# Seminars & Colloquia Calendar

## Locality preserving hash functions, a partial order and tiles in binary space

#### Victor S. Miller -- IDA Center for Communications Research, Princeton

Location: ** zoom**

Date & time: Thursday, 29 April 2021 at 5:00PM - 6:00PM

*Abstract*: A "tile" in the space B^n of bit vectors of length n, is a subset S of B^n, such that there is another subset A of B^n so that every element of B^n can be written uniquely in the form a + s, where a in A and s in S. A particular class of tiles are the subsets of minimum weight elements in the cosets of a linear code over GF(2). In systematically investigating locality preserving hash functions, we generated the list of all possible tiles of cardinality <=64 satisfying a certain optimality condition. All but 6 of them turned out to be the sets of minimum weight elements described above. Attempts to prove the same for the remaining 6 remained elusive. Instead we found two computational criteria -- one using linear programming, and the other using combinatorial bin packing, which showed that the remaining 6 could not be tiles.

[Joint with Don Coppersmith, Dan Gordon and Peter Ostapenko]

password: 6564120420

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

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