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Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota)

February 25 @ 12:15 pm - 1:10 pm

The talk will concentrate on open questions related to the optimal bounds for the discrepancy of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of points in axis-parallel rectangles, and thus measures the equidistribution of the set. This notion has been explored by H. Weyl, K. Roth, and many others, however many questions still remain open, especially in higher dimensions.  We shall discuss the two main conjectures on the order of star-discrepancy and present evidence in support of each one, as well as their connections to various areas of mathematics. In addition, we shall talk about discrepancy in other geometrical settings (rotated rectangles, balls, points on the sphere etc).

Details

Date:
February 25
Time:
12:15 pm - 1:10 pm
Event Category:

Other

Speaker Name
Dmitriy Bilyk (University of Minnesota)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map

Details

Date:
February 25
Time:
12:15 pm - 1:10 pm
Event Category:

Other

Speaker Name
Dmitriy Bilyk (University of Minnesota)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map