MPS-Ascend: Ergodic Schrödinger Operators and Quasicrystals

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。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），以开展与扩大STEM中代表性不足的群体参与相关的研究和活动计划。Takase博士的研究项目名为“MPS-Ascend：遍历Schrödinger算子和准晶体”，由两位赞助科学家指导。在第一个主办机构密歇根州立大学（Michigan State University）， Takase博士将从2022年8月到2023年7月与赞助科学家伊利亚·卡赫科夫斯基（Ilya Kachkovskiy）博士一起工作。从2023年8月到2025年7月，大卫·达马尼克博士将在莱斯大学担任Takase博士的赞助科学家。该项目的目标是研究遍历Schrödinger算符的谱理论，重点关注量子力学中出现的用于模拟物理现象的显式多维算符。PI计划研究Penrose tilings上的拉普拉斯算子来描述谱的拓扑结构，Schrödinger算子在耦合常数趋近于零时的谱特征连续性，以及具有可分离势的遍历Schrödinger算子。PI计划通过引导阅读项目参与本科生研究指导和专业发展活动。为了扩大对数学和物理科学的参与，Takase博士带来了他作为梅隆梅斯大学本科生研究员的个人经验和他作为社区教育推广项目Math CEO的研究生成员参与中学推广的见解。他参加了几次在hsi和hbcu的推广活动，并计划在未来继续这些活动。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.