Now showing items 21-30 of 43
Fundamental domains and generators for lattice Veech groups
(European Mathematical Society Publishing House, 2017)
The moduli space QMg of non-zero genus g quadratic differentials has a natural action of G=GL+2(R) / ⟨±(1001) ⟩. The Veech group PSL(X,q) is the stabilizer of (X,q)∈QMg in G. We describe a new algorithm for finding elements ...
Lecture notes in mathematics: rudiments of Riemann surfaces
(Rice University, 1971)
On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data
(American Mathematical Society, 2015)
We consider the KdV equation ∂tu+∂3xu+u∂xu=0 with quasi-periodic initial data whose Fourier coefficients decay exponentially and prove existence and uniqueness, in the class of functions which have an expansion with ...
Handle Addition for Doubly-Periodic Scherk Surfaces
(De Gruyter, 2012)
We prove the existence of a family of embedded doubly periodic minimal surfaces of (quotient) genus g with orthogonal ends that generalizes the classical doubly periodic surface of Scherk and the genus-one Scherk surface ...
Log minimal model program for the moduli space of stable curves: the first flip
(Department of Mathematics, Princeton University, 2013)
We give a geometric invariant theory (GIT) construction of the log canonical model M¯g(α) of the pairs (M¯g,αδ) for α∈(7/10–ϵ,7/10] for small ϵ∈Q+. We show that M¯g(7/10) is isomorphic to the GIT quotient of the Chow variety ...
A Birman exact sequence for Aut(Fn)
The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact sequence for the automorphism group of a free ...
The complex of partial bases for Fn and nite generation of the Torelli subgroup of Aut(Fn)
We study the complex of partial bases of a free group, which is an analogue for Aut(Fn) of the curve complex for the mapping class group. We prove that it is connected and simply connected, and we also prove that its ...
Hodge Theory and Lagrangian Planes on Generalized Kummer Fourfolds
(Independent University of Moscow, 2013)
Knot Concordance and Homology Cobordism
(American Mathematical Society, 2013-06)
We consider the question: “If the zero-framed surgeries on two oriented knots in S3 are Z-homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?” We show that this ...
Effective Computation of Picard Groups and Brauer-Manin Obstructions of Degree Two K3 Surfaces Over Number Fields
Using the Kuga-Satake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields.