwarf galaxies but have the sizes as large as $L^*$galaxies, the so called "ultra-diffuse galaxie" (UDGs). The lack of tidalfeatures of UDGs in dense environments suggests that their host halos areperhaps as massive as that of the Milky Way. On the other hand, galaxyformation efficiency should be much higher in the halos of such masses. Here weuse the model galaxy catalog generated by populating two large simulations: theMillennium-II cosmological simulation and Phoenix simulations of 9 big clusterswith the semi-analytic galaxy formation model. This model reproduces remarkablywell the observed properties of UDGs in the nearby clusters, including theabundance, profile, color, and morphology, etc. We search for UDG candidatesusing the public data and find 2 UDG candidates in our Local Group and 23 inour Local Volume, in excellent agreement with the model predictions. Wedemonstrate that UDGs are genuine dwarf galaxies, formed in the halos of $\sim10^{10}M_{\odot}$. It is the combination of the late formation time andhigh-spins of the host halos that results in the spatially extended feature ofthis particular population. The lack of tidal disruption features of UDGs inclusters can also be explained by their late infall-time.

Supermassive black holes are found at the centre of massive galaxies. Duringthe growth of these black holes they light up to become visible as activegalactic nuclei (AGN) and release extraordinary amounts of energy across theelectromagnetic spectrum. This energy is widely believed to regulate the rateof star formation in the black holes' host galaxies via so-called "AGNfeedback". However, the details of how and when this occurs remains uncertainfrom both an observational and theoretical perspective. I review some of theobservational results and discuss possible observational signatures of theimpact of super-massive black hole growth on star formation.

A striking signal of dark matter beyond the standard model is the existenceof cores in the centre of galaxy clusters. Recent simulations predict that aBrightest Cluster Galaxy (BCG) inside a cored galaxy cluster will exhibitresidual wobbling due to previous major mergers, long after the relaxation ofthe overall cluster. This phenomena is absent with standard cold dark matterwhere a cuspy density profile keeps a BCG tightly bound at the centre. We testthis hypothesis using cosmological simulations and deep observations of 10galaxy clusters acting as strong gravitational lenses. Modelling the BCG wobbleas a simple harmonic oscillator, we measure the wobble amplitude, A_w, in theBAHAMAS suite of cosmological hydrodynamical simulations, finding an upperlimit for the CDM paradigm of $A_w < 2$ kpc at the 95% confidence limit. Wecarry out the same test on the data finding a non-zero amplitude of $A_w =11.82^{+7.3}_{-3.0}$~kpc with the observations dis-favouring $A_w = 0$ at the$3\sigma$ confidence level. This detection of BCG wobbling is evidence for adark matter core at the heart of galaxy clusters. It also shows that stronglensing models of clusters cannot assume that the BCG is exactly coincidentwith the large scale halo. While our small sample of galaxy clusters alreadyindicates a non-zero Aw, with larger surveys, e.g. Euclid, we will be able tonot only to confirm the effect but also to use it to determine whether or notthe wobbling finds its origin in new fundamental physics or astrophysicalprocess.

We explore the H-alpha emission in the massive quiescent galaxies observed bythe KMOS-3D survey at 0.7 < z < 2.7. The H-alpha line is robustly detected in20 out of 120 UVJ-selected quiescent galaxies, and we classify the emissionmechanism using the H-alpha line width and the [NII]/H-alpha line ratio. Wefind that AGN are likely to be responsible for the line emission in more thanhalf of the cases. We also find robust evidence for star formation activity innine quiescent galaxies, which we explore in detail. The H-alpha kinematicsreveal rotating disks in five of the nine galaxies. The dust-corrected H-alphastar formation rates are low (0.2 - 7 Msun/yr), and place these systemssignificantly below the main sequence. The 24micron-based infraredluminosities, instead, overestimate the star formation rates. These galaxiespresent a lower gas-phase metallicity compared to star-forming objects withsimilar stellar mass, and many of them have close companions. We thereforeconclude that the low-level star formation activity in these nine quiescentgalaxies is likely to be fueled by inflowing gas or minor mergers, and could bea sign of rejuvenation events.