[Colloquium] 5/25 TTIC Colloquium: Nati Linial: Hebrew University

[Mary Marre]

*Please Note: Unusual Day and Time!*


When:     Wednesday, May 25th at 11:00 a.m.

Where:    TTIC, 6045 S. Kenwood Avenue, 5th Floor, Room 526

Speaker:  Nati Linial: Hebrew University


Title:          High-dimensional Permutations and Discrepancy

Abstract: This is part of our ongoing effort to develop what we call
"High-dimensional combinatorics". In joint work with my (then) PhD student
Zur Luria several years ago, we introduced the notion of a high-dimensional
permutation. Briefly, we equate a permutation with a permutation matrix,
namely an nxn array of 0/1 in which every line (row or column) has exactly
one 1. A 2-dimensional permutation is defined as an nxnxn array of 0/1 in
which every line (row, column or shaft) has exactly one 1. It is not hard
to see that 2D permutation is synonymous with a Latin square, and the
notion of a d-dimensional permutation suggests itself very naturally. By
now we have resolved quite a few basic problems concerning high-dimensional
permutations, and in this lecture I will emphasize the emerging questions
concerning low-discrepancy high-dimensional permutation. Without going into
technical details, we wish the 1's in the array to be as "uniformly spread
out" as possible. This raises many fascinating challenges as I will try to
explain. For example, we still do not know how to randomly generate
high-dimensional permutations and what their typical properties are. It is
conceivable that random high-dimensional permutations minimize discrepancy,
but we are still far from resolving this.


Host: Julia Chuzhoy, cjulia at ttic.edu



For more information on the colloquium series or to subscribe to the
mailing list, please see http://www.ttic.edu/colloquium.php



Mary C. Marre
Administrative Assistant
*Toyota Technological Institute*
*6045 S. Kenwood Avenue*
*Room 504*
*Chicago, IL  60637*
*p:(773) 834-1757*
*f: (773) 357-6970*
*mmarre at ttic.edu <mmarre at ttic.edu>*
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