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  • May
    20

    Quasi-Monte Carlo Integration and Discrepancy

    Department of Industrial Engineering and Management Sciences (IEMS)

    10:45 AM A230, Technological Institute

    EVENT DETAILS

    Abstract: A classical approach to numerically integrating a function f is using Monte Carlo (MC) methods. Here, one evaluates f at random points and the estimation error scales as \sigma(f)/n^{1/2} with n samples, where \sigma(f) is the standard deviation of f. A different approach, widely used in practice, is using quasi-Monte Carlo (QMC) methods, where f is evaluated at carefully chosen deterministic points and the error scales roughly as 1/n. Both methods have distinctive advantages and shortcomings, and a key question has been to find a method that combines the advantages of both.

    In this talk, I will introduce the fascinating area of QMC methods and their connections to various areas of mathematics and to geometric discrepancy. I will then show how recent developments in algorithmic discrepancy theory can be used to give a method that combines the benefits of MC and QMC methods, and even improves upon previous QMC approaches in various ways. The talk will be completely self-contained and elementary, and no prior knowledge of either discrepancy or integration is required.

    Based on joint work with Haotian Jiang (U. Chicago).

    Bio: Nikhil Bansal is the Patrick C. Fischer professor of Computer Science and Engineering at the University of Michigan. He completed his PhD in 2003 from Carnegie Mellon University, and has previously worked at IBM Research, TU Eindhoven and CWI

    Amsterdam. He is broadly interested in theoretical computer science with focus on the design and analysis of algorithms, discrete mathematics and combinatorial optimization. His work has been recognized by several best paper awards. He is an ACM fellow and was an invited speaker at ICM 2022.

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    TIME Tuesday, May 20, 2025 at 10:45 AM - 12:00 PM

    LOCATION A230, Technological Institute    map it

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    CONTACT Kendall Minta    kendall.minta@gmail.com EMAIL

    CALENDAR Department of Industrial Engineering and Management Sciences (IEMS)