[Colloquium] REMINDER: 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

Who:       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>*

On Tue, May 24, 2016 at 12:05 PM, Mary Marre <mmarre at ttic.edu> wrote:

> *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
>
> Who:       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 <%28773%29%20834-1757>*
> *f: (773) 357-6970 <%28773%29%20357-6970>*
> *mmarre at ttic.edu <mmarre at ttic.edu>*
>
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