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Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We
then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of
eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume
and the dynamics of their geodesic flows.
eBook
Bored Bella learns about fiction and nonfiction
Teaches young readers the differences between works of fiction and nonfiction.
Book
Z-nucleic acid-mediated PANoptosis in infection, inflammation, and cancer
Nucleic acids serve not only as carriers of genetic information but also as potent immunological signals that shape innate and adaptive immune responses. Their immunogenicity is determined by their origin, subcellular localization, structural conformation, and the host sensors that detect them. Within this landscape, Z-nucleic acids, including Z-RNA and Z-DNA, have emerged from biological noise to key regulators of immune activation, particularly through their ability to induce inflammatory cell death pathways. Both host and pathogens can generate Z-nucleic acids, yet the mechanisms governing their formation and regulation remain incompletely understood. In mammals, ZBP1 and ADAR1 are the only known Z-nucleic acid sensors, while some pathogens encode Z-binding proteins to evade detection. Although critical for host defense, dysregulated Z-nucleic acid signaling can drive autoimmunity and chronic inflammation. This review synthesizes current structural and functional principles of Z-nucleic acid recognition and highlights emerging therapeutic opportunities across infectious diseases, inflammatory disorders, and cancer.
This review summarizes the mechanisms underlying the generation and regulation of Z-nucleic acids and discusses their sensing by ADAR1 and ZBP1 in cell death and inflammatory signalling, with broad implications for infection, inflammation, and cancer.
Journal Article
What is form?
Readers will learn that many different three-dimensional forms are part of our world and are used in numerous ways by artists. They will also learn how artists can make objects look three-dimensional in a two-dimensional artwork.
Book
The canonical ring of a stacky curve
Generalizing the classical theorems of Max Noether and Petri, we describe generators and relations for the canonical ring of a stacky
curve, including an explicit Gröbner basis. We work in a general algebro-geometric context and treat log canonical and spin canonical
rings as well. As an application, we give an explicit presentation for graded rings of modular forms arising from finite-area quotients
of the upper half-plane by Fuchsian groups.
eBook