Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some connections between Falconer's distance set conjecture, and sets of
  Furstenburg type   In this paper we investigate three unsolved conjectures in geometric
combinatorics, namely Falconer's distance set conjecture, the dimension of
Furstenburg sets, and Erdos's ring conjecture. We formulate natural
$\delta$-discretized versions of these conjectures and show that in a certain
sense that these discretized versions are equivalent. In particular, it appears
that to progress on any of these problems one must prove a quantitative
statement about the existence of sub-rings of $R$ of dimension 1/2.

26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics