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February 2020
Nano Knot theory, methods to study tiny knot in nature
Knotting in living organisms is a feature that is visible to the careful observer of biological life. Since the 1970’s, with the increasing power of electron microscopes, scientists have been able to capture images of such structures in living organisms at near atomic levels. We will explore the mathematics of knotting that has provided tools study these phenomena and, time permitting, describe new methods being developed to analyze these spatial structure.
Find out more »Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota)
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…
Find out more »Dmitriy Bilyk: Energy optimization on the sphere
Many problems, arising in discrete and metric geometry, signal processing, physics, etc, can be reformulated as questions of optimizing discrete or continuous measures. We shall review some of such conjectures, as well as approaches to determining optimal (or at least good) point distributions and measures, and connections to other problems, such as discrepancy, sphere packings etc. We shall also discuss several manifestations of the phenomenon of clustering of minimizing measures, which is often observed theoretically, numerically, or experimentally: in many…
Find out more »March 2020
GEMS Workshop: The Mathematics of Reapportionment and Census Data with Professor Adolfo Rumbos of Pomona College
TOPIC: The Mathematics of Reapportionment and Census Data Every ten years, the United States Census Bureau conducts a count of all persons living in the United States; one of those population counts will be carried out this year (2020). This Census is mandated by the US Constitution; it counts all people residing in the United States, regardless of citizenship or immigration status. The data collected from the Census are used to make sure that everyone is equally represented in our…
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