On surfaces of general type with pg=q=1,K2=3p_g=q=1, K^2=3

The moduli space $\mathscr{M}$ of surfaces of general type with $p_g=q=1, K^2=g=3$ (where $g$ is the genus of the Albanese fibration) was constructed by Catanese and Ciliberto in \cite{CaCi93}. In this paper we characterize the subvariety $\mathscr{M}_2 \subset \mathscr{M}$ corresponding to surfaces containing a genus 2 pencil, and moreover we show that there exists a non-empty, dense subset $\mathscr{M}^0 \subset \mathscr{M}$ which parametrizes isomorphism classes of surfaces with birational bicanonical map.Comment: 35 pages. To appear in Collectanea Mathematic

Surfaces of general type with pg=q=1,K2=8p_g=q=1, K^2=8 and bicanonical map of degree 2

We classify the minimal algebraic surfaces of general type with $p_g=q=1, K^2=8$ and bicanonical map of degree 2. It will turn out that they are isogenous to a product of curves, so that if $S$ is such a surface then there exist two smooth curves $C, F$ and a finite group $G$ acting freely on $C \times F$ such that $S = (C \times F)/G$. We describe the $C, F$ and $G$ that occur. In particular the curve $C$ is a hyperelliptic-bielliptic curve of genus 3, and the bicanonical map $\phi$ of $S$ is composed with the involution $\sigma$ induced on $S$ by $\tau \times id: C \times F \longrightarrow C \times F$, where $\tau$ is the hyperelliptic involution of $C$. In this way we obtain three families of surfaces with $p_g=q=1, K^2=8$ which yield the first known examples of surfaces with these invariants. We compute their dimension, and we show that they are three smooth and irreducible components of the moduli space $\mathcal{M}$ of surfaces with $p_g=q=1, K^2=8$. For each of these families, an alternative description as a double cover of the plane is also given, and the index of the paracanonical system is computed.Comment: 36 pages. To appear in Transactions of the American Mathematical Societ

Representations of braid groups and construction of projective surfaces

Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will focus on their algebraic-geometric aspects, explaining how the representation theory of higher genus braid groups can be used to produce interesting examples of projective surfaces defined over the field of complex numbers.Comment: Note written for the Proceedings of the Conference "Group 32 - The 32nd International Colloquium on Group Theoretical Methods in Physics", held on Czech Technical University (Prague) on July 9-13, 201

Tuning gain and bandwidth of traveling wave tubes using metamaterial beam-wave interaction structures

We employ metamaterial beam-wave interaction structures for tuning the gain and bandwidth of short traveling wave tubes. The interaction structures are made from metal rings of uniform cross section, which are periodically deployed along the length of the traveling wave tube. The aspect ratio of the ring cross sections are adjusted to control both gain and bandwidth. The frequency of operation is controlled by the filling fraction of the ring cross section with respect to the period

Spectral-based Propagation Schemes for Time-Dependent Quantum Systems with Application to Carbon Nanotubes

Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices. While time-dependent Hamiltonian problems can be formally solved by propagating the solutions along tiny simulation time steps, a direct numerical treatment is often considered too computationally demanding. In this paper, however, we propose to go beyond these limitations by introducing high-performance numerical propagation schemes to compute the solution of the time-ordered evolution operator. In addition to the direct Hamiltonian diagonalizations that can be efficiently performed using the new eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a basis transformed propagation scheme (BTPS) which allow to reduce considerably the simulation times needed by time intervals. It is outlined that BTPS offers the best computational efficiency allowing new perspectives in time-dependent simulations. Finally, these numerical schemes are applied to study the AC response of a (5,5) carbon nanotube within a 3D real-space mesh framework

On surfaces with p_g=q=2, K^2=5 and Albanese map of degree 3

We construct a connected, irreducible component of the moduli space of minimal surfaces of general type with $p_g=q=2$ and $K^2=5$, which contains both examples given by Chen-Hacon and the first author. This component is generically smooth of dimension 4, and all its points parametrize surfaces whose Albanese map is a generically finite triple cover.Comment: 35 pages, 2 figures. Final version, to appear in the Osaka Journal of Mathematic