The 2007-2008 MBI Year in Mathematical Bioengineering will focus around six workshops on Metabolic Engineering, Cell and Tissue Engineering, Neuroengineering, Brain Imaging, and Neuromechanics, the latter being covered in two linked workshops. Tutorials will be offered to prepare participants, especially students and postdoctoral fellows interested in entering the field. While omitting large areas...

During the 2007-08 academic year, Roman Bezrukavnikov of MIT will lead a special program on algebraic geometry and physics in representation theory.
The focus of the year will be on related recent developments in representation theory, algebraic geometry and physics.

The first conference, "Gauge Theory and Representation Theory", will be held during the week of November 26-30, 2007.

The sec...

Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology promise significant scientific breakthroughs in the near future. Mathematics (broadly defined) is positioned to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists. The critical need, which h...

This full-year SAMSI program will address fundamental issues in risk analysis, as well as associated problems associated with extreme events and decision theory. The program will engage researchers from the statistical sciences, applied mathematical sciences and decision sciences, including operations research. The goals is produce genuine impact on the practice of risk analysis and assessment, as...

The field of random media is a classical one which is presently receiving widespread attention as new theory, approximation techniques, and computational capabilities are applied to emerging applications. Due to the breadth of the field, the inherent deterministic, stochastic and applied components have typically been investigated in isolation. However, it is increasingly recognized that these com...

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 ...

In representation theory, abstract algebraic structures are represented using matrices or geometry. These representations provide a bridge between the abstract symbolic mathematics and its explicit applications in nearly every branch of mathematics as well as in related fields such as physics, chemistry, engineering, and statistics.
In Combinatorial Representation Theory, combinatorial objects ar...

Founded by Frobenius and Schur more than a century ago, the representation theory of finite groups is today a thriving field with many recent successes. Current research centers on the many open questions, particularly regarding representations over the integers or rings of positive characteristic. Brauer developed block theory to understand better such representations, and it proved important ...

The general problem of irrigation and transportation in physics and biology is to transport in the most economical way a source mass distribution onto a fixed well distribution. Both source and wells distributions are usually modeled as positive measures in a Cartesian space or in a metric space. This problem can be looked at as a generalization of the optimal assignment or the optimal flow proble...

With the completion of numerous genome projects for bacteria, yeast, and humans, there is an increasing interest in understanding how molecules encoded within the genomes interact to define various functional networks of the cell. These intra-cellular networks may be classified as gene regulatory networks, protein interaction networks, or metabolic networks. Such networks of integrated molecular r...

This workshop will be devoted
to the modeling, simulation and analysis of the ferroelectric phenomena
in soft matter systems such as liquid crystals, elastomers and gels.
The ferroelectric phenomena of these materials, such as its interaction
with electric fields in switching processes, introduce new challenging
problems that can only be properly addressed with a combined effort of
theoret...

The themes of the workshop will include: spike sorting and tracking; cortical decoding of command signals for control of assistive devices; deep brain stimulation; and epilepsy detection and intervention.

This program comprises two weeks of research, mixing tutorials, research presentations and working group activities on the subject. The goal of this program is three-fold: 1) to bring the area to the attention of statistical researchers, whose expertise is critical to substantiate and clarify the necessary statistical theory and methodology; 2) to nurture the necessary interdisciplinary collaborat...

The workshop will bring together a diverse group of researchers from the medical imaging community with various backgrounds including radiology, psychiatry, signal and image processing, surgery, physics, mathematics, and neurophysiology.

The workshop will focus on the following topics:

(a) Medical Imaging Modalities for Brain Imagery: MRI, fMRI, DTI, PET, SPECT, CT:

(b) Medical Imaging Pr...

Neuroscience is becoming increasingly quantitative and the need for theoreticians interested in collaborating with experimental neuroscientists will only increase in the coming years. In addition to a need for modeling, the kinds of problems which arise in neuroscience applications are mathematically interesting in their own right. For example, much of the theory behind Evans functions was develop...

The goal of this workshop is to facilitate the development of an integrated “systems biology” of decision-making processes that spans multiple spatio-temporal scales and levels of biological organization, and accounts for the perspectives of biologists, psychologists, economists, mathematicians, and engineers.

The RIPS Program provides an opportunity for high-achieving undergraduate students to work in teams on a real-world research project proposed by a sponsor from industry or a national lab. Projects are selected to have a major mathematical component and to be something that will pose an interesting challenge to talented undergraduates. Applications are due Feb. 15, 2008.

