Tata Institute of Fundamental Research
Progression-Free Sets in $Z_p^n$, and Applications
STCS Student Seminar
Speaker:
Aditya Potukuchi (Rutgers University
Department of Computer Science
United States of America)
Organiser:
Tulasi mohan Molli
Date:
Friday, 22 Jul 2016, 16:00 to 17:30
Venue:
A-201 (STCS Seminar Room)
(Scan to add to calendar)
Abstract:
In this talk, I would like to attempt to give a brief glimpse at and around the recent developments related to the Cap Sets problem:
Recently, there has been a string of breakthrough results which started with a paper of Croot-Lev-Pach, related to bounds on progression free sets in $Z_4^n$. This was followed up by a great improvement to a longstanding problem on the bound on Cap Sets (progression free sets in $Z_3^n$) by Ellenberg-Gijswijt. The proof is surprisingly simple, and has found several applications, most notably in proving the Erdos-Szemeredi Sunflower conjecture, improvements in bounds on tri-coloured sum free sets, great improvements in removal lemmas in $Z_2^n$ etc..
| Speaker: | Aditya Potukuchi (Rutgers University Department of Computer Science United States of America) |
| Organiser: | Tulasi mohan Molli |
| Date: | Friday, 22 Jul 2016, 16:00 to 17:30 |
| Venue: | A-201 (STCS Seminar Room) |
(Scan to add to calendar)
Abstract:
In this talk, I would like to attempt to give a brief glimpse at and around the recent developments related to the Cap Sets problem:
Recently, there has been a string of breakthrough results which started with a paper of Croot-Lev-Pach, related to bounds on progression free sets in $Z_4^n$. This was followed up by a great improvement to a longstanding problem on the bound on Cap Sets (progression free sets in $Z_3^n$) by Ellenberg-Gijswijt. The proof is surprisingly simple, and has found several applications, most notably in proving the Erdos-Szemeredi Sunflower conjecture, improvements in bounds on tri-coloured sum free sets, great improvements in removal lemmas in $Z_2^n$ etc..
Recently, there has been a string of breakthrough results which started with a paper of Croot-Lev-Pach, related to bounds on progression free sets in $Z_4^n$. This was followed up by a great improvement to a longstanding problem on the bound on Cap Sets (progression free sets in $Z_3^n$) by Ellenberg-Gijswijt. The proof is surprisingly simple, and has found several applications, most notably in proving the Erdos-Szemeredi Sunflower conjecture, improvements in bounds on tri-coloured sum free sets, great improvements in removal lemmas in $Z_2^n$ etc..