Sponsored Institutes: AIM, IMA, IPAM, MBI, MSRI, PIMS, SAMSI Supported by National Science Foundation: DMS-0938070. Description: This is the second workshop on contemporary research in mathematics sponsored by all the US-based Math Institutes. The topics of the workshop are related to programs that will occur in the Institutes during the academic year 2010-2011. All presentations will be expository, intended for mathematical scientists and students not necessarily working in these areas, but interested in learning about new developments and the possibility of spending some time at one of the Math Institutes. We will also have a ‘mini course’ for the undergraduate students on Wednesday, October 14, 2009. The topic of this mini course will be "An Elementary Approach to Wavelets with Applications." On Thursday October 15 we will have a key note address by Rafael Irizarry who recently received the President's Award by the Committee of Presidents of Statistical Societies in "recognition of outstanding contributions to the statistics profession". All students and postdocs encouraged to apply. For additional information, please contact Cheri Shakiban at shakiban@ima.umn.edu . Connection with SACNASThe Modern Math workshop will directly precede the annual meeting of the Society for Advancement of Chicanos and Native Americans in Science. SACNAS members are strongly encouraged to take part in this workshop; and conversely, we anticipate that many workshop participants will remain for the annual meeting.
Schedule
Wednesday, October 14, 2009, 1:00 pm to 6:00 pm Session 1Presentations - The Seminar Theater
Session 2 - Austin Ballroom 2
Thursday, October 15, 2009 - The Seminar Theater
Titles and Abstracts:
Hannah Callender Cell motility is an essential process in the life cycle of many organisms, as it plays a crucial role in a variety of areas such as embryonic development, wound healing, the immune response, and cancer cell metastasis. Furthermore, errors during cell migration have serious consequences including mental retardation, vascular disease, tumor formation, and metastasis. Therefore, an understanding of the mechanism by which cells migrate may lead to the development of novel therapeutic strategies for controlling, for example, invasive tumor cells. Cells adhere to and move across their surroundings via protein complexes known as focal adhesions. Focal adhesions serve both as mechanical links from the cell to its surroundings (via transmembrane integrin receptors) and as biochemical signaling hubs to concentrate and direct numerous signaling proteins within the cell. Here we present a mathematical model to describe the initial process of integrin clustering, which leads to formation of nascent focal adhesions. These efforts are providing insight into the necessary components and the role of each (with a particular emphasis on the activation of integrin receptors) in the growth and fate of the focal adhesions.
Judy Day Every day our bodies are bombarded by foreign microbes that we inhale or ingest; and every day our immune system works to eliminate them, orchestrating an amazing response consisting of numerous cell types and molecules. Sometimes this response is not even noticeable to the host and other times not only are the effects (e.g. fever, headaches, elevated heart rate) clearly felt, it is possible that the immune response is not capable of effectively resolving the conflict. (e.g. think of the mortality associated with the black plague, circa 1340!) Consequently, in order for therapies and vaccines to be effectual, it is necessary to have a good understanding of the way in which disease causing agents (pathogens) interact with a host's defense system. Mathematical modeling provides a tool to explore this complex process. In particular, this talk will focus on modeling how the lung responds to Mycobacterium tuberculosis (MTb) infection. A system of ordinary differential equations is developed to describe the interactions between the various immune mediators in response to the bacteria. The model gives insight into the timing of particular immune events that could potentially be altered in such a way as to make vaccines and therapies more effective. Nathanial Dean To understand the interactions between entities (for example, people, objects or groups) systems of interactions can be modeled as graphs linking nodes (entities) with edges that represent various types of connections between the entities. After data collection there are many statistical approaches to analyzing the data, but our approach is to model data as a graph and explore the graph using a variety of tools such as optimization and visualization. In this talk we discuss ways to construct graphs from data, and we show how to use the graphs to reveal patterns. The limitations of this approach are discussed explaining why some graphs cannot be visualized and hence why certain data cannot be understood. Ronald DeVore Mathematics plays a central role in image processing. We shall give examples of how mathematics is used in image compression and the design of sensors. This talk will preview the forthcoming workshop on Image Processing to be held next summer in Park City, Utah.
Olivier Diaz-Espinosa We introduce a technique, based on perturbation theory for Hamiltonian PDEs, to derive the asymptotic equations of the motion of a free surface of a fluid over a rough bottom (one dimension). The rough bottom is described by a realization of a stationary mixing process which varies on short length scales.We show that the problem in this case does not fully homogenize, and random effects are as important as dispersive and nonlinear phenomena in the scaling regime. We will explain how these technique can be generalized to higher dimensions
Keynote speaker: Rafael A. Irizarry Abstract: In this talk I will give a brief introduction to Epigenetics and describe the need for quantitative work. Specifically, I will describe my experience designing 1) a measurement instrument, 2) an experiment and 3) data analysis techniques for finding regions with different methyalation levels among human tissues. We also applied these to mouse tissues and tumor/normal matched samples. I will describe some of the genomic properties we discovered including the location of these regions.
Rajul Pandya According to the IPCC, the evidence that humans are causing climate change is “unequivocal”. While this statement represents a culmination of years of research, it also opens new opportunities for research—particularly research that connects to the priorities of historically underserved communities. This talk will review the evidence of human influence on climate, including an introduction to the numerical models that are used to simulate the Earth system and project future changes. In discussing the models, the talk will provide a brief window into some mathematical challenges in climate modeling including representing cloud processes, integrating disparate time scales, and new techniques for efficiently integrating differential equations on a sphere using multiple processors. In addition, the talk will focus on the opportunity for climate and weather research to serve the priorities of diverse communities. We will explore two particular examples: the first is projections to inform adaptation and mitigation on tribal lands, and the second will describe a new project that seeks to use improved precipitation forecasts to better manage Meningitis in Ghana and evaluate the result in economic terms. Finally, the talk will close with a discussion of opportunities at the National Center for Atmospheric Science.
Günter Uhlman Inverse problems are problems where one tries to determine the inside properties of a medium by making observations on the outside or by remote observations. We give some examples of inverse problems and some applications, including medical imaging, oil exploration, global seismology, and remote sensing. We will also describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves, acoustic waves and other types of waves. Maxwell's equations have transformation laws that allow for design of electromagnetic materials that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. The object, which would have no shadow, is said to be cloaked. We recount the recent history of the subject and discuss some of the mathematical and physical issues involved.
Mini Course- Patrick Van Fleet and Catherine Beneteau The theory of wavelets is relatively new and was advanced by researchers in mathematics, engineering, physics, computer science, and geology. Even within mathematics, the area is quite multidisciplinary engaging researchers whose areas of expertise are approximation theory, harmonic, complex, functional, and numerical analysis. Applications of the topic are widespread: computer engineers use wavelets to perform signal and image processing while geologists use them to search for underground reservoirs of oil. The internet is an important tool in our everyday lives and many of the pages we visit contain digital images. An overwhelming number of these images are stored in a compressed format known as JPEG. At the turn of the century, this format was overhauled and the result was a vastly improved wavelet-based compression method called JPEG2000. In this mini course, we will present a basic introduction to wavelets and demonstrate how wavelets can be used in image processing applications. We will also discuss the role of wavelets in JPEG2000. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||