Mahler Lectures — Perth
Name: | Mahler Lectures — Perth |
Calendar: | 1-day meetings & lectures |
When: | Thu, August 11, 2011, 10:00 am - Sat, August 13, 2011, 10:00 am |
Description: |
Title: Randomness in number theory
Title: Thin integer matrix groups and the affine sieve Biography
Abstracts
By way of concrete examples we discuss the dichotomy that in number theory the basic phenomena are either very structured or if not then they are random. The models forrandomness for different problems can be quite unexpected and understanding, and establishing the randomness is often the key issue. Conversely the fact that certain number-theoretic quantities behave randomly is a powerful source for the construction of much sought-after pseudo-random objects.
Infinite index subgroups of integer matrix groups like \operatorname{SL}(n,Z) which are Zariski dense in \operatorname{SL}(n) arise in geometric diophantine problems (eg, Integral Apollonian Packings) as well as monodromy groups associated with families of varieties. One of the key features needed when applying such groups to number theoretic problems is that the congruence graphs associated with these groups are "expanders". We will introduce and explain these ideas and review some recent developments especially those connected with the affine sieve. Access GridIf you want to listen to the AGR lecture on August 12 in ELT1 from 1.30–2.30pm WST, please book an AGR room from 1–3pm WST or 3–5pm EST, and let Jason Tan (jason.tan@uwa.edu.au) and Jason Bell (jason.bell@arcs.org.au) know that you will be participating. Links |
Location: | University of Western Australia Map |
URL: | http://www.austms.org.au/tiki-read_article.php?articleId=129 |
Created: | 12 Jul 2011 11:52 pm UTC |
Modified: | 22 Jul 2011 06:54 pm UTC |
By: | rmoore |
Status: | Confirmed |