We prove several Kählerness criteria for compact Hermitian surfaces under semi-definiteness assumptions on natural Ricci curvatures of the Strominger-Bismut connection. The key tools for proving these results are explicit identities relating these Ricci curvatures to the torsion of the Strominger-Bismut connection, together with corresponding Chern number identities on compact Hermitian surfaces. The results may be viewed as Strominger-Bismut analogues and reformulations of Yang's Kählerness criteria for compact complex surfaces.

An elementary particle such as a photon cannot be cut in two pieces. Still it must be possible to truncate a photon with an optical shutter. The result is neither another photon nor a mix of a photon and a vacuum. Instead it is a superposition and mix of photon numbers up to infinity. This state is rather complicated, but nevertheless locally equivalent to a single photon or vacuum to the left and right, respectively, of a narrow transition region.

A variant of consensus based distributed gradient descent (\textbf{DGD}) is studied for finite sums of smooth but possibly non-convex functions. In particular, the local gradient term in the fixed step-size iteration of each agent is randomly perturbed to evade saddle points. Under regularity conditions, it is established that for sufficiently small step size and noise variance, each agent converges with high probability to a specified radius neighborhood of a common second-order stationary point, i.e., local minimizer. The rate of convergence is shown to be comparable to centralized first-order algorithms. Numerical experiments are presented to validate the efficacy of the proposed approach over standard \textbf{DGD} in a non-convex setting.

Active Galactic Nuclei (AGN) feedback is essential in cosmological simulations of galaxy formation, yet its implementation has to rely on subgrid models due to limited resolution. We present a novel subgrid jet-launching method for galaxy formation simulations and implement it in three hydrodynamical codes: the smoothed particle hydrodynamics (SPH) code SWIFT, the moving-mesh code AREPO, and the Eulerian grid code PLUTO. To isolate the impact of hydrodynamical solvers on jet evolution, we compare idealised jets and their remnants in uniform and stratified media across resolutions and jet parameters. In uniform media, all jets drive bow shocks, inflate hot lobes, exhibit backflows, and evolve self-similarly. For the parameters explored, SWIFT lobes are shorter, wider, and hotter; AREPO lobes are longer, thinner, and cooler; while PLUTO lobes display complex flows with intermediate characteristics. In stratified media, jets deviate from self-similar evolution, inflating longer and thinner lobes due to lower external ram pressure. After switch-off, SWIFT jets evolve into smooth cylindrical bubbles, AREPO jets produce long filamentary remnants, and PLUTO jets yield intermediate-length remnants with varying degrees of mixing. Despite such differences, all jets and remnants have a similar impact on the ambient medium. We conclude that variations in lobe properties between codes emerge even for identical subgrid prescriptions, since the coupling of jet feedback to resolvable scales and the effective resolution depend on the hydrodynamical method. In structure formation simulations, these solver differences are likely subdominant to uncertainties in subgrid modelling and calibration, while averaging over galaxy populations may lessen their impact.

A regular lattice of magnetic skyrmions is the ground state of thin ferromagnetic films with Dzyaloshinskii-Moriya interaction in a relatively wide range of external magnetic fields. It was previously theoretically shown that upon the increase of magnetic field a topological transition in the magnon spectrum of such skyrmion crystal (SkX) may occur. Non-uniform magnetic field may lead to localized magnon states emerging at the interface between two half-planes of SkX. Using semiclassical quantization and the stereographic projection approach, we study such appearing edge states both in a full band structure calculation and in simplified effective model. The latter effective model described by extended Dirac equation is applicable to two relevant magnon bands near $Γ$ point. We show that both the chirality of emerging edge states and the degree of its localization at the interface is controlled by magnetic field profile. We demonstrate that the localization length may be as small as a few inter-skyrmion distances.

We study the noisy dynamics of periodically driven, discrete-step quantum walks in a one-dimensional photonic lattice. We find that in the bulk, temporal noise that is constant within a Floquet period leads to decoherence-free momentum subspaces, whereas fully random noise destroys coherence in a few time steps. When considering topological edge states, we observe decoherence no matter the type of temporal noise. To explain these results, we derive a non-perturbative master equation to describe the system's dynamics. We experimentally confirm our findings in a time multiplexed photonic lattice implemented in a double-fiber ring setup subject to laser pulse input states, in which we engineer different types of temporal noise.