This program consists of two parts: (a) two weeks of introductory lectures plus short projects and a computer lab, and (b) a summer long research experience (6 weeks to be followed immediately after the 2 weeks) devoted to projects in the interface of mathematics, statistics, and biological sciences.

From Monday, June 30 through Friday, July 25, 2008, Iowa State University will be the host of the Institute for Mathematics and its Applications (IMA) Summer Graduate Program in Mathematics. The course will concentrate on Linear Algebra and Applications.

Linear algebra is a subject of central importance in both mathematics and a variety of other disciplines. Research in linear algebra is very a...

Each summer the MBI hosts a 3-week education program. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following 2 weeks are spent working on guided team projects and participating in a miniconference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergr...

The interplay between geometry and physics in the material world is a rich source of questions close to experience, amenable to experiments and open to a range of theoretical approaches, from scaling and asymptotics to computation and geometric/topological methods. The breakup of a drop or the coalescence of two, the collapse of a bubble or the birth of one, the crumpling and wrinkling of a sheet ...

This two-week intensive workshop will focus on mathematical techniques applied to brain images to measure, map and model brain structure and function. Topics will range from modeling anatomical structures in MRI scans, and mapping connectivity in diffusion tensor images, to statistical analysis of functional brain images from fMRI, EEG, and MEG.

This workshop will be devoted to
translating questions from quantum computing, complexity theory,
statistical learning theory, signal processing, and data analysis
to problems in geometry and representation theory. In all these areas
varieties in spaces of tensors invariant under linear changes
of coordinates appear as central objects of study. Despite their
different origins, there are str...

This workshop concerns extensions
and applications of the method of theta correspondence, including a
discussion of outstanding problems and future directions.

Growth, movement and differentiation of cells are three key processes involved in pattern formation and morphogenesis in developing systems. Pattern formation involves the expression of genes at the correct point in space at the correct time, and this in turn typically involves spatially- and temporally-varying signals, and mechanisms for signal transduction and activation or repression of gene ex...

This workshop will bring together
experimental and mathematical researchers in neuroendocrinology to
study and develop mathematical models for rhythmogenic mechanisms in
the hypothalamus and pituitary.

The IMA is holding a 10-day workshop on Mathematical Modeling in Industry. The workshop is designed to provide graduate students and qualified advanced undergraduates with first hand experience in industrial research.

This workshop will introduce
undergraduate faculty to current research opportunities
in linear algebra and number theory that will equip them with the
necessary tools to mentor students in undergraduate research in
mathematics.

This workshop will be devoted to
frame theory in finite dimensions with an emphasis on compressive
sensing and quantization theory for frames.

A central problem in modern mathematics is that of extending analytic constructions which are well understood in the setting of smooth compact manifolds to a broader class of spaces which are allowed to be singular. Such objects arise naturally in many geometric contexts: Singular varieties in algebraic geometry not only occur naturally as fundamental objects themselves, but even the moduli space...

Much recent work in ergodic theory has been motivated by interactions with combinatorics and with number theory. A particular is example is Szemer'edi's Theorem, which states that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. The original argument was an intricate use of combinatorics; another proof was given using ergodic theory and more recen...

Geometric Partial Differential Equations2008-2009Organizer: Alice Chang (Princeton University)The special program for the academic year 2008-09 will be on geometric PDE.The emphasis will be on non-linear partial differential equations withapplications to problems in differential, conformal and convex geometry.Topics that will be covered include Yamabe type equations, Q-curvatureequations, fully n...

Computational chemistry has reached a stage of development where many chemical properties of both simple and complex systems may now be computed more accurately, more economically, or more speedily than they can be measured. Further advances in accuracy and practicality will depend on the development of both new theory and new algorithms, and mathematical techniques will play an important role in ...

The workshop is intended to broaden the scientific perspective of young researchers in mathematical biology and to encourage interactions with other scientists.

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists.

We cordially invite young mathematical biologists to participate.

This 12 month SAMSI program will develop new approaches to scientific/statistical computing using innovative Sequential Monte Carlo (SMC) methods. The program will address fundamental challenges in developing effective sequential and adaptive simulation methods for computations underlying inference and decision analysis. The research will blend conceptual innovation in new and emerging methods wit...

