This talk will focus on the methodologies for efficiently
capturing the macroscale behavior of a system using microscopic models.
I will try to give a candid assessment of the current status of the
field, discussing both the main successes and the major difficulties.
I will start by reviewing some of the classical methodologies.
I will then discuss the attempts that have been made to construct
general frameworks.
I will present a relatively new strategy for constructing seamless
techniques that do not require going back and forth between the
macro and micro states of the system.
If time permits, I will also discuss some typical instabilities
and inconsistencies that can arise in multiscale methods.
Finally, I will discuss what can be done for systems that do not have
scale separation or any other special features.
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