STARKs have recently received quite a lot of attention due to their small proof size and supposedly simple assumptions. The paper introduction itself seems to mainly state that their construction is solely based on collision-resistant hash functions. However, further down in the paper they seem to require some conjectures related to reed-solomon codes (see conjectures B.16 and B.17 as well as Appendix D.3).
Can somebody explain these conjectures in simple words? Are these conjectures crucially required for the asymptotic proof size that STARKs achieve or are they only required for some practical performance improvements?