In a recent work of Duke, Imamoḡlu, and Tóth, the linking number of certain links on the
space SL (2, Z)\SL (2, R) is investigated. This linking number has an alternative …

We give a new proof of Faberʼs intersection number conjecture concerning the top
intersections in the tautological ring of the moduli space of curves Mg. The proof is based on …

We present certain new properties about the intersection numbers on moduli spaces of
curves $\bar {\sM} _ {g, n} $, including a simple explicit formula of $ n $-point functions and …

We study the intersection ring of the space $\mathcal {M}(\alpha _1,\ldots,\alpha _m) $ of
polygons in $\mathbb {R}^ 3$. We find homology cycles dual to generators of this ring and …

The first purpose of this note is to explain how to compute intersection numbers of divisors
on the moduli spaces M,, n of stable pointed curves. The Witten conjecture, proved by …

A PROOF OF THE FABER INTERSECTION NUMBER CONJECTURE Kefeng Liu & Hao Xu
Abstract 1. Introduction Starting from the work of M Page 1 j. differential geometry 83 (2009) …

Let G be a discrete subgroup of PSL (2, R), and consider closed geodesics on the quotient
of the upper half plane by G. In this thesis, we study how these geodesics intersect when G …

The existence of the limiting pair correlation for angles between reciprocal geodesics on the
modular surface is established. An explicit formula is provided, which captures geometric …

arXiv:0808.1974v2 [math.AG] 3 Mar 2010 Page 1 arXiv:0808.1974v2 [math.AG] 3 Mar 2010
CALCULATING INTERSECTION NUMBERS ON MODULI SPACES OF CURVES STEPHANIE …

The arithmetic, p-arithmetic, and incoherent intersections between pairs of closed geodesics
on a modular or Shimura curve are defined, and some of their expected algebraicity and …