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Lattice reduction algorithms have been proved to be one of the most powerful and versatile tools in public key cryptanalysis. In this talk, we primarily concentrate on lattice attacks against (EC)DSA ...
Dyck paths are classical Catalan objects. The peak distribution of Dyck paths is an important topic of combinatorics, and further the representation of symmetric groups.
Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many...
The full Kostant-Toda lattice defined on simple Lie algebras can be viewed as finite version of KP type hierarchies. In this talk I will show you how to explicitly construct (all) rational solutions o...
The theory of tetragonal curves is established and first applied to the study of algebro-geometric quasi-periodic solutions of discrete soliton equations. Using the zero-curvature equation and the dis...
We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological ...
The main model studied in this paper is a lattice of pendula with a nearestneighbor coupling. If the coupling isweak, then the system is near-integrable and KAM tori fill most of the phase space. For ...
In rotor-router aggregation on the square lattice Z2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the clus...
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-...
Many 2D integrable lattice spin models known: Ising, XXZ, RSOS, etc.Systematic construction of solutions of Y-B equations: quantum groups.Not many integrable 3D models: almost all generalizations of Z...
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
This study examines finite deformation patterns of zircon grains from high-temperature natural shear zones. Various zircon-bearing rocks were collected in the Western Tauern Window, eastern Alps, wher...
I discuss the progress in the use of analytic techniques for low energy QCD, in particular as applied to kaon physics. These methods are becoming increasingly powerful and we have gained a good deal o...
We study (by an exact numerical scheme) the single-particle density matrix of ~103 ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to th...
Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable superfluid and insulating ground states with rich and nontrivial phase diagram. The structure of the grou...

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