MPS-Ascend: Ergodic Schrödinger Operators and Quasicrystals

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。PI Takase被授予美国国家科学基金会数学和物理科学上升博士后研究奖学金（NSF MPS-Ascend），以开展与扩大STEM代表性不足的群体参与有关的研究和活动计划。高濑博士的奖学金在两位赞助科学家的指导下支持题为“MPS-Ascend：遍历薛定谔算子和准晶体”的研究项目。在第一个主办机构密歇根州立大学，高濑博士将与赞助科学家伊利亚·卡奇科夫斯基博士合作，从2022年8月到2023年7月。大卫Damanik博士将从2023年8月到2025年7月在莱斯大学担任Takase博士的赞助科学家。该项目的目标是研究遍历薛定谔算子的谱理论，重点是量子力学中出现的显式多维算子来模拟物理现象。PI计划研究彭罗斯平铺上的拉普拉斯算子，以描述谱的拓扑结构，薛定谔算子在耦合常数接近零时的谱特征的连续性，以及具有可分离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导师和专业发展活动。为了扩大数学和物理科学的参与，高濑博士带来了他自己作为梅隆梅斯大学本科研究员的经验，以及他作为社区教育推广计划的研究生成员参与中学推广活动的见解。他参加了几个外展活动在HSIs和HBCUs和计划继续在未来这些举措。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

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.