This workshop has the goal of
determining the isoperimetric function of SL(n,Z). Related questions,
such as concerning isodiametric functions, asymptotic cones, higher
dimensional isoperimetric functions, other arithmetic groups, Aut(F_n)
and Out(F_n), will also receive attention.

The main focus of this IPAM program will be on innovations and breakthroughs in the theoretical foundations and practical implementations of a network-centric multi-resolution analysis (MRA), and will be firmly grounded in a number of key Internet MRA target problems, such as cyber-security, traffic/network engineering, and network control.

In recent years, methods from algebra, algebraic geometry, and discrete mathematics have found new and unexpected applications in systems biology as well as in statistics, leading to the emerging new fields of "algebraic biology" and "algebraic statistics." Furthermore, there are emerging applications of algebraic statistics to problems in biology. This year-long program will provide a focus for t...

This workshop concerns Legendrian
and transverse knots in contact three-dimensional manifolds. The focus
will be on the interplay between topological knot theory and contact
topology.

Cell movement is fundamental to embryogenesis and developmental biology, and is hence an excellent core topic for this special emphasis year. Not only is cell motion important in morphogenesis and formation of the organism but also, it plays a central role in wound healing, immune surveillance, and invasive malignant growth in cancer. In this workshop, we plan to bridge the scales between the subc...

This workshop will bring together
researchers with expertise in simulation-based optimization, sampling
techniques, optimization using surrogates, and hydrology, to tackle
complex issues that arise in water resources management applications.

E. coli and Dictyostelium are two of the most widely studied organisms in this area, so this workshop will focus in the main on these, but it is important that it is not restricted to these two examples. Research in this area falls naturally into the two broad categories of
(a) single cell,
(b) population level dynamics. We consider each in more detail below:

(a) At the single cell level, the...

Modern biological research attempts to systematically catalogue various types of molecules, cells, tissues, organisms, populations, and ecosystems, and interactions between them [1,2]. A very large amount of experimental data describes the structure of biological interaction networks, but this does not always lead to understanding the role played by these interactions. In particular, there is a gr...

Many common data sets can be modeled by a mixture of simple geometric objects, e.g., manifolds. A well known example of such data is the NIST images of hand-written digits. The effective modeling of such data together with its careful analysis is a challenging mathematical problem. Earlier work at the beginning of the current century revealed effective methods for modeling data by a single manifol...

Complex biological modeling efforts include predictive multiscale simulations consisting of different submodels at each scale, scalable parallelism for heterogeneous dynamical simulations, a data-rich environment with experimentally determined model parameters and, finally, distributed multidisciplinary research teams and resources. The goal of this focused group meeting is to bring together resea...

Charles Darwin's book On the Origin of Species, first published in 1859, put forth the theory that organisms evolve over many generations through the process of natural selection. One hundred and fifty years hence, we have determined the chemical basis of inheritance in the structure of DNA, we have sequenced the genomes of thousands of organisms, including our own, and have made good progress in ...

This workshop has the goal of providing
a description of GL_3 automorphic forms and their L-functions
amenable to analytic number theorists and to explain the various
approaches available to perform harmonic analysis on these spaces.
A second objective will be to discuss the extension of some of the
important tools existing in the GL_2 theory to the GL_3 context:
a typical example is Kuznetz...

Many engineering, operations, and scientific applications involve both discrete decisions and nonlinear relationships that significantly affect the feasibility and optimality of solutions. Mixed-integer nonlinear programming (MINLP) problems combine the difficulty of optimizing over discrete variable sets with the challenges of handling nonlinear functions. MINLP is one of the most flexible modeli...

This workshop will focus on animal morphogensis. Morphogensis involves the development from a single cell to a complex organism. This process involves many interrelated mechanisms including cell-signaling, differentiaion, cell migration, growth, the formation and movement of tissues. The workshop will focus on several well characterized developmental systems including the frog Xenopus, the worm C....

This workshop will be devoted to
the study of nonnegative matrices and their generalizations. The goal
is to make progress both in specific areas and on the global themes
that unify this subject.

This workshop will be devoted to
a theme common to Irregularity of Distributions, Approximation Theory,
Probability Theory and Harmonic Analysis. In each of these subjects,
there are outstanding conjectures in dimensions three and higher that
stipulate that functions which satisfy certain conditions on its mixed
derivative are necessarily large in sup norm. This workshop will survey
these...

