## Jiuya Wang

#### Foerster-Bernstein Postdoctoral Fellow

Email: wangjiuy "at" math.duke.edu
Office: Physics Building 214

I am a first year postdoc in the math department of Duke University. Previously I am a graduate student from the math department of University of Wisconsin, Madison

My research interest is in number theory on both the algebraic side and the analytic side. I am currently mostly working on arithmetic statistics. I am also interested in other algebraic topics.

My advisor is Melanie Matchett Wood.
This is my CV.

### Research

• Malle's conjecture for $$S_n\times A$$ for $$n = 3,4,5$$, submitted for publication, [ arxiv ] [pdf].

• We propose a framework to prove Malle's conjecture for the compositum of two number fields based on proven results of Malle's conjecture and good uniformity estimates. Using this method we can prove Malle's conjecture for $$S_n\times A$$ over any number field $$k$$ for $$n=3$$ with $$A$$ an abelian group of order relatively prime to 2, for $$n= 4$$ with $$A$$ an abelian group of order relatively prime to 6 and for $$n= 5$$ with $$A$$ an abelian group of order relatively prime to 30. As a consequence, we prove that Malle's conjecture is true for $$C_3\wr C_2$$ in its $$S_9$$ representation, whereas its $$S_6$$ representation is the first counter example of Malle's conjecture given by Klueners.

• Secondary Term of Asymptotic Distribution of $$S_3\times A$$ Extensions over $$\mathbb{Q}$$ , submitted for publication, [ arxiv ] [pdf].

• We combine a sieve method together with good uniformity estimates to prove a secondary term for the asymptotic estimate of $$S_3\times A$$ extensions over $$\mathbb{Q}$$ when $$A$$ is an odd abelian group with minimal prime divisor greater than 5. At the same time, we prove the existence of a power saving error when $$A$$ is any odd abelian group.

• The 2-Class Tower of $$\mathbb{Q}(\sqrt{-5460})$$ , with Nigel Boston, submitted for publication, [ arxiv ] [pdf].

• The seminal papers in the field of root-discriminant bounds are those of Odlyzko and Martinet. Both papers include the question of whether the field $$\mathbb{Q}(\sqrt{-5460})$$ has finite or infinite 2-class tower. This is a critical case that will either substantially lower the best known upper bound for lim inf of root-discriminants (if infinite) or else give a counterexample to what is often termed Martinet's conjecture or question (if finite). Using extensive computation and introducing some new techniques, we give strong evidence that the tower is in fact finite, establishing other properties of its Galois group en route.