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Mathematical Sciences Research Institute

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Upcoming Summer Graduate Schools

  1. Introduction to water waves [Virtual Summer Graduate School]

    Organizers: Mihaela Ifrim (University of Wisconsin-Madison), Daniel Tataru (University of California, Berkeley)
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    Overturning wave, artistic drawing by E. Ifrim

    Due to the COVID-19 pandemic, this summer school will be held online.

    The purpose of this two weeks school is to introduce graduate students to the state of the art methods and results in the study of incompressible Euler’s equations in general, and water waves in particular. This is a research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.

     

    The goal is to present the main current research directions in water waves. We will begin with the physical derivation of the equations, and present some of the analytic tools needed in study. The final goal will be two-fold, namely (i) to understand the local solvability of the Cauchy problem for water waves, as well as (ii) to describe the long time behavior of solutions.

    Through the lectures and associated problem sessions, students will learn about a number of new analysis tools which are not routinely taught in a graduate school curriculum. The goal is to help students acquire the knowledge needed in order to start research in water waves and Euler equations.

    Updated on Jun 07, 2020 11:09 PM PDT
  2. Foundations and Frontiers of Probabilistic Proofs (Zurich, Switzerland)

    Organizers: Alessandro Chiesa (University of California, Berkeley), Tom Gur (University of Warwick)
    Proofs main logo
    Several executions of a 3-dimensional sumcheck protocol with a random order of directions (thanks to Dev Ojha for creating the diagram)

    Due to the COVID-19 pandemic, this summer school is taking place in summer 2021.

    Proofs are at the foundations of mathematics. Viewed through the lens of theoretical computer science, verifying the correctness of a mathematical proof is a fundamental computational task. Indeed, the P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.

    The complexity-theoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit local-to-global structure that allows verifying a proof by reading only a minuscule portion of it. As another example, interactive proofs allow for verification via a conversation between a prover and a verifier, instead of the traditional static sequence of logical statements. The study of such proof systems has drawn upon deep mathematical tools to derive numerous applications to the theory of computation and beyond.

    In recent years, such probabilistic proofs received much attention due to a new motivation, delegation of computation, which is the emphasis of this summer school. This paradigm admits ultra-fast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recently-deployed technology, for example, as part of cryptographic constructions known as succinct non-interactive arguments of knowledge (SNARKs).

    This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

    Updated on May 04, 2020 11:36 AM PDT