[Theory] 12/16 TTIC Colloquium: Nikhil Bansal, University of Michigan

[Mary Marre via Theory]

*When:*         Monday, December 16, 2024 at* 11:30** am** CT   *


*Where:       *Talk will be given *live, in-person* at

                   TTIC, 6045 S. Kenwood Avenue

                   5th Floor, Room 530


*Virtually:*   *via panopto: **livestream*
<https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=99c36a24-7e58-430d-aeef-b242001316be>





*Who: *         Nikhil Bansal, University of Michigan



*Title:*          Quasi-Monte Carlo Integration and Discrepancy

*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).

*Host: **Avrim Blum* <avrim at ttic.edu>




Mary C. Marre
Faculty Administrative Support
*Toyota Technological Institute*
*6045 S. Kenwood Avenue, Rm 517*
*Chicago, IL  60637*
*773-834-1757*
*mmarre at ttic.edu <mmarre at ttic.edu>*
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