**Abstract: **“We introduce the idea of β-expansions for non-integral β > 1, and then discuss the generating random β-transformation, which we can view as a suitable dynamical system. As an interlude we will then provide an exposition of the theory of g-measures most often associated with thermodynamical formalism, and illustrate some of their most useful properties and applications. Finally, inspired by the Dyson model coming from statistical physics, we explain how we use the machinery of g-measures to construct a new family of invariant measures for the random β-transformation for certain algebraic β.”

**Abstract: **“In Capture-Recapture experiment designs, when we work with Open Population models, we assume that individuals can Arrive and Depart at any time. Hence, each individual has each own presence history that should be inferred. For doing that we define a time-grid with all possible Arrival-Departure patterns, on which we place a Polya Tree Prior, which is a useful tool when working on grid spaces. In this talk, we will discuss how a Polya Tree Prior works, how it can be applied to Open Population Capture-Recapture data, and lastly what might be a potential solution for efficiently applying that kind of model when the number of sampling occasion is large.”

**Abstract: **“Let g be a nilpotent Lie algebra, U (g) an enveloping algebra of g and P a primitive ideal of U (g). Dixmier proved that the factor algebra U (g)/P is isomorphic to an nth Weyl algebra A_n (C), where n ∈ N ≥1 . Launois has verified Dixmier’s result for the first Weyl algebra A_1 (C). In this talk, we will investigate the result for the second Weyl algebra A_2 (C). More precisely, if q is a root of unity, then one of the primitive quotients of the quantized enveloping algebra U_q + (G_2 ), which we denote by A_α,β , is a quantum deformation/analogue of A_2 (C) for some appropriate choices of α and β. As in the case of A_2 (C), all derivations of A_α,β are inner.”

**Abstract: **“The BeeWalk is the only citizen science survey specifically targeting bumblebees in the UK. Volunteers walk along transects counting the number of bumblebees they detect and identifying their species and caste, where possible. In this talk, I will present our model for modelling BeeWalk data. This model produces estimates of key demographic parameters such as caste-specific phenology and average nest productivity, in the wild. In addition, I will also present our recently developed R shiny app that allows one to use our model without any knowledge of R needed.”

**Abstract: **“Projective dimension is an important invariant of modules that tells us how far a module is from being projective. We can use the projective dimension to measure how complicated the representation theory of a ring is. For example, in Mod-ℤ = Ab, the category of abelian groups, all modules have projective dimension at most one, illustrating the relative simplicity of the structure of abelian groups. However, some rings have modules of infinite projective dimension but still have pretty simple representation theory. Quasi-projective dimension is a generalisation of projective dimension that allows us to measure some of that simplicity. This talk will begin with a review of projective dimension before introducing quasi-projective dimension and some of its properties.”

**Abstract: **“In this paper we propose a novel method to deal with Vector Autoregressive models, when the Normal-Wishart prior is considered. In particular, we depart from the current approach of setting ν=m+1 by setting a loss-based prior on ν. Doing so, we have been able to exploit any information about ν in the data and achieve better predictive performances than the method currently used in the literature. We show how this works both on simulated and real data sets where, in the latter case, we used data of macroeconometric fashion as well as viral data. In addition, we show the reason why we believe we achieve a better performance by showing that the data appears to suggest a value of ν far from the canonical m+1 value.”

As usual we will meet at 4pm on Friday on Microsoft Teams.

**Abstract: **“The aggressive expansion of anthropogenic activities is placing increasing pressure on global biodiversity. These impacts are particularly pronounced in tropical forest ecosystems that support exceptional concentrations of biodiversity but have been subjected to the highest rates of habitat loss. Here conservation efforts are hindered by a paucity of information on species ecology and a failure of policy instruments to reconcile multiple stressors of land-use change. While the protected area network remains central to global conservation efforts, there is a general consensus that protectionist strategies alone will be insufficient to mitigate the magnitude of threats facing biodiversity in vulnerable regions. Conservationists must pursue new paradigms that recognise the fundamental role of human-modified landscapes, particularly logged forests and agricultural concessions, which occupy vast swathes of land across the tropics. Capitalising on environmental policies that enhance biodiversity values in production landscapes is thus central to the global conservation agenda.

During this seminar I will demonstrate how modern advances in remote technologies and statistical methods can be practically applied to provide novel insights into species ecology in tropical habitats and develop robust, evidence-based policy options for vulnerable biodiversity in human-modified landscapes. To this end, I will draw on insights from Sabah, Malaysian Borneo, a region prone to pervasive habitat modification due to the proliferation of selective logging and commodity agriculture. Throughout, applications will focus on tropical mammals as they are particularly sensitive to land-use change, occupy key trophic positions in tropical forest ecosystems and are frequently prioritised by conservation interventions.”

]]>This week, Javier will be talking about A-infinity algebras in the context of operads. We will convene as usual at 4pm on Friday in Microsoft Teams.**Abstract**: In this talk we will introduce A_\infty-algebras, a generalization of associative algebras, and we will explain the framework of Operads, in which we will give an alternative description of A_\infty-algebras.