Programme

10:00-10:10 Welcome by Helge Holden, chair of the Abel Committee, moderator
10:10-11:10 Karen Uhlenbeck, University of Texas at Austin, IAS, Abel Prize laureate 2019
11:10-11:45 break
11:45-12:45 Daniel Spielman, Yale University: "Discrepancy Theory is Mathematics, Computer Science, and Statistics"
12:50-14:00 Lunch
14:00-15:00 Hong Wang, IHES and NYU
15:00-15:30 Tea
15:30-16:30 Curtis McMullen, Harvard University: “Quintics, braids and billiards, after Abel”
16:30 Conclusion of symposium

The Abel Prize Committee will also be present:
• Helge Holden, NTNU (Chair)
• Hee Oh, Yale University
• Jonathan Pila, Oxford University
• Yoshiko Ogata, Kyoto University
• Benny Sudakov, ETH, Zürich

Abstracts

Daniel Spielman, Yale University:
"Discrepancy Theory is Mathematics, Computer Science, and Statistics"

Theorems in Discrepancy Theory tell us that it is possible to divide a set of vectors into two sets that look surprisingly similar to each other. In particular, these sets can be much more similar to each other than those produced by a random division.  The development of discrepancy theory has been motivated by applications in fields including combinatorics, geometry, optimization, and functional analysis.

Until a breakthrough of Bansal in 2010, the major algorithmic problems of discrepancy theory were thought to be computationally intractable. We now know efficient algorithms that solve many discrepancy problems, and the development of these algorithms has led to new proof techniques and new theorems.

We expect the greatest impact of discrepancy theory will be to the design of randomized controlled trials (RCTs), where it can be used to ensure similarity of test and control groups.

This talk will survey major mathematical and algorithmic results of discrepancy theory, along with recent advances, open problems, and applications.