This paper reports on a systematic first-principles molecular dynamics investigation of binary (TlO$_{0.5}$)$_{y}$-(TeO$_2$)$_{1-y}$ and ternary $(TiO$_{2}$)$_{x}$-(TlO$_{0.5}$)$_{y}$-(TeO$_2$)_{1-x-y}$ tellurite glasses. The obtained structural models are validated against available measured X-ray pair distribution functions. In the binary system, increasing TlO$_{0.5}$ content induces network depolymerization through the reduction of Te coordination number, the substitution of Te-O-Te linkages with Te=O$^{-}$...Tl$^{+}$ units, and the proliferation of non-bridging oxygens. In addition, rings analysis demonstrates a loss of the network connectivity via the opening of small n-membered rings. In contrast, TiO$_2$ acts as a network former in ternary glasses, preserving Te coordination number, and promoting a high fraction of bridging oxygens. Ti atoms induces a network repolymerization that manifests through the formation of smaller Ti-containing n-membered rings thereby balancing the strong effect of Tl$_2$O modifier. Beside the structural analysis, we also computed Raman spectra and non-linear optical properties on the obtained large periodic models. Our results reproduce experimental trends in Raman band shifts with composition, while nonlinear optical calculations show that <$χ^{(3)}$> remains stable with TlO$_{0.5}$ addition in binary glasses, consistent with experiment. In the case of ternary systems, we find that the inclusion of a small fraction of TiO$_2$ preserves the high optical nonlinearity of the TeO$_2$ network while maintaining the overall network connectivity. These results establish a predictive framework for tailoring the atomic structure and nonlinear optical response of tellurite glasses through the controlled interplay of modifiers nature and concentration.

$T$-varieties are normal varieties equipped with an action of an algebraic torus $T$. When the action is effective, the complexity of a $T$-variety $X$ is $\dim(X)-\dim(T)$. Matrix Schubert varieties, introduced by Fulton in 1992, are $T$-varieties consisting of $n \times n$ matrices satisfying certain constraints on the ranks of their submatrices. In this paper, we focus on the complexity of certain torus-fixed affine subvarieties of matrix Schubert varieties. Concretely, given a matrix Schubert variety $\overline{X_{w}}$ where $w\in S_n$, we study the complexity of $Y_w$ obtained by the decomposition $\overline{X_{w}} = Y_{w} \times \mathbb{C}^{k}$ with $k$ as large as possible. Building up from results by Escobar and Mészáros and Donten-Bury, Escobar, and Portakal, we show that for a fixed $n$, the complexity of $Y_{w}$ with respect to this action can be any integer between $0$ and $(n-1)(n-3)$, except $1$.

In this paper, we study the moduli space of unipotent Weil-Deligne representations valued in a split reductive group $G$ and characterise which irreducible components are smooth. We apply the smoothness results proved to show that a certain space of ordinary automorphic forms is a locally generically free module over the corresponding global deformation ring.

Women comprise the majority of students and early-career scholars in psychology, yet they are less likely to remain active in research over time. This pattern raises a central question: At what stages of academic careers do women disproportionately leave academia, and what factors drive their attrition? Using large-scale bibliometric data tracking 78,216 psychologists who began publishing between 2000 and 2014, we examine gender differences in research career attrition operationalized through publishing activity across the full trajectory from entry onward. Although women accounted for more than 60\% of new entrants, they experienced higher attrition rates than men, with the gender gap peaking approximately five years after first publication. Early-career performance, particularly first-authored publications, was the strongest predictor of subsequent retention, whereas last-authored publications were most closely associated with continued activity at later career stages. Collaboration patterns and institutional context also shaped career persistence, though less strongly than publication indicators. Notably, gender differences in research attrition persisted even after accounting for these career determinants, especially during early career stages. These findings suggest that gender inequality in psychology is driven less by recruitment than by differential retention over time. Addressing early-career vulnerability may therefore be essential to achieving equitable representation in senior academic leadership within the discipline.

The following learning problem arises naturally in various applications: Given a finite sample from a categorical or count time series, can we learn a function of the sample that (nearly) maximizes the probability of correctly guessing the values of a given portion of the data using the values from the remaining parts? Unlike classical approaches in statistical inference, our approach avoids explicitly estimating the conditional probabilities. We propose a non-parametric guessing function with a learning rate independent of the alphabet size. Our analysis focuses on a broad class of time series models that encompasses finite-order Markov chains, some hidden Markov chains, Poisson regression for count processes, and one-dimensional Gibbs measures. We provide a margin condition that controls the rate of convergence for the risk. Additionally, we establish a minimax lower bound for the convergence rate of the risk associated with our guessing problem. This lower bound matches the upper bound achieved by our estimator up to a logarithmic factor, demonstrating its near-optimality.

