The model of Lorentzian three-dimensional dynamical triangulations provides a non-perturbative definition of three-dimensional quantum gravity. The theory has two phases: a weak-coupling phase with quantum fluctuations around a " semiclassical " background geometry which is generated dynamically despite the fact that the formulation is explicitly background-independent, and a strong-coupling ph...

My research is in differential geometry. Generally speaking, I am interested in symplectic geometry, Lie groups and gauge theories, and geometric invariants relating to index theory. Specifically, I have researched the moduli space MG(M) of flat G-connections over a manifold M of dimension greater than two. These spaces, formally introduced in Section 2.1, arise naturally in physics as the spac...

The twistor space of representations on an open variety maps to a weight two space of local monodromy transformations around a divisor component at infinty. The space of σ-invariant sections of this slope-two bundle over the twistor line is a real 3 dimensional space whose parameters correspond to the complex residue of the Higgs field, and the real parabolic weight of a harmonic bundle.

The twistor space of representations on an open variety maps to a weight two space of local monodromy transformations around a divisor component at infinty. The space of σ-invariant sections of this slope-two bundle over the twistor line is a real 3 dimensional space whose parameters correspond to the complex residue of the Higgs field, and the real parabolic weight of a harmonic bundle.

The change of land use/land cover has been known as an imperative force in environmental alteration, especially in arid and semi-arid areas. This research was mainly aimed to assess the validity of two major types of land change modeling techniques via a three dimensional approach in Birjand urban watershed located in an arid climatic region of Iran. Thus, a Markovian approach based on two suit...

Following the “spatial turn” of the last 3 decades in humanities and social sciences and the structure of semiotic object, this research studies space as the main semiotic object of Calvino’s (1972) Invisible Cities. Significance of this application resides in examining the possibility of providing a more concrete methodology based on the integration of Zoran’s (1984) 3 vertical levels of const...

Constructing houses in the form of garden-house became popular among Statesmen and the privileged class in Naseri period. Iranian traditional houses which used to be formed around a central courtyard, now were organized around a garden. So the transition from houses with courtyard to garden-houses created a new order of relationships between spaces, resulted in redefining spaces and their forms...

On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional uniication, a geometric model is presented that associates with each quantum phase an element of a transformation group.

The ever-increasing size and complexity of aerospace systems often drive developers to validate using modeling and Monte Carlo simulations confined around expected points of operation in a hyper-dimensional parameter space. This paper describes an alternative that explores large regions of the parameter space with explicit coverage guarantees, searching for n parameter relations that characteri...