Stellar evolution predicts that some massive stars will end up with black holes (BHs), however, due to pair-instability there is an upper limit for BH mass from this scenario (about 70 solar masses). On the other hand, there is strong evidence that supermassive black holes (SMBHs) exist in most galaxies, whose mass is beyond 100,000 solar masses. There is a mass gap between the two groups of BHs, which are called intermediate-mass black holes (IMBHs). IMBHs are predicted but less observed with ordinary telescopes. Particularly, IMBH was observed by LIGO through gravitational waves of binary BH mergers. This brings the puzzle of IMBH formation, and how can we detect them.

The record of the highest redshift quasars has been flashing (e.g., see this page). The SMBHs in these systems can weigh 1000,000,000 solar masses when the Universe was still very young. Moreover, there are observational constraints that SMBHs form from the accretion of ambient gaseous material. Still, these high-redshift SMBHs need a very high accretion rate. People are interested in the exact conditions for this kind of rapid mass accretion.

Feedback from BHs may leave a huge impact on the evolution of galaxies or other systems. For example, strong feedback from BHs, in the forms of radiation, mechanical outflows, and cosmic rays may disrupt dense gaseous regions of galaxies, which are typically the birthplace for stars, and therefore shut down star formation. Research in these directions may help people understand how BHs shape the evolution of galaxies and provide hints about hunting for these SMBHs/IMBHs.

Baryon acoustic oscillation (BAO) is the sound wave of baryon-photon fluid in the early Universe (redshift above ~1100). After the decoupling of photons and baryons, the traces of BAO were hidden in the distribution of galaxies and somewhat "frozen" since then (this is especially true at large scales). The feature provides a "standard ruler" for cosmology, which can be used for constraining cosmological parameters that describe the history of our Universe. Still, there are some challenges at small scales for BAO: due to non-linear evolution at these scales, BAO signals are largely smeared. People are also interested in reconstructing the initial density field which can ease the difficulty and recover more BAO information.

The information inside the distribution of galaxies can be described with correlation functions, which can be correlations between 2 points (the most popular one), or even 3 points in the Universe. The 3-point correlation function can provide some information beyond the 2-point one, like the non-Gaussianity which is predicted in some early Universe inflation models. In Fourier space, we typically call the 3-point correlation bispectrum. Though there are challenges in measuring bispectrum from galaxy distributions, bispectrum can be used as a new path to constrain cosmological parameters.

One important step in constraining cosmological parameters from LSS is to measure accurate correlation functions (power spectrum, bispectrum). This is challenged by many factors, including the redshift distortion effect, which arises from the peculiar velocity of galaxies. The traditional way of describing the effect is through a fixed line-of-sight direction, which is good for small-angle or plane-parallel conditions, but causes problems in wide-angle (or even "full-sky") conditions. To reconcile the problem, people can study LSS just like CMB, but with additional eigenfunctions in the radial direction (what is called "spherical Fourier-Bessel decomposition", SFB). The technique can be applied to future surveys like SPHEREx, which covers 75% of the sky.