[Theory] TODAY: 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).

*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.

*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>*


On Sun, Dec 15, 2024 at 3:11 PM Mary Marre <mmarre at ttic.edu> wrote:

> *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>*
>
>
> On Mon, Dec 9, 2024 at 7:23 PM Mary Marre <mmarre at ttic.edu> wrote:
>
>> *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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