The DocCourse spans three months with two main Intensive Courses and several Thematic Seminars. During the period of the course, the participants will undertake a Research Project under the supervision of a local advisor.

Topics covered in the course include: structure of sets with small sumset, zero-sum problems, additive basis, arithmetic Ramsey theory and non-unique factorizations in Krull monoids.

One of the features of contemporary Additive Combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This diversity makes the subject particularly suited for training young researchers at both pre-doctoral and post-doctoral levels, introducing them in an area which is attracting a strong interest in the mathematical community for its many open problems and its wide range of applications.

http://www.crm.cat/AdditiveCombinatorics/

Surgical simulation of soft tissues is an increasingly viable tool for predicting surgical outcomes and in training medics and residents. Simulated procedures include laproscopic surgery, craniofacial reconstruction, z-plasty, breast reduction, gastrointestinal surgery and reconfiguration of musculoskeletal geometry. In these and many other scenarios, a subject specific simulation environment in which procedures can be practiced is of immeasurable value for training as well as for actual research and development of surgical techniques. Several technological and algorithmic problems currently limit the applicability of surgical simulation; the solutions to these problems require collaboration between mathematicians, computer scientists, engineers and clinicians. For example, until recently most simulation techniques for soft tissues were too computationally burdensome to be applicable in a real or interactive time environment. Offline computations have always been of use in helping to determine the results of a procedure, however many algorithms were developed that sacrificed accuracy for speed in an attempt to satisfy interactive frame rates. In the process, many of these algorithms were doomed to produce scientifically unreliable results making them of little use in accurately predicting surgical outcomes. As computer performance improves, computational power is less and less frequently precluding the use of more widely accepted scientific computing algorithms for soft tissues at interactive rates. Also, larger regions of the body can be simulated (e.g. in examining musculoskeletal procedures related to motion). In this short course, we will be investigating the most promising directions for algorithm design, use of architectures, surgical simulation interface design and procedures that lend themselves to simulation by encouraging interdisciplinary cooperation between medicine, engineering, applied math and computer science.

http://www.ipam.ucla.edu/programs/vs2008/

Searches for gravitational waves from coalescing compact binary systems rely on concrete knowledge of the resulting waveform to achieve maximum sensitivity to these sources. LIGO is already acquiring data at design sensitivity, enabling the detection of gravitational waves from binary black hole coalescence out to several hundred Mpc through optimally matched filtering searches. Direct observation of gravitational waves from these systems will have significant and far-reaching consequences for both gravitational physics and astronomy. To develop a complete picture of these systems will require complex numerical simulations, approximation techniques, and a strong interplay between theorists and observers. Advances in data analysis and in numerical simulation techniques offer the promise of cross-fertilization between workers in these complementary areas. This two-week workshop is intended to foster further and stronger collaborations between researchers in disciplines related to the search for gravitational waves.

http://www.kitp.ucsb.edu/activities/auto/?id=944

http://www.him.uni-bonn.de/semester-w-0708-workshops

http://www.math.ias.edu/selberg/

Environmental sensor networks have the capability of capturing local and broadly-dispersed information simultaneously; they also have the capacity to respond to sudden change in one l ocation by triggering observations selectively across the network while simultaneously updating the underlying complex system model and/or reconfiguring the network. Data gathered by wireless sensor networks, either fixed or mobile, pose unique challenges for environmental modeling: a complex system is being observed by a dynamical network. Technical challenges in statistics (sampling design to prediction and prediction uncertainty), in mathematics (computational geometry to data fusion to robotics), and in computers science (self-organizing networks to algorithm analysis) combine with the technical challenges of the models themselves and the sciences that underlie them.

This program will bring together an interdisciplinary group of ecologists, mathematicians, statisticians, and computer scientists with the objective of formulating and addressing optimization of data gathering, data analysis, data coverage, modeling and inference when the network itself is a dynamic system of self-organizing nodes. This collaborative effort will include both development of new mathematical, computational and statistical tools and also specific application to existing environmental networks designed to study biosphere-atmospheric interactions.

http://www.samsi.info/programs/2007sensornetprogram.shtml

This workshop, sponsored by AIM and the NSF, will be devoted to arithmetic properties of preperiodic points for morphisms on projective space. It is known that such morphisms have only finitely many preperiodic points defined over any given number field. A fundamental conjecture in arithmetic dynamics asserts that there is a uniform bound for the number of such points that depends only on the degree of the field, the degree of the map, and the dimension of the space. This is a dynamical analog of the conjecture that torsion on abelian varieties is uniformly bounded by the degree of the field and the dimension of the variety.

A primary goal of the workshop is to develop tools and a strategy for proving the first (highly) nontrivial case of the uniform boundedness conjecture in dynamics, namely for quadratic polynomials in one variable over Q. This special case represents a dynamical analog of Mazur's theorem that elliptic curves over Q have bounded torsion.

http://www.aimath.org/ARCC/workshops/arithdynamics.html

http://www.him.uni-bonn.de/semester-w-0708-workshops

The primary aim of the Conference is the presentation of important recent advances and future trends by leading researchers in the fields of representation theory of finite and infinite dimensional Lie and super Lie groups, and its application to geometry, physics, and differential equations.

http://www.math.ucla.edu/symmetry/

Understanding the hierarchical organization of molecules, multi-protein assemblies, organelles and networks within the interior of a eukaryotic cell is a challenge of fundamental interest in cell biology. A wide variety of microscopic and spectroscopic methods already exist for imaging intact cells and their components: modern fluorescence microscopic methods provide powerful tools for imaging at spatial resolutions in the micron range, while emerging methods in electron microscopy can be used to image the arrangement of protein assemblies at resolutions of 1 nm or better. To take advantage of these rapid advances in imaging technology, it is critical to develop and apply advanced computational strategies for image processing that can cope both with the volume and complexity of the data. This conference seeks to bring together leaders at this interdisciplinary interface of image processing and stimulate new partnerships to address computational problems at this exciting frontier of cell biology. The one-week meeting will bring together biologists, physicists, mathematicians and specialists in microscopy and image analysis.

http://www.ipam.ucla.edu/programs/imm2008/