We have witnessed a recent revival of interest in the rich structure and profound properties of metric spaces. Much contemporary research on metric geometry is motivated by the discovery of unexpected connections linking fundamental questions in geometry and analysis with combinatorial optimization, computational complexity, and statistics. This has led to the emergence of an impressive and growin...

Algebraic geometry has long been a central subject, with deep and substantial connections to almost every aspect of modern mathematics. There are numerous different approaches to the field, utilizing widely varying technical tools: Commutative algebra, complex analysis, sheaf theory, cohomological methods, and combinatorial techniques all play important rôles.
This multiplicity of techniques and...

This workshop aims to bring together an interdisciplinary group of researchers from mathematics, physics, quantum information, computer science, and other related disciplines, to discuss advances in the computational description of quantum many-body systems. The workshop consists of two parts: During the first three days we will have a short course for young researchers with lectures and hands-on ...

Cancer and tumor-induced angiogenesis has a natural place in the Special Year on Developmental Biology as cancer is often thought of as a result of a faulty development process. Experimental and clinical oncology forms a massive literature aimed at understanding and treating cancer. Despite the enormity of the data available, clinical oncologists and tumor biologists proceed without a comprehensiv...

The investigation of eigenvalues and eigenfunctions of the Laplace operator in a bounded domain or a manifold is a subject with a history of more than two hundred years. This is still a central area in mathematics, physics, engineering, and computer science, and activity has increased dramatically in the past twenty years. This workshop is an opportunity to discuss various aspects of new or long-s...

Scientific and technological advancements in many fields strongly demand the investigation of problems involving small or multiple scales, motivating the development of new mathematical and computational methods for physical laws that at the mesoscopic, microscopic and even quantum scales, or a mixture of them. In these small or multiscale problems, one has to apply fundamental physical laws, such...

Abnormal healing of wounds in, for example, diabetics, or aged patients, as well as formation of scar tissue, has resulted in the need to understand the fundamental processes involved in wound healing. This workshop aims to bring together experimentalists, clinicians and theoreticians working at the different scales apparent in this problem and to determine approaches for combining these in a mult...

The last twenty years have witnessed greatly increasing interest in higher order differential equations for problems involving geometric motion, fluid interfaces, materials applications, and biological membranes. The research problems have necessitated the development of mathematical theory of higher order partial differential equations (PDE) alongside numerical algorithm development and model dev...

This workshop will be devoted to
the 3D Euler equations of incompressible fluids and the 2D surface
quasi-geostrophic (QG) equation of geophysical flows.

This workshop will be devoted to a
selection of problems on lattice polytopes that arise in the theory of
toric varieties. Besides structural results, we will work on search
strategies and computational approaches to these questions.

In the mammalian nervous system, a classic example of pattern formation is the formation of "maps". These include the continuous mapping of the sensory periphery (e.g. the retina, or a fingertip) onto a central structure, preserving topographic relationships, and the continuous mapping of derived stimulus features such as the dominant eye or the preferred stimulus orientation for driving a central...

The workshop will cover four broad topics that are particularly well-suited for quantitative analysis: genome analysis, pattern formation of the early embryo and wing imaginal disk, computational modeling of signal transduction pathways, and the elucidation and analysis of gene regulation networks.

As of this writing, the genomes of 12 different Drosophilids have been completely sequenced and a...

The first week of the program will be largely devoted to tutorial sessions and general survey lectures. These will be targeted at young researchers and Ph.D. students who know only some basic facts on the subject and want to get familiar with the main lines of current research.

The following two weeks will contain more specialized research talks with one or two themes each day. These talks will...

Analytic Number Theory(2009-2010)During one term of the 2009-2010 academic year, Enrico Bombieri of the School and Peter Sarnak of Princeton University will lead a program on analytic number theory. (preliminary information - more to come.)

This program is broadly concerned with fundamental challenges of modeling, analysis and computation for (mostly) incompressible fluid dynamics. Much attention will be focused on non-Newtonian fluids in which complex material constitutions produce nonlinear and/or nonlocal relationships between stresses and rates-of-strain (and sometimes strains) leading to unique and often unforeseen flow phenomen...

Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas. It studies discrete objects and their properties. This program will focus specifically on several major research topics in modern Discrete Mathematics, including Probabilistic Methods, Extremal Problems for Graphs and Set Systems, Ramsey Theory, Additive Number Theory, Combinatorial...