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1. Scattering for the Defocusing, Nonlinear Schrödinger Equation With Initial Data in a Critical Space

   https://doi.org/10.1093/imrn/rnac296  

   Dodson, Benjamin (October 2022, International Mathematics Research Notices)

   Abstract In this note, we prove scattering for a defocusing nonlinear Schrödinger equation with initial data lying in a critical Besov space. In addition, we obtain polynomial bounds on the scattering size as a function of the critical Besov norm. 

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2. Scale-invariant tangent-point energies for knots

   https://doi.org/10.4171/JEMS/1479  

   Blatt, Simon; Reiter, Philipp; Schikorra, Armin; Vorderobermeier, Nicole (April 2025, Journal of the European Mathematical Society)

   We investigate minimizers and critical points for scale-invariant tangent-point energies{\mathrm{TP}}^{p,q}of closed curves. We show that (a) minimizing sequences in ambient isotopy classes converge to locally critical embeddings at all but finitely many points and (b) locally critical embeddings are regular. Technically, the convergence theory (a) is based on a gap estimate for fractional Sobolev spaces with respect to the tangent-point energy. The regularity theory (b) is based on constructing a new energy\mathcal{E}^{p,q}and proving that the derivative\gamma'of a parametrization of a{\mathrm{TP}}^{p,q}-critical curve\gammainduces a critical map with respect to\mathcal{E}^{p,q}acting on torus-to-sphere maps. 

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3. Global Well-Posedness and Refined Regularity Criterion for the Uni-Directional Euler-Alignment System

   https://doi.org/10.1093/imrn/rnae246  

   Li, Yatao; Miao, Qianyun; Tan, Changhui; Xue, Liutang (October 2024, International Mathematics Research Notices)

   Abstract We investigate global solutions to the Euler-alignment system in $$d$$ dimensions with unidirectional flows and strongly singular communication protocols $$\phi (x) = |x|^{-(d+\alpha )}$$ for $$\alpha \in (0,2)$$. Our paper establishes global regularity results in both the subcritical regime $$1<\alpha <2$$ and the critical regime $$\alpha =1$$. Notably, when $$\alpha =1$$, the system exhibits a critical scaling similar to the critical quasi-geostrophic equation. To achieve global well-posedness, we employ a novel method based on propagating the modulus of continuity. Our approach introduces the concept of simultaneously propagating multiple moduli of continuity, which allows us to effectively handle the system of two equations with critical scaling. Additionally, we improve the regularity criteria for solutions to this system in the supercritical regime $$0<\alpha <1$$. 

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4. Towards a Framework for Developing a Critical Statistical Literacy

   https://doi.org/10.52041/iase.icots11.T1C3  

   Weiland, Travis; Sundrani, Anita (January 2022, Towards a framework for developing a critical statistical literacy)

   Peters, S. (Ed.)

   In this theoretical paper we hypothesize a developmental framework for a critical statistical literacy based on our anecdotal observations from working with teachers and empirical evidence from a pilot study. We create the framework by taking Watson and Callingham’s hierarchical framework for statistical literacy and reframing it as a developmental framework. We then combine it with Weiland’s Critical Statistical Literacy framework, which serves as an end goal of the developmental framework. We provide excerpts from a pilot study as a proof of concept and make suggestions for future research. 

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5. Characterizing TES power noise for future single optical-phonon and infrared-photon detectors

   https://doi.org/10.1063/5.0011130  

   Fink, C_W; Watkins, S_L; Aramaki, T.; Brink, P_L; Ganjam, S.; Hines, B_A; Huber, M_E; Kurinsky, N_A; Mahapatra, R.; Mirabolfathi, N.; et al (August 2020, AIP Advances)

   In this letter, we present the performance of a 100 μm × 400 μm × 40 nm W Transition-Edge Sensor with a critical temperature of 40 mK. This device has a noise equivalent power of 1.5×10-18 W/Hz, in a bandwidth of 2.6 kHz, indicating a resolution for Dirac delta energy depositions of 40 ± 5 meV (rms). The performance demonstrated by this device is a critical step toward developing a O(100) meV threshold athermal phonon detector for low-mass dark matter searches. 

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