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Progress toward the development of a safe and effective treatment for AIDS has been slow because the Human Immunodeficiency Virus has the ability to mutate its own structure. This mutation enables the virus to become resistant to previously effective drug therapies. Apart from the traditional role of preventing progression from HIV to AIDS Antiretroviral drugs have an additional clinical benefit of substantially reducing infectiousness thus making them an important strategy in the fight against HIV.
This talk will include a pot-pourri of geo-related problems that may benefit from elegant applied mathematics analyses.
This talk will be a tour through the combinatorics of reduced
decompositions in the symmetric group (and, if time permits, the affine
symmetric and hyperoctahedral groups). This subject has connections to
many areas of mathematics. For instance, it is closely tied to the
geometry of the Grassmannian and of the flag variety, through the theory
of Schubert polynomials. Also there are also some very surprising (and,
apparently, very difficult) analytic and probabilistic questions about
large reduced decompositions.
A garbled circuit (GC) is a way of encrypting a computation in a way that reveals only the final output and none of the intermediate state. In this talk, I'll describe Yao's classical GC construction (1987), and its application to secure two-party computation protocols. Starting in the early 2000s, interest gained in actually implementing secure computation protocols. As a result, garbled circuits became the focus of an interesting line of combinatorial optimizations, which I will present. These works culminated in a recent GC construction that can be proven optimal in some sense.