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   https://doi.org/10.1093/imrn/rnae085  

   Biswas, Indranil; Mukhopadhyay, Swarnava; Wentworth, Richard (May 2024, International Mathematics Research Notices)

   For a simple, simply connected, complex group G, we prove an explicit formula to compute the Atiyah class of parabolic determinant of cohomology line bundle on the moduli space of parabolic G-bundles. This generalizes an earlier result of Beilinson-Schechtman. 

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2. “Zyflex”: Next generation plasma chamber for complex plasma research in space

   https://doi.org/10.1063/5.0062165  

   Knapek, C_A; Konopka, U.; Mohr, D_P; Huber, P.; Lipaev, A_M; Thomas, H_M (October 2021, Review of Scientific Instruments)

   In this paper, we give a detailed description of a novel plasma chamber—the Zyflex chamber—that has been specifically designed for complex/dusty plasma research under reduced gravitational influence as realized during parabolic flight or aboard the International Space Station. The cylindrical, radio-frequency driven discharge device includes a variety of innovations that, for example, allow us to flexibly adjust plasma parameters and its volume via enhanced plasma generation control and a movable, multi-segmented electrode system. The new complex/dusty plasma research tool also supports, due to its overall increased size compared to former space based complex plasma experiments such as PKE-Nefedov or PK-3 Plus, much larger particle systems. Additionally, it can be operated at much lower neutral gas pressures, thus reducing the damping of particle motion considerably. Beyond the technical description and particle-in-cell simulation based characterization of the plasma vessel, we show sample results from experiments performed with this device in the laboratory as well as during parabolic flights, both of which clearly demonstrate the new quality of complex/dusty plasma research that becomes accessible with this new plasma device. 

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3. Matrix Li–Yau–Hamilton estimates under Ricci flow and parabolic frequency

   https://doi.org/10.1007/s00526-024-02668-x  

   Li, Xiaolong; Zhang, Qi S. (February 2024, Calculus of Variations and Partial Differential Equations)

   Abstract We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply these estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature. 

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4. Structure of partially hyperbolic Hénon maps

   https://doi.org/10.4171/JEMS/1074  

   Lyubich, Mikhail; Peters, Hans (January 2021, Journal of the European Mathematical Society)

   We describe the structure of “substantially dissipative” complex Hénon maps admitting a dominated splitting on the Julia set. We prove that the Fatou set consists of only finitely many components, each either attracting or parabolic periodic. In particular, there are no wandering components and no rotation domains. 

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5. A Hitchin connection on nonabelian theta functions for parabolic 𝐺-bundles

   https://doi.org/10.1515/crelle-2023-0049  

   Biswas, Indranil; Mukhopadhyay, Swarnava; Wentworth, Richard (September 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract For a simple, simply connected complex affine algebraic group 𝐺, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli spaces of semistable parabolic 𝐺-bundles for families of smooth projective curves with marked points. 

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