The attracting properties of gravity enable matter present in cores to collapse into stars with seven orders of magnitude change in space and time making modelling of star formation a challenging multi-scale process. To circumvent this scale problem stars are replaced by a sub-grid sink particle at a much larger scale. Sink particles are created above a threshold density and acquire mass and momentum through accretion. In models where binary star systems form and migrate to separations of a few cells, the accretion flow is unresolved and the relative accretion rate to the sink particles may become inaccurate. We introduce a new recipe for accretion onto binary sink particles that have overlapping accretion regions and implement an algorithm to track the angular momentum of sink particles as a proxy for the stellar spin. Our preferential binary accretion recipe uses a virtual binary sink particle for the purpose of accretion and redistribute the accreted mass onto the sink particles according to results from models investigating binary accretion in detail. This solves problems common to current algorithms in many codes: (i) accretion is not suppressed due to large velocity differences between gas and stars, when that velocity is only internal to the binary system, (ii) the accretion rates are smoother for the unresolved close binaries in eccentric orbits, and (iii) non-physical suppression of accretion onto the secondary sink particle when the primary dominates the potential is eliminated. We test our implementation by comparing simulations at increasing resolution until the binaries are resolved. While not perfect, it mitigates undesired properties of current algorithms and in particularly for global models of starforming regions. It may also be applied to other unresolved accreting binaries, such as compact objects in clusters and binary supermassive black holes in cosmological models.

We introduce the concept of chiral geometric operators and use Gilkey's invariance theory to prove the local index theorem for these operators. In other words, we demonstrate that the supertrace of the heat kernel of a given geometric operator converges as time approaches zero and that this limit is the Chern-Weil form of the Atiyah-Singer integrand. In addition to classical Dirac-type operators that appear in geometry, chiral geometric operators include all higher Dirac operators. This includes in particular the Rarita-Schwinger operator. We also construct a new class of such operators on four-manifolds called higher signature operators.

The use of a Si pixel-based particle tracking scheme in muSR will, among others, allow measurements using a ten-fold increased stopped muons rate and samples ten times smaller than currently possible. Here we present simulation results to assess the effects of magnetic fields on two spectrometer configurations using a two-layered tracking scheme for the incoming and outgoing particles. At a low magnetic field of up to ~50 mT, the tracking and reconstruction accuracy is only minimally influenced. Beyond a magnetic field of ~80 mT the tracking capabilities diminish significantly. Operating a two-layered scheme using small magnetic fields hence does not require adaptations. Only at large magnetic fields, a tracking scheme that makes use of an accurate field map or the use of at least three layers must be employed to achieve reliable particle tracking.

Maintaining high energy efficiency (EE) in wireless networks is crucial, particularly with the adoption of massive MIMO technology. This work introduces a resource allocation framework that jointly optimizes transmit power assigned to each user and the number of active antennas, while explicitly accounting for a nonlinear Power Amplifier (PA). We consider a downlink MU-MIMO-OFDM transmission with zero forcing (ZF) precoding, Rayleigh fading channels, and soft-limiter PAs, with both ideal and realistic PA architectures. In contrast to existing formulations, our optimization framework avoids imposing an explicit transmit power constraint, since the nonlinear distortion inherently limits the feasible operating region. To solve the resulting non-convex problem, an alternating optimization approach is adopted that, by exploiting properties of the EE function, guarantees convergence to a stationary point. Extensive simulations demonstrate consistent performance gains over distortion-neglecting and power-only optimized baselines. In a scenario of a 5 km radius cell serving 60 randomly distributed users, the median EE gains over the distortion-neglecting allocation reach 40% for ideal PAs and 20% for Class B PAs, confirming high impact of the proposed solution.

Spin-orbit coupling and quantum geometry are fundamental aspects in modern condensed matter physics, with their primary manifestations in momentum space being spin textures and Berry curvature. In this work, we investigate their interplay with high-harmonic generation (HHG) in two-dimensional non-centrosymmetric materials, with an emphasis on even-order harmonics. Our analysis reveals that the emergence of finite even-order harmonics necessarily requires a broken twofold rotational symmetry in the spin texture, as well as a non-trivial Berry curvature in systems with time-reversal invariance. This symmetry breaking can arise across various degrees of freedom and impact both spin textures and optical response via spin-orbit interactions. We also show that HHG is particularly sensitive to dynamical rotational-symmetry breaking, as even high-order components can be modulated by a time-dependent symmetry breaking. These findings underscore the potential of HHG as a tool for exploring electronic phases with broken rotational symmetry, as well as the associated phase transitions in two-dimensional materials, and provide novel perspectives for designing symmetry-dependent nonlinear optical phenomena.

