Friday, February 16, 2018

1:20 PM - 4:00 PM (ET)

Exley Science Center Tower ESC 618

Event Type

Seminar/Colloquium

Contact

Canalia, Caryn

2182

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=79061

Wai Kiu Chan, Wesleyan

*Warings problem for integral quadratic forms*

*Abstract*:
For every positive integer *n*, let *g*(*n*) be the smallest
integer such that if an integral quadratic form in *n* variables can be written as a sum of squares of integral linear forms,
then it can be written as a sum of *g*(*n*) squares of integral linear forms. As
a generalization of Lagranges Four-Square Theorem, Mordell (1930) showed that *g*(2) = 5 and later that year Ko (1930)
showed that *g*(*n*) = *n* + 3 when *n* ≤
5. More than sixty years later, M.-H. Kim and B.-K. Oh (1996) showed that *g*(6) = 10, and later (2005) they showed
that the growth of *g*(*n*) is at most an exponential of* n*. In this talk, I will discuss a recent
improvement of Kim and Oh's result showing that the growth of *g*(*n*)
is at most an exponential of $\sqrt{n}$.

. This is a joint work with Constantin Beli, Maria
Icaza, and Jingbo Liu.* *