[photo of Ken]

Stanley Yao Xiao Postdoctoral Fellow

HU 1015 Department of Mathematics University of Toronto Toronto, Ontario M5S 2E4 CANADA Email: syxiao@math.toronto.edu

I am a Postdoctoral Fellow at the Department of Mathematics at the University of Toronto. My mentors are John Friedlander , Arul Shankar, and Jacob Tsimerman. Previously I was a NSERC Postdoctoral Fellow at the Mathematical Institute, University of Oxford.

My primary area of interest is Number Theory. Specific topics that I am interested in include arithmetic geometry, arithmetic statistics, analytic number theory, and algebraic geometry.

I obtained my Ph.D in pure mathematics from the University of Waterloo in 2016. My doctoral advisor was Professor Cameron L. Stewart.

My Erdős number is two, through Cameron L. Stewart.

Here is my CV.

Here is the long version of my research statement, and here is the short version.

Here is my entry at the Math Genealogy Project.

Current Classes

Previous Classes (at Toronto)


The number of quartic D4-fields with monogenic cubic resolvent ordered by conductor, joint work with Cindy Tsang, to appear in Transactions of the AMS. [Arxiv]

On prime values of binary quadratic forms with a thin variable, joint work with Peter Cho-Ho Lam and Damaris Schindler, to appear in Journal of the London Mathematical Society. [JLMS] [Arxiv]

Zeroes of polynomials with prime inputs and Schmidt's h-invariant, joint work with Shuntaro Yamagishi, Canadian Journal of Mathematics 72 (2020), 805-833. [CJM][Arxiv]

On binary cubic and quartic forms, Journal de Théorie des Nombres de Bordeaux, 31 (2019), 323-341 . [Arxiv][JNTB]

On the representation of integers by binary forms, joint work with Cameron Stewart, Mathematische Annalen 375 (2019), 133-163. [MA][Arxiv]

On the representation of k-free integers by binary forms, joint work with Cameron Stewart, to appear in Revista Matemática Iberoamericana. [Arxiv]

Density of power-free values of polynomials, joint work with Kostadinka Lapkova, Mathematika (4) 65 (2019), 1038-1050.[MAT] [Arxiv]

Binary quartic forms with bounded invariants and small Galois groups, joint work with Cindy Tsang, Pacific Journal of Mathematics 302 (2019), 249-291. [Arxiv][PJM]

Square-free values of decomposable forms, Canadian Journal of Mathematics 70 (2018), 1390-1415. [CJM][Arxiv]

Powerfree values of binary forms and the global determinant method, International Mathematics Research Notices Vol. 2017 (2017), 5078-5135. [IMRN][Arxiv]

Under Revision:

Binary quartic forms with vanishing J-invariant , under revision at IMRN. [Arxiv]

Submitted papers and preprints:

On monic abelian cubics, submitted. [Arxiv]

On the ζ3-Pell equation, joint work with Erick Knight, submitted. [Arxiv]

Density of power-free values of polynomials II, joint work with Kostadinka Lapkova, submitted. [Arxiv]
This page is currently under construction. Last update July 2020.