We study group fairness in the context of feedback loops induced by meritocratic selection into programs that themselves confer additional advantage, like college admissions. We introduce a stylized, yet novel inter-generational model for the setting and analyze it in situations where there are no underlying differences between two populations. When the benefit of the program (or the harm of not getting into it) is completely symmetric, we show that disparities between the two populations will vanish on average in the long term, although in the short term disparities will continue to arise and dissipate cyclically. Further, the time an accumulated advantage takes to dissipate can be significant, and increases as a function of the relative importance of the program in conveying benefits. Interestingly, significant disparities can arise purely due to randomness even from completely symmetric initial conditions, especially when populations are small. The introduction of even a slight asymmetry, where the group that has accumulated an advantage becomes slightly preferred, leads to a completely different outcome. In these instances, starting from completely symmetric initial conditions, disparities between groups arise stochastically and then persist over time, yielding a permanent advantage for one group. Our analysis precisely characterizes conditions under which disparities persist or diminish, with a particular focus on the role of the scarcity of available spots in the program and its effectiveness. We also present extensive simulations in a richer model that further support our theoretical results in the simpler, stylized model. Our findings are relevant for the design and implementation of algorithmic fairness interventions in similar selection processes.

Control variates have seen recent interest as a powerful technique to reduce the variance of summary statistics measured from costly cosmological $N$-body simulations. Of particular interest are the class of control variates which are analytically calculable, such as the recently introduced 'Zeldovich control variates' for the power spectrum of matter and biased tracers. In this work we present the construction of perturbative control variates in Eulerian and Lagrangian perturbation theory, and adopt the matter bispectrum as a case study. Eulerian control variates are analytically tractable for all $n$-point functions, but we show that their correlation with the $N$-body $n$-point function decays at a rate proportional to the sum-of-squared wavenumbers, hampering their utility. We show that the Zeldovich approximation, while possessing an analytically calculable bispectrum, is less correlated at low-$k$ than its Eulerian counterpart. We introduce an alternative -- the 'shifted control variate' -- which can be constructed to have the correct tree-level $n$-point function, is Zeldovich-resummed, and in principle has an analytically tractable bispectrum. We find that applying this shifted control variate to the $z=0.5$ matter bispectrum is equivalent to averaging over $10^4$ simulations for the lowest-$k$ triangles considered. With a single $V=1({\rm Gpc}/h)^3$ $N$-body simulation, for a binning scheme with $N\approx 1400$ triangles from $k_{\rm min} = 0.04 h {\rm Mpc}^{-1}$ to $k_{\rm \max} = 0.47 h {\rm Mpc}^{-1}$, we obtain sub-2% precision for every triangle configuration measured. This work enables the development of accurate bispectrum emulators -- a probe of cosmology well-suited to simulation-based modeling -- and lays the theoretical groundwork to extend control variates for the entire $n$-point hierarchy.

A formal system called cologic is proposed for the study of compacta. A counterpart of countable model theory is developed for this system, and it is applied to model theory of the pseudo-arc.

We have obtained the binding energy of the deuteron on a quantum simulator using the variational quantum eigensolver for renormalization group (RG)-based low-momentum effective interactions. The binding energy (BE) has been calculated in the truncated harmonic oscillator (HO) basis, using the Qiskit-Aer simulator in both noise-free and noisy cases. The noise models have been taken from the actual IBM quantum hardware, and the results obtained have been extrapolated to the zero noise limit. The number of HO basis states (hence qubits) needed for computing the BE to within 1 percent of the experimental value in the quantum simulator, decreases with decreasing RG parameter $λ$. The $λ$-dependence of the extent of entanglement between the oscillator modes has been analysed.

We show that for a real rational homology sphere $Y$ equipped with a real $\mathrm{spin^c}$ structure $\mathfrak{s}$, the real monopole Floer homology defined by Li and the real Seiberg-Witten Floer homology defined by Konno, Miyazawa and Taniguchi are isomorphic. As corollaries, we identify some Froyshov-type invariants and prove two Smith-type inequalities.

