Continuing their study of cluster algebras associated with marked Riemann surfaces
with holes and punctures, Fomin and Thurston turn from the combinatorial construction of the cluster complex that their first paper emphasized, to geometry.
For her work in "the dynamics and geometry of Riemann surfaces
and their moduli spaces", Mirzakhani was awarded the Fields Medal, the most prestigious award in mathematics in 2014.
Buser, Geometry and spectra of compact Riemann surfaces
, Progress in Mathematics, 106, Birkhauser Boston, Inc., Boston, MA, 1992.
Tuite, "Free bosonic vertex operator algebras on genus two Riemann surfaces
I," Communications in Mathematical Physics, vol.
On a similar note, despite his different view of Riemann's conceptual approach, Weierstrass has offered an essential contribution to the representation of functions on Riemann surfaces
(3) (Weyl, 2010).
Recall that the Selberg zeta-function attached to compact Riemann surfaces
satisfies the functional equation M(s) = M(1 - s), where
A criterion for holomorphic families of Hideki MIYACHI Riemann surfaces
to be virtually isomorphic Communicated by Shigefumi MORI, M.J.A.
Despite the statistics I stated above, Mirzakhani won for her work in Geometry-specifically, for the dynamics of Riemann surfaces
She won for her work on "the dynamics and geometry of Riemann surfaces
and their moduli spaces."
In 1980s, based on Hirota bilinear forms, Nakamura proposed a comprehensive method to construct a kind of multiperiodic solutions of nonlinear equations in his papers [12, 13], such a method of solution does not need any Lax pairs and their induced Riemann surfaces
for the considered equations.