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DTSTART;TZID=America/New_York:20250303T163000
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SUMMARY:Large value estimates in number theory and computer science
DESCRIPTION:Colloquium \nSpeaker: Larry Guth\, MIT \nTitle: Large value estimates in number theory and computer science \nAbstract: A large value estimate for a matrix M is a simple type of estimate in quantitative linear algebra. Estimates of this type appear in many parts of math\, both pure and applied. One example is the large value problem for Dirichlet polynomials from analytic number theory\, which is related to estimates about the zeroes of the Riemann zeta function. We will also give some examples from computer science. Many large value problems are difficult. On the pure math side\, the sharp conjecture about large values of Dirichlet polynomials has been open for a long time and is out of reach of current methods. On the computer science side\, we don’t know any efficient algorithm to approximately solve the large value problem for a given matrix M. Many experts think that such an algorithm does not exist. In this talk we will survey how large value estimates come up\, the known methods for working on them\, and some of the obstacles to fully understanding them. \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-3325/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-3.3.2025.png
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DTSTART;TZID=America/New_York:20250324T163000
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LAST-MODIFIED:20250321T163829Z
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SUMMARY:The Toda Lattice as a Soliton Gas
DESCRIPTION:Colloquium \nSpeaker: Amol Aggarwal\, Columbia University \nTitle: The Toda Lattice as a Soliton Gas \nAbstract: A basic tenet of integrable systems is that\, under sufficiently irregular initial data\, they can be thought of as dense collections of many solitons\, or “soliton gases.” In this talk we focus on the Toda lattice\, which is an archetypal example of an integrable Hamiltonian dynamical system. We explain how the system\, under certain random initial data\, can be interpreted through solitons\, and provide a framework for studying how these solitons asymptotically evolve in time. The arguments use ideas from random matrix theory\, particularly the analysis of Lyapunov exponents governing the decay rates of eigenvectors of random tridiagonal matrices.
URL:https://cmsa.fas.harvard.edu/event/colloquium-32425/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-3.24.2025.docx.final_.png
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