University COVID-19 update

The University of Waterloo is constantly updating our most Frequently Asked Questions.

Questions about buildings and services? Visit the list of Modified Services.

Please note: The University of Waterloo is closed for all events until further notice.

USRA seminarExport this event to calendar

Wednesday, April 24, 2013 — 1:00 PM EDT

Jamie Murdoch, Pure Mathematics, University of Waterloo

"Almost every set of the correct density is Λ(p)"

I give an overview of Bourgain’s argument in his 1989 paper, Bounded orthogonal systems and the Λ(p)-set problem. Through a rather complex argument, Bourgain was able to show, using elementary probabilistic methods, that for any 2 < p < ∞, almost every random set is Λ(p), where the mean density of the random sets is 2/p. Prior attempts at this problem
by Rudin in 1960 and Hajela in 1986 had focused on the case where p is an even integer, in which case the p-norm can be expanded explicitly using a multinomial expansion, and sets can be constructed by number-theoretic and combinatorial arguments. Bourgain’s result is remarkable because it estimates the p-norm directly for arbitrary p. I aim to give an overview of his highly technical argument, focusing on the key steps where the mean density is used.

Location 
MC - Mathematics & Computer Building
5045
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

S M T W T F S
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
2
3
4
5
6
  1. 2020 (70)
    1. July (2)
    2. June (1)
    3. May (3)
    4. March (16)
    5. February (26)
    6. January (22)
  2. 2019 (199)
    1. December (7)
    2. November (26)
    3. October (19)
    4. September (13)
    5. August (7)
    6. July (12)
    7. June (18)
    8. May (22)
    9. April (11)
    10. March (25)
    11. February (17)
    12. January (22)
  3. 2018 (219)
  4. 2017 (281)
  5. 2016 (335)
  6. 2015 (211)
  7. 2014 (235)
  8. 2013 (251)
  9. 2012 (135)