High-purity Germanium (HPGe) detectors are a type of semiconductor detector that are commonly used to measure the radioactivity of detector materials used in the construction of particle physics experiments. Since all materials emit some level of radiation, it is crucial to accurately characterize their intrinsic radioactivity and select the least radioactive ones, particularly for detectors hunting for rare phenomena such as detecting the invisible matter of the universe. HPGe detectors are the ideal detectors for this purpose because of their exceptional energy resolution and sensitivity, enabling precise gamma-ray spectroscopy of trace contaminants in materials. At the University of California, Los Angeles, I work in a research laboratory that is commissioning a new HPGe detector to support the material assay campaign for next-generation dark matter experiments. My work focuses on developing a Geant4 Monte Carlo simulation to model the HPGe detector’s efficiency for different material compositions, geometries, positions, and sources. This presentation will describe the process of constructing my simulation in Geant4, discuss the validation process, as well as the comparative results between my simulation and in-situ measurements I have performed. This simulation allows us to accurately determine detector efficiency across a range of source geometries and materials, enabling reliable quantification of trace radioactivity.

The earliest chapters of an exoplanet’s life are the most dramatic— yet they are the least observed. Most known exoplanets are billions of years old, creating a knowledge gap that limits our ability to study planetary evolution since most evolutionary processes occur early, either when the planet is enshrouded by its natal disk, or within tens of millions of years of disk dispersal. The sampling bias arises due to the intrinsic rarity of young stars and due to the challenges associated with detecting transiting planets around stars that exhibit starspot and flare-induced variability. Recently, NASA’s Transiting Exoplanet Survey Satellite (TESS) has surveyed the Scorpius-Centaurus (Sco-Cen) Association, which is located 130 pc from Earth and which contains 90% of nearby pre-main sequence stars. Sco-Cen is an ideal region to search for young transiting exoplanets with typical ages of 5-15 Myr. I will summarize my recent work analyzing the new TESS data acquired from December 2024 to June 2025, which primarily covers the Lower Centaurus-Crux and Upper Scorpius regions of Sco-Cen. To isolate potential transits, I apply specialized windowed-sliders that assist in removing stellar variability while preserving transit-like signals. I will present my findings on candidate events and discuss the vetting and follow-up efforts underway. This work contributes to the growing effort to identify and characterize the youngest exoplanets in the solar neighborhood.

Randomized Kaczmarz is an iterative method for large-scale linear systems that, at each iteration, projects the current iterate onto the hyperplane defined by a single sampled equation <a_i, x> = b_i. This paper presents online Kaczmarz methods for the structured streaming setting, where samples (a_i, b_i) arrive from correlated latent sources and the solver seeks x satisfying  <a_i, x> ≈ b_i. Standard uniform sampling is inefficient: data points drawn from the same cluster produce redundant projection updates. This paper formalizes a structured source model in which each of m sources belongs to one of K latent clusters, with a-vectors generated as Gaussian perturbations of cluster prototypes. The Streaming Block Kaczmarz (SBK) algorithm is a structure-aware online solver that builds cluster representatives from streamed data and uses them to guide sample selection and form two-equation block updates. SBK requires no prior knowledge of the cluster structure, inferring it online via cosine similarity. In consistent systems, SBK substantially outperforms uniform sampling by exploiting block redundancies; in inconsistent systems, SBK can either accelerate convergence or diverge depending on the relative scales of data noise and right-hand-side inconsistency. These results highlight the promise of structure-aware streaming solvers and identify open questions around stability guarantees for inconsistent systems.

The projection (nearest point problem) onto an implicitly defined manifold arises in many areas of scientific computing and machine learning, and remains computationally challenging in high-dimensional, non-convex settings. In this work, we study methods to solve this problem for neural network robustness verification. Robustness requires that the distance to the decision boundary from an input exceeds 𝜀, which translates to a projection problem. We propose a novel approach using Riemannian Flow Matching, a framework for learning transport vector fields over implicit manifolds that can generate on-manifold samples, to approximate projections onto implicitly defined decision boundaries. To sample training data and to provide baselines, we use constrained gradient-based Markov Chain Monte Carlo to sample from the decision manifold and to approximate solutions to the projection problem. After learning a distribution supported on the manifold, we introduce guidance techniques that bias sample generation towards feasible and optimal samples for the nearest-point objective. One of the primary aims of this work is to establish theory on the guidance of Riemannian Flow Matching. Solving the projection problem for implicitly defined manifolds has many applications, and with the increasing use of neural networks in high-stakes settings, it is crucial to verify robustness efficiently and reliably. These preliminary results suggest that flow matching methods may be a promising framework for robustness verification.

Upcoming surveys will produce billions of galaxy images but comparatively few spectra, motivating models that learn cross-modal representations. We build a dataset of 134,533 galaxy images (HSC-PDR2) and spectra (DESI-DR1) and adapt a Multi-Modal Masked Autoencoder (MMAE) to embed both images and spectra in a shared representation. The MMAE is a transformer-based architecture, which we train by masking 75% of the data and reconstructing missing image and spectral tokens. We use this model to test three applications: spectral and image reconstruction from heavily masked data and redshift regression from images alone. It recovers key physical features, such as galaxy shapes, atomic emission line peaks, and broad continuum slopes, though it struggles with fine image details and line strengths. For redshift regression, the MMAE performs comparably or better than prior multi-modal models in terms of prediction scatter even when missing spectra in testing. These results highlight both the potential and limitations of masked autoencoders in astrophysics and motivate extensions to additional modalities, such as text, for foundation models.