Counts, Clustering & Collapse: Analytical Methods for Large Scale Structure (Joint DTP - DAA Colloquium)

Understanding the origin and evolution of the so-called Cosmic Web is
one of the oldest questions in modern cosmology. With the advent of
deep, wide-field galaxy surveys, this question has become intimately
connected with more fundamental ones such as the origin of dark energy
or the nature of the initial phase of inflation. Quantities which
encapsulate our understanding of the former -- such as the mass
function and clustering properties of gravitationally bound dark
matter halos -- are now potentially tools that can also help us answer
the latter. I will discuss recent advances in our analytical
understanding of these tools, which in principle open up several means
of exploiting the large quantities of data that are becoming
available. On a sobering note, these advances also highlight that we
cannot yet fully answer a basic question: Where does gravitational
collapse occur? I will discuss some possible ways forward in building
a more complete analytical understanding of the locations of collapse.