16 citations · 30 across the 5 of their papers we have counts for
5 papers
Dirichlet eigenvalues of Schwarz triangle (3/2 3/2 3/2)
Jim Tao
In this paper we compute the first two Dirichlet eigenvalues and corresponding eigenfunctions of the equilateral Schwarz triangle (3/2 3/2 3/2) on the sphere.
A twisted local index formula for curved noncommutative two tori
Farzad Fathizadeh, Franz Luef, Jim Tao
We consider the Dirac operator of a general metric in the canonical conformal class on the noncommutative two torus, twisted by an idempotent (representing the -theory class of…
The Theory of Pseudo-differential Operators on the Noncommutative n-Torus
Jim Tao
The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential opera…
Spin Glass Models of Syntax and Language Evolution
Karthik Siva, Jim Tao, Matilde Marcolli
Using the SSWL database of syntactic parameters of world languages, and the MIT Media Lab data on language interactions, we construct a spin glass model of language evolution. We t…
Pattern occurrence statistics and applications to the Ramsey theory of unavoidable patterns
Jim Tao
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occ…