Workshop Support for "Particulate Matter: Does Dimensionality Matter?"; Max Planck Institute for the Physics of Complex Systems; Dresden, Germany

《Flatland》这个故事帮助19世纪的读者理解了第四维度的隐喻作用。高维现在帮助21世纪的科学家更好地理解我们相对低维的世界。桌上堆着的硬币图案或杂货店摊位上堆着的橙子图案既有相似之处，也有不同之处。通过在高于两维或三维的维度上考察类似问题，我们能够获得额外的比较点。类似地，对胶体、颗粒材料、玻璃或乳剂等致密颗粒物质的理解也开始从比较和对比不同空间维度上相关现象的行为开始。各种实验和理论技术允许这种探索，但有趣的是，不同的方法有时会导致维度如何影响现象的不同答案。有些人甚至认为维度在他们的子领域中起不到什么作用。我们能弄明白这个谜题吗？由于许多大洲和不同领域（数学、工程和基础科学）都在取得进展，因此有必要将研究人员聚集在一起，在一段较长的时间内集中精力，勾勒出未来的道路，并抓住这些往往独立发展所创造的势头。这笔资金将用于资助来自美国的研究生和博士后学员参加在德国德累斯顿举行的关于密集颗粒物维度问题的研讨会。这些初级研究人员将能够向各个分领域的国际专家观众发表演讲和海报。学生和博士后参与国际研讨会是培养具有国际竞争力的劳动力的关键，在这个快速发展的领域，大学课程还不存在。该研讨会有两个特点，旨在鼓励初级科学家与国际社会建立未来的合作：将正式会谈与有组织的讨论结合起来，以及分配时间进行小组互动。

The story Flatland helped 19th century readers understand the metaphorical role of the fourth dimension. Higher dimensions now help 21st century scientists to better understand our comparatively low-dimensional world. The pattern of coins packed on a tabletop or oranges piled on a grocer's stand have both similarities and differences. By examining similar problems in dimensions higher than two or three, we are able to obtain additional points of comparison. Similarly, progress in understanding dense particulate matter such as colloids, granular materials, glasses, or emulsions is starting to arise from comparing and contrasting the behavior of related phenomena in different spatial dimensions. A variety of experimental and theoretical techniques allow for this exploration, but interestingly, different approaches sometimes lead to differing answers as to how dimensionality influences a phenomenon. Some even argue that dimension plays little role on their subfield. Can we make sense of this conundrum? Since progress is taking place on many continents and in different fields (mathematics, engineering, and basic sciences), there is a need to bring researchers together for an extended and focused period of time to sketch the road ahead and to capture the momentum created by these often independent developments. This grant will help support the travel of graduate students and postdoctoral trainees from the US to a workshop addressing questions of dimensionality in dense particulate matter to be held in Dresden, Germany. These junior researchers will be enabled to present talks and posters to the international audience of experts in the various sub-fields.The participation of students and postdoctoral fellows in international workshops is key to training an internationally competitive workforce in this rapidly developing field for which university coursework does not yet exist. The workshop has two features that are aimed at encouraging junior researchers to build future collaborations with the international community: the pairing of formal talks with organized discussions, and the allotment of time for small-group interactions.