Interactive. Coding for Interactive Communication and the Power of Adaptivity

error correcting codes allow for reliable transmission of data over unreliable channels. the 70 years of development that went into the study of error correction, following shannon's ground-breaking paper in 1948, yielded a fairly complete theory with far reaching applications to other theoretical and practical fields. however, many modern communication settings are not simply about transmitting information, but rather operate over many rounds of interactive communication between different parties. cloud computing, cryptographic protocols, and distributed computing schemes are prime examples of such settings. due to the overwhelming success of classical error correcting codes, and because interaction is central in many applications, we strongly believe that the theory of interactive error correcting codes will be transformative. crafting error correcting codes tailored for interactive settings, as well as understanding their fundamental limitations, is the main goal of this proposal. we will study some of the most exciting fundamental open problems in interactive communication. in particular, this includes computing the rate distance trade-off for interactive coding, and building error resilient schemes for distributed computing. we will consider a diverse set of ``classical'' questions in the interactive setting, as well as aspects of interactive coding that are unique and have no counterparts in classical coding. further, we will build adaptive coding schemes which will achieve better rates than non-adaptive counterparts. indeed, one of the main powers of interactive communication, and an integral part of this proposal, is adaptivity. here, each party can adapt its actions based on previous communication. as our research draws ideas from several scientific communities, it will lift our understanding of interdisciplinary connections between them to new heights.