The Thief Orienteering Problem (ThOP) is a discrete routing optimization problem that seeks to find the best possible sequence of items to collect along a feasible simple path connecting a pair of given terminals. ThOP is to be solved under strict limitations, including a time constraint. ThOP combines the following classic combinatorial optimization problems: the Knapsack Problem (KP) and the Orienteering Problem (OP). As such, each of the now subproblem's components become dependent. Existing dynamic programming approaches that can efficiently solve ThOP on directed acyclic graphs (DAGs) have motivated the study of graph transformations that extend these methods to broader classes of graphs. As supervised by Andrew Bloch-Hansen, this research continues to build on his previous work specifically considering ThOP on the following planar graph classes with maximum treewidth 2: 2-terminal series-parallel and outerplanar graphs. This research furthers the research by investigating ThOP on Halin graphs. Halin graphs are also planar, but have a maximum treewidth of 3, meaning, when compared to a tree graph structure, wherein only one unique simple path exists between any pair of vertices, a Halin graph is structurally more complex than either a series-parallel or outerplanar graph. Complementing the theoretical work, implementation efforts included coding exact and polynomial-time approximation scheme (PTAS) dynamic programming solvers, and supporting software infrastructure, for ThOP based off Bloch-Hansen's previous publications, in Python. This research was completed over the 2026 summer in parallel with other undergraduate students also supervised by Bloch-Hansen: Ayla Ventura, Yacob Mesfun, and Yanishka Gahlot. Overall, this research aimed to identify graph structures and families that admit efficient DAG transformations and thereby expand the applicability of dynamic programming methods for solving ThOP.

Many graph problems become easier to solve when the graph is a directed acyclic graph (DAG), but many real-world graph classes contain cycles. This presentation explores the problem of transforming cyclic graph classes into DAGs while preserving all valid traversals required for the Thief Orienteering Problem (ThOP). We examine transformation techniques based on edge orientation and vertex duplication. We also investigate how graph properties such as pathwidth may help explain the complexity of these transformations and predict their growth as graph structure becomes more complex.

Automatic speech recognition (ASR) is a crucial accessibility technology for many populations, yet the people who rely on it the most tend to see the worst performance. Modern speaker-independent ASR systems such as OpenAI's Whisper present a tantalizing promise of high out-of-the-box performance for English language transcription, without the need for lengthy speaker enrollment processes common with previous generations of ASR technology. However, exceptional benchmark accuracy easily drops to 30% error rates or worse for anyone who isn't a young, able, white female American. Fine-tuning can improve speech recognition accuracy by improving coverage of under-represented speech features in the model, but existing processes for fine-tuning Whisper present a major technical barrier for laypeople seeking to improve ASR accuracy for their own voice and accessibility needs. 

I present a software implementation project that automates the technically challenging aspects of data gathering, preparation, and fine-tuning the Whisper tiny.en speech recognition model. Preliminary results show that for a single speaker, marked improvements in ASR accuracy are possible with a limited amount of audio data. 

Researching abstract math is not as complicated as it might sound. Really, research is as much, if not more, about learning as it is about writing new things. In this presentation, I will discuss my experience doing math research, a little about the conclusions of that research, as well as what (in my opinion) abstract math is all about. 

The multi-trip capacitated prize-collecting vehicle routing problem (MT-CPC-VRP) with depot release dates generalizes classical VRP by allowing multiple depot-to-depot trips per vehicle within a workday horizon, treating customer visits as optional and profit-maximizing, and restricting service by release date. This combination is common in same-day delivery and field-service settings but underrepresented in the routing literature.

This work builds an experiment framework for the MT-CPC-VRP and implements multiple solution methods: an exact CPLEX-based formulation, an exact bitmask dynamic-programming solver, and a heuristic label-setting algorithm that constructs feasible depot-to-depot trips while pruning dominated partial routes. An independent evaluator recomputes feasibility and profit from returned solutions rather than trusting solver-reported values.

These baselines establish the performance floor and ceiling against which an upcoming adaptive large neighborhood search (ALNS) metaheuristic will be benchmarked.