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1. Nilpotent varieties in symmetric spaces and twisted affine Schubert varieties

   https://doi.org/10.1090/ert/613  

   Hong, Jiuzu; Korkeathikhun, Korkeat (June 2022, Representation Theory of the American Mathematical Society)

   We relate the geometry of Schubert varieties in twisted affine Grassmannian and the nilpotent varieties in symmetric spaces. This extends some results of Achar–Henderson in the twisted setting. We also get some applications to the geometry of the order 2 nilpotent varieties in certain classical symmetric spaces. 

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2. Scalable trapping of single nanosized extracellular vesicles using plasmonics

   https://doi.org/10.1038/s41467-023-40549-7  

   Hong, Chuchuan; Ndukaife, Justus C. (August 2023, Nature Communications)

   Abstract Heterogeneous nanoscale extracellular vesicles (EVs) are of significant interest for disease detection, monitoring, and therapeutics. However, trapping these nano-sized EVs using optical tweezers has been challenging due to their small size. Plasmon-enhanced optical trapping offers a solution. Nevertheless, existing plasmonic tweezers have limited throughput and can take tens of minutes for trapping for low particle concentrations. Here, we present an innovative approach called geometry-induced electrohydrodynamic tweezers (GET) that overcomes these limitations. GET generates multiple electrohydrodynamic potentials, allowing parallel transport and trapping of single EVs within seconds. By integrating nanoscale plasmonic cavities at the center of each GET trap, single EVs can be placed near plasmonic cavities, enabling instant plasmon-enhanced optical trapping upon laser illumination without detrimental heating effects. These non-invasive scalable hybrid nanotweezers open new horizons for high-throughput tether-free plasmon-enhanced single EV trapping and spectroscopy. Other potential areas of impact include nanoplastics characterization, and scalable hybrid integration for quantum photonics. 

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3. DEVELOPING PRACTICAL MEASURES TO SUPPORT THE IMPROVEMENT OF GEOMETRY FOR TEACHERS􀂶 COURSES

   Ion, M. (January 2019, Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.)

   Otten, S. (Ed.)

   This paper reports on an ongoing project aimed at developing an inter-institutional system of professional support for the improvement of the Geometry for Teachers (GeT) courses that mathematics departments teach to preservice secondary teachers. In alignment with the literature on improvement science (see Bryk et al., 2015; Lewis, 2015), it is essential to develop and deploy practical measurement tools to inform improvement. We describe three key forms of measurement our team has been using to drive this work as well as some preliminary findings. 

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4. HOW INSTRUCTORS OF UNDERGRADUATE MATHEMATICS COURSES MANAGE TENSIONS RELATED TO TEACHING COURSES FOR TEACHERS?

   Brown, A; Herbst, P; Ion, M (November 2023, University of Nevada, Reno.)

   Lamberg, T; Moss, D (Ed.)

   For centuries, there has been a debate about the role of undergraduate education in society. Some have argued that universities should focus on practical skills and knowledge to prepare students for the workforce, while others have supported the idea that universities should prioritize providing a broad understanding of disciplinary knowledge and practices. In this paper, we leverage data collected from 32 interviews to explore how instructors of the undergraduate geometry course for teachers (GeT) talk about the various tensions they experience in their work. Three distinct ways of talking about tensions emerged from the data: the tension as a dilemma that needs to be managed, the tension as a place to take sides, the tension as an opportunity to reframe aspects of the work. In closing we draw connections between these patterns in the data and the two perspectives about the role of undergraduate mathematics courses in preparing PTs for the work of teaching. 

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5. Synthetic Biology Pathway to Nucleoside Triphosphates for Expanded Genetic Alphabets

   https://doi.org/10.1021/acssynbio.3c00060  

   Li, Yubing; Abraham, Clay; Suslov, Oleg; Yaren, Ozlem; Shaw, Ryan W; Kim, Myong-Jung; Wan, Shuo; Marliere, Philippe; Benner, Steven A (June 2023, ACS Synthetic Biology)

   : One horizon in synthetic biology seeks alternative forms of DNA that store, transcribe, and support the evolution of biological information. Here, hydrogen bond donor and acceptor groups are rearranged within a Watson−Crick geometry to get 12 nucleotides that form 6 independently replicating pairs. Such artificially expanded genetic information systems (AEGIS) support Darwinian evolution in vitro. To move AEGIS into living cells, metabolic pathways are next required to make AEGIS triphosphates economically from their nucleosides, eliminating the need to feed these expensive compounds in growth media. We report that “polyphosphate kinases” can be recruited for such pathways, working with natural diphosphate kinases and engineered nucleoside kinases. This pathway in vitro makes AEGIS triphosphates, including third-generation triphosphates having improved ability to survive in living bacterial cells. In α32P-labeled forms, produced here for the first time, they were used to study DNA polymerases, finding cases where third-generation AEGIS triphosphates perform better with natural enzymes than second-generation AEGIS triphosphates. 

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