Paul Aspinwall : String Theory and Derived Categories
- Other Meetings and Events ( 41 Views )Abstract: The derived category of coherent sheaves almost certainly plays a role of fundamental importance in string theory on an algebraic variety. We review the various ideas that have led to this belief and outline the resulting consequences for geometry and physics.
Allan Seheult : Bayesian Forecasting and Calibration for Complex Phenomena Using Multi-level Computer Codes
- Other Meetings and Events ( 40 Views )We describe a general Bayesian approach for using computer codes for a complex physical system to assist in forecasting actual system outcomes. Our approach is based on expert judgements and experiments on fast versions of the computer code. These are combined to construct models for the relationships between the code's inputs and outputs, respecting the natural space/time features of the physical system. The resulting beliefs are systematically updated as we make evaluations of the code for varying input sets and calibrate the input space against past data on the system. The updated beliefs are then used to construct forecasts for future system outcomes. While the approach is quite general, it has been developed particularly to handle problems with high-dimensional input and output spaces, for which each run of the computer code is expensive. The methodology will be applied to problems in uncertainty analysis for hydrocarbon reservoirs.
Richard Kenyon : Random maps from Z^{2} to Z
- Other Meetings and Events ( 40 Views )One of the most basic objects in probability theory is the simple random walk, which one can think of as a random map from Z to Z mapping adjacent points to adjacent points. A similar theory for random maps from Z^{2} to Z had until recently remained elusive to mathematicians, despite being known (non-rigorously) to physicists. In this talk we discuss some natural families of random maps from Z^{2} to Z. We can explicitly compute both the local and the large-scale behavior of these maps. In particular we construct a "scaling limit" for these maps, in a similar sense in which Brownian motion is a scaling limit for the simple random walk. The results are in accord with physics.
Michael Thaddeus : Mirror Symmetry and Langlands Duality
- Other Meetings and Events ( 33 Views )Strominger, Yau and Zaslow have proposed that Calabi-Yau mirror partners should be families of special Lagrangian tori over the same base which are dual to each other. I will exhibit some striking evidence for this proposal: pairs of Calabi-Yau orbifolds satisfying the requirements of SYZ for which the expected equality of stringy Hodge numbers can be completely verified. This is in a sense the first enumerative evidence supporting SYZ. The construction I will present is the first of several suggesting a general principle: for any construction using a compact Lie group to construct a Calabi-Yau, mirror partners arise from applying the construction to Langlands dual groups.