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Aim: To investigate the actual attitude of Radiation Oncologists in the prescription of hormonal therapy in prostate cancer (PC) with or without Radiation Therapy (RT). Materials and methods: In 2019, a survey named Prescription of Radiation Oncologists ACtual Attitude including 18 items was sent to all Italian Radiation Oncologists of the Italian Association of Radiotherapy and Clinical Oncology. The first 4 items were about the Radiation Oncology Centers characteristics and years of practice of the respondents. The remaining 14 items concerned the setting in which hormone therapy was prescribed in PC patients (radical, postprostatectomy/oligometastatic state), the kind of drug, the choice modality (Multidisciplinary Group/autonomy decision) and other factors. Results: A total of 127 questionnaires were returned, mainly by Northern Italy Radiation Oncology Centres (44.9%), and by experienced Radiation Oncologists (78%), who declared to prescribe independently hormone therapy in 85.8% of cases. The Androgen deprivation therapy (ADT) prescription in castration naive PC was made independently by 56.7% of respondents and associated with radical RT, postoperative or salvage RT according to various risk factors. In castration-sensitive oligorecurrent PC, the majority (51.2%) administered ADT only if local ablative treatment was not feasible, while in metastatic castration resistant disease novel hormone therapy use was established in almost half of cases within multidisciplinary board. Radiation Oncologists could prescribe these drugs independently in 64% of cases. Conclusion: Our survey established the prescription attitude of ADT and new hormonal agents (abiraterone, enzalutamide, apalutamide) by Italian Radiation Oncologists and highlighted the importance of expertise in global PC management.

homotopy theory provides a framework in which any site S can be embedded and its objects studied. In this context, objects of the site appear distinguished among more general ones. The purpose of this framework is to create an environment where the site S and supplementary “combinatorial/homotopical” data can blend together. Such a blending is achieved by a well-established mathematical procedure, the localization. The challenge in using this framework in practice is to find close ties between these general objects and the ones in S. I will describe the results that G. Tomassini and I have obtained on these topics.

In this article we give two notions of hyperbolicity for groupoids on the analytic site of complex spaces, which we call Kobayashi and Brody hyperbolicity. In the special case the groupoid is a complex analytic space, these notions of hyperbolicity give the classical ones due to Kobayashi and Brody. We prove that such notions are equivalent if the groupoid is a compact Deligne–Mumford analytic stack (in analogy with the Brody theorem). Moreover, under the same assumptions, such notions of hyperbolicity are completely detected by the coarse moduli space of the stack. We finally show that stack hyperbolicity, as we defined it, is expected to impose a peculiar behavior to the stack itself, much like hyperbolicity for complex spaces. For instance, a stronger notion of it (hyperbolicity of the coarse moduli space) implies a “strong asymmetry” on the stack in the compact case, namely that its automorphism 2-group has only finitely many isomorphism classes.

The paper's aim is to develop a theory in which the concept of Brody hyperbolicity of a complex space (cfr. [2]) is interpreted in terms of homotopy-theoretic structures. We contend that this interplay will be particularly useful if implemented by applying homotopy-theoretical techniques and constructions to get information on hyperbolic spaces. Imitating the construction of homotopy groups, we will define holotopy groups that will be able to tell apart different complex structures. From our point of view, the most important feature of these groups is that they vanish in a certain range if evaluated on a Brody hyperbolic complex space (see Theorem 4.1), providing therefore a way to reduce the proof of non hyperbolicity of a complex space to the existence of a nonzero holotopy class in these groups.

In the paper [Borghesi S. Algebraic Morava K-theories. Invent. Math. 151, 381-413 (2003)] we constructed (co)homology theories on the category of smooth schemes which share some of the some of the defining properties of the (co)homology theories induced by the Morava k-theory spectra in classical homotopy theory. Some proofs used the topological realization functor. The existence of that functor requires the base field $k$ to be embedded in $\mathbb{C}$. In this manuscript we investigate up to what extent we can obtain the same results under the sole assumption of perfectness of the base field. The results proved here guarantee the existence of spectra $\ph_i$ satisfying the same properties as in [Borghesi S. Algebraic Morava K-theories. Invent. Math. 151, 381-413 (2003)], provided that the algebra of all the bistable motivic cohomology operations verifies an assumption involving the Milnor operation $Q_t$.

Questo manoscritto è un'introduzione al concetto di formule del grado e a qualche loro applicazione. Si dà una formalizzazione di quello che si intenderà con formula del grado, vengono enunciati due esempi: uno cosiddetto di primo livello ed uno più generale. Successivamente si descrivono le componenti di queste formule: i numeri e gli ideali di ostruzione. Dopo un breve accenno alla dimostrazione, il testo si conclude con una sezione in cui si analizzano esplicitamente varietà algebriche a cui si possono applicare le formule di primo livello.