Department of Mathematics and Computer Science
Number Theory and Combinatorics Seminar
Fall 2014
Talks are at noon on Monday in room B660 of University Hall
For more information, or to receive an email announcement of each week's seminar,
contact Nathan Ng < ng AT cs DOT uleth DOT ca > or Dave Morris <>.
                The next talk:

Oct 27
at noon
in UHall B660

Kevin Henriot
(University of British Columbia)
Linear equations in dense subsets of the squares
We discuss the solvability of certain linear equations in sparse subsets of the squares. Specifically, we investigate equations of the form $$\lambda_1 n_1^2 + \dotsb + \lambda_s n_s^2 = 0,$$ where \(s \geq 7\) and the coefficients \(\lambda_i\) sum to zero and satisfy certain sign conditions. We show that such equations admit non-trivial solutions in any subset of \([N]\) of density \((\log N)^{-c_s}\), improving upon the previous best of \((\log\log N)^{-c}\).

Talks in the series this semester:
(Click on any title for more info, including the abstract. Then click on it again to hide the info.)

Date Speaker Title

Sept 8 everyone Open problem session

Sept 15 Joy Morris Colour-permuting automorphisms of Cayley graphs

Sept 22 Farzad Aryan On Binary and Quadratic Divisor Problem

Sept 29 Adam Tyler Felix Common divisors of the index and order of \(a\) modulo \(p\)

Oct 6 Nathan Ng Inclusive Prime Number Races

Oct 20 Sean Fitzpatrick Characters of induced representations

Oct 27 Kevin Henriot Linear equations in dense subsets of the squares

Nov 3 Amir Akbary Title TBA

Nov 10 James Parks Title TBA

Nov 17 Manoj Kumar Title TBA

Nov 24 Soroosh Yazdani Title TBA

Dec 1 Speaker TBA Title TBA
Past semesters: Fall 2007 Fall 2008 Fall 2009 Fall 2010 Fall 2011 Fall 2012 Fall 2013
Spring 2008 Spring 2009 Spring 2010 Spring 2012 Spring 2013 Spring 2014