MPS-Ascend: Ergodic Schrödinger Operators and Quasicrystals

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。Pi Takase被授予国家科学基金会数学和物理科学提升博士后研究奖学金(NSF MPS-Ascend)，以开展一项与扩大STEM中代表性不足的群体的参与相关的研究和活动。Takase博士的这笔奖学金支持在两名赞助科学家的指导下进行的名为“MPS-Ascend：遍历薛定谔算符和准晶”的研究项目。在第一个主办机构密歇根州立大学，高ase博士将在2022年8月至2023年7月期间与发起研究的科学家伊利亚·卡奇科夫斯基博士合作。David Damanik博士将在2023年8月至2025年7月期间担任Takase博士在莱斯大学的赞助科学家。这个项目的目标是研究遍历薛定谔算符的谱理论，重点是出现在量子力学中用来模拟物理现象的显式多维算符。PI计划研究Penrose瓦片上的拉普拉斯算子，以描述谱的拓扑结构、当耦合常数趋于零时薛定谔算子的谱特征的连续性以及具有可分势的遍历薛定谔算子。PI计划通过定向阅读计划参与本科生研究、指导和职业发展活动。为了扩大对数学和物理科学的参与，Takase博士从自己作为梅隆大学本科生研究员的经历，以及作为社区教育推广项目Math CEO的研究生成员参与中学推广活动中获得了见解。他参与了HSIS和HBCU的几项外展活动，并计划在未来继续这些活动。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Takase is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research and activities related to broaden participation by groups underrepresented in STEM. This fellowship to Dr. Takase supports the research project entitled "MPS-Ascend: Ergodic Schrödinger Operators and Quasicrystals", under the mentorship of two sponsoring scientists. At the first host institution, Michigan State University, Dr. Takase will work with the sponsoring scientist Dr. Ilya Kachkovskiy, from August 2022 through July 2023. Dr. David Damanik will be Dr. Takase’s sponsoring scientist at Rice University from August 2023 through July 2025. The goal of this project is to investigate the spectral theory of ergodic Schrödinger operators, with a focus on explicit multi-dimensional operators that appear in quantum mechanics to model physical phenomena. The PI plans to study Laplacians on Penrose tilings to describe the topological structure of the spectrum, continuity of spectral characteristics of Schrödinger operators as the coupling constant approaches zero, and ergodic Schrödinger operators with separable potentials. The PI plans to engage with undergraduate research mentorship and professional development activities through directed reading programs. To broaden participation in mathematical and physical sciences, Dr. Takase brings insights from his own experience as a Mellon Mays Undergraduate Fellow and his engagement with middle school outreach as a graduate student member of a community educational outreach program called Math CEO. He has participated in several outreach activities at HSIs and HBCUs and plans to continue these initiatives in future.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.