(abridged) We aim to characterize kinematic processes in the G012.80 protocluster. We principally focus on the N$_2$H$^+$(1$-$0) emission to trace the dense and cold gas. Additionally, we use lines such as DCN(3$-$2), H41$α$, C$^{18}$O(1$-$0), and SiO(5$-$4), as well as continuum maps. We perform a N$_2$H$^+$ hyperfine spectral line fitting to analyze multiple velocity components and spectral parameters. We estimate velocity gradients, column densities, and line-mass profiles for the two main filaments in G012, named R1 and R2. Line-mass profiles follow $λ$($ω$) = 5660 M$_{\odot}$ pc$^{-1}$($ω$/pc)$^{0.30}$ (R1) and $λ$($ω$) = 6943 M$_{\odot}$ pc$^{-1}$($ω$/pc)$^{0.20}$ (R2), which are much larger than those of typical low-mass filaments. R1 and R2 show disparate position-velocity (PV) features. R1 exhibits a transverse velocity gradient of 10.4 kms$^{-1} $pc$^{-1}$ and few dense cores. This gradient is interpreted with a simple rotation toy model, combined with line-mass profile, and corresponds to a rotational timescale of 0.1 Myr. In contrast, R2 exhibits compact velocity structures ($Δ$V < 2 kms$^{-1}$), likely due to collapse, as evidenced by the presence of a comparatively large number of massive cores and protostellar outflows. R2 is forming prestellar and protostellar cores at a rate of 55.3 M$_{\odot}$ Myr$^{-1}$, with an efficiency similar to the Orion Integral Shaped Filament (ISF). The R1 filament, in contrast, lacks protostellar cores and only contains a few prestellar cores, resulting in an estimated SFR of 4.2 M$_{\odot}$ Myr$^{-1}$, more than an order of magnitude below that of R2. Combining these lines of evidence, we suggest that R1 is younger and still rotating, while R2 has evolved to collapse with a higher SFR. G012 thus hosts filaments at different evolutionary stages.

We present the Social Influence Game (SIG), a framework for modeling adversarial persuasion in social networks with an arbitrary number of competing players. Our goal is to provide a tractable and interpretable model of contested influence that scales to large systems while capturing the structural leverage points of networks. Each player allocates influence from a fixed budget to steer opinions that evolve under DeGroot dynamics, and we prove that the resulting optimization problem is a difference-of-convex program. To enable scalability, we develop an Iterated Linear (IL) solver that approximates player objectives with linear programs. In experiments on random and archetypical networks, IL achieves solutions within 7% of nonlinear solvers while being over 10x faster, scaling to large social networks. This paper lays a foundation for asymptotic analysis of contested influence in complex networks.

A growing number of introductory physics instructors are implementing active learning methods in their classrooms, and they are modifying the methods to fit their local instructional contexts. However, we lack a detailed framework for describing the range of what these instructor adaptations of active learning methods look like in practice. Existing studies apply structured protocols to classroom observations and report descriptive statistics, but this approach overlooks the complex nature of instruction. In this study, we apply network analysis to classroom observations to define a typology of active learning that considers the temporal and interactional nature of instructional practices. We use video data from 30 instructors at 27 institutions who implemented one of the following named active learning methods in their introductory physics or astronomy course: Investigative Science Learning Environment (ISLE), Peer Instruction, Tutorials, and Student-Centered Active Learning Environment with Upside-down Pedagogies (SCALE-UP). We identify five types of active learning instruction: clicker lecture, dialogic clicker lecture, dialogic lecture with short groupwork activities, short groupwork activities, and long groupwork activities. We find no significant relationship between these instruction types and the named active learning methods; instead, implementations of each of the four methods are spread across different instruction types. This result prompts a shift in the way we think and talk about active learning: the names of developed active learning methods may not actually reflect the specific activities that happen during instruction. We also find that student conceptual learning does not vary across the identified instruction types, suggesting that instructors may be flexible when modifying these methods without sacrificing effectiveness.

We explore the phenomenological consequences of non-minimal hidden sector interactions on observable correlations in the Higgs sector, mediated through the $\mathbb{Z}_2$-symmetric Higgs portal. Particular attention is given to non-standard momentum dependencies of the hidden sector scalar, which arise naturally in an effective field theory (EFT) framework, e.g. in Composite Scalar Dark Matter theories. We discuss the implications of such hidden sector interactions for the thermal history of the universe. We show that aspects of such non-standard momentum dependencies can be probed at future lepton colliders such as a FCC-ee, potentially also through radiative corrections. This gives rise to precision probes for regions where direct detection constraints and relic abundance can be accounted for as predicted in, e.g., Composite Scalar Dark Matter theories.

