Topics in Applied Nonlinear Analysis: Recent Advances and New Trends

该奖项将为将于2016年7月18-20日在匹兹堡卡内基梅隆大学非线性分析中心(CNA)举行的“应用非线性分析主题：最新进展和新趋势”会议的与会者提供支持。会议将致力于应用分析的主题，这些主题在许多方面给该领域带来了革命性的变化，特别是对于我们对材料行为的理解和具有所需性能的材料的设计。这些领域对于保持美国在科学技术方面的领导地位至关重要，最近启动的多机构材料基因组倡议就是明证。会议将延续CNA的传统，为学生和初级研究人员提供非凡的网络和培训机会，与一批杰出的国内和国际顶尖应用分析研究人员进行互动。这次会议将为应用数学和材料科学领域的顶尖研究人员提供一个特殊的场所，与不同的观众互动和分享最新的进展。预计这次会议将在数学界和工程界产生影响。已经制定了详细的计划，以帮助从科学界招募不同的参与者群体，包括妇女和少数群体。将组织科学和社会活动，让青年实习生接触并促进他们的卓越。其中包括一次海报会议，由一群从这两个领域的顶级专家中挑选出来的评委评选出四张最佳海报的奖项。会议的成果将通过一个专门的网站传播，其中包括所有受邀演讲的录像：https://www.math.cmu.edu/CNA/kinderlehrer75/index.html本次会议将把非线性分析的当代趋势集中在一起，强调古典与现代、理论与应用在分析中的相互作用特别突出的两个科学领域：(1)最优传输和(2)材料数学。其中，主题包括：-变分不等式、非凸变分问题、伽玛收敛和最优传输的最新进展；-在偏微分方程中的应用；-材料科学中问题的建模和分析：材料微结构和智能材料的设计；-计算方法及其在材料科学和数学生物学中的应用：有限元方法、虚拟元素方法和准连续统方法的最新发展。这一活动中可能出现的新的合作将有可能促进理论/应用偏微分方程式和不同工程学科之间的研究，并将导致思想的交叉授粉。

This award will provide support for participants of the conference on "Topics in Applied Nonlinear Analysis: Recent Advances and New Trends," to be held at the Center for Nonlinear Analysis (CNA) at Carnegie Mellon University, Pittsburgh, in July 18-20, 2016. The conference will be devoted to the topics of applied analysis that in many ways revolutionized the field, especially for our understanding of behavior of materials and design of materials with desired properties. These areas are of critical importance to maintaining US leadership in science and technology as evidenced, for instance, by the recently launched, multi-agency Materials Genome Initiative. The conference will continue the CNA tradition of offering extraordinary networking and training opportunities for students and junior researchers to interact with a remarkable group of leading national and international researchers in applied analysis. This conference will provide an exceptional venue for top researchers in applied mathematics and in materials science to interact and share recent advances with a diverse audience. The impact of the conference is expected in both the mathematical and engineering communities. Detailed plans have been made to help recruit a diverse group of participants from the scientific community, including women and minorities. Scientific and social activities will be organized to give young trainees exposure and promote their excellence. These include a poster session with awards for four best posters, identified by a group of judges selected from top experts in both fields. The results of the conference will be disseminated by means of a dedicated website featuring video recordings of all invited presentations: https://www.math.cmu.edu/CNA/kinderlehrer75/index.html This conference will bring under one umbrella contemporary trends in nonlinear analysis, emphasizing two scientific areas where the interplay between the classical and the modern, the theoretical and the applied in analysis has been especially prominent: (1) Optimal Transport and (2) Mathematics of Materials. Among others, the topics will include: - Recent advances in variational inequalities, non-convex variational problems, Gamma-convergence and optimal transport;- Applications to PDE;- Modeling and Analysis of Problems in Materials Science: materials microstructure and design of smart materials;- Computational Methods with Application to Problems in Materials Science and Mathematical Biology: recent developments in Finite Element Methods, Virtual Element Methods and Quasi-Continuum Methods.New collaborations that are likely to emerge from this activity will have a potential to catalyze research at the interface between theoretical/applied partial differential equations and various engineering disciplines, and will result in cross-pollination of ideas.