Deep learning offers new tools for portfolio optimization. We present an end-to-end framework that directly learns portfolio weights by combining Long Short-Term Memory (LSTM) networks to model temporal patterns, Graph Attention Networks (GAT) to capture evolving inter-stock relationships, and sentiment analysis of financial news to reflect market psychology. Unlike prior approaches, our model unifies these elements in a single pipeline that produces daily allocations. It avoids the traditional two-step process of forecasting asset returns and then applying mean--variance optimization (MVO), a sequence that can introduce instability. We evaluate the framework on nine U.S. stocks spanning six sectors, chosen to balance sector diversity and news coverage. In this setting, the model delivers higher cumulative returns and Sharpe ratios than equal-weighted and CAPM-based MVO benchmarks. Although the stock universe is limited, the results underscore the value of integrating price, relational, and sentiment signals for portfolio management and suggest promising directions for scaling the approach to larger, more diverse asset sets.

Consider a holomorphic contact manifold. Holomorphic discs tangent to the contact planes define a pseudometric on the manifold. This pseudometric integrates to a pseudodistance. When the pseudodistance is a distance, we call the contact manifold \emph{contact-hyperbolic}, by analogy with Kobayashi hyperbolicity. The goal of this paper is to construct explicit examples of contact-hyperbolic contact manifolds with large automorphism groups. We study Reeb manifolds: holomorphic contact structures equipped with a Reeb vector field whose flow acts freely. Our first main theorem shows that every proper Reeb manifold admits a holomorphic symplectic quotient. It also identifies which symplectic manifolds arise this way. The isomorphism classes of proper Reeb manifolds over a fixed symplectic base manifold are parameterised by the first cohomology. Our second main theorem: a proper Reeb manifold is (complete) contact-hyperbolic if and only if its symplectic quotient manifold is (complete) Kobayashi hyperbolic. This theorem allows us to construct many new explicit examples of contact-hyperbolic contact manifolds. Finally, we study the group of contact biholomorphisms. Contact hyperbolicity implies that this group is a finite-dimensional Lie group. For contact $3$-manifolds, we sharply bound the dimension of the automorphism group. We give examples with automorphism groups reaching every possible dimension. Our third main theorem: the unique maximally symmetric example, up to isomorphism, is the contact manifold $\mathbb B^2_{z,w}\times\mathbb C_y$ with contact form $dy+(1-z)^{-2}dw$.

The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields, while full Hilbert space treatments are often computationally prohibitive. To address these challenges, we develop a framework based on coupled stochastic processes with a common cross-covariance structure that can be easily coupled to various types of Maxwell solvers. Our approach accounts for the non-commutativity in the quantum-to-classical transition in a natural way, and has the ability to capture quantum optical signatures while retaining compatibility with classical electromagnetics. For benchmarking, we compare our simulation results with experimental emission spectra of a strongly driven InGaAs quantum dot, finding excellent agreement. Our results highlight the potential of tailored stochastic processes for simulating non-classical light in complex photonic environments.

We study the problem of hedging unit linked life insurance policies whose benefits depend on an investment fund that incorporates environmental criteria in its selection process. Offering these products poses two key challenges: constructing a green investment fund and developing a hedging strategy for policies written on that fund. We address these two problems separately. First, we design a portfolio selection rule driven by firms' carbon intensity that endogenously selects assets and avoids ad hoc pre-screens based on ESG scores. The effectiveness of our new portfolio selection method is tested using real market data. Second, we consider an insurance company issuing unit linked policies written on this fund. Such contracts are exposed to market, carbon, and mortality risk, which the insurance company seeks to hedge. Due to market incompleteness, we address the hedging problem via a quadratic approach aimed at minimizing the variance of the hedging costs. Finally, we also make a numerical analysis to assess the performance of the hedging strategy. For our simulation study, we use an efficient weak second-order scheme that allows for variance reduction.

We compute the trace of Frobenius on the sheaf of nearby cycles for the integral model of the Siegel modular variety with pro-p Iwahori level structure, constructed by Haines and Stroh, in the case of $\text{GSp}_4$. To this end, we make use of a semistable resolution of this model due to Shadrach. Finally, we compare our results with calculations made by Horn, confirming a conjecture of Haines and Kottwitz in this case.