Applications of Partial Differential Equations to Convex Geometry

These notes were written following a summer mini-course given by the author at the XXIII School of Mathematics Lluis Santaló held at the Universidad Internacional Menendez Pelayo (UIMP) in Santander, Spain, in 2024. The course comprised four one-hour lectures and introduced geometric equations, with particular emphasis on applications in convex geometry. The notes start by exploring standard parametrizations of smooth convex bodies and their connection to various curvature measures. Fundamental tools such as the inverse Gauss map parametrization and the support function are introduced, resulting in the derivation of the curvature function of a convex body in spherical coordinates. These tools are employed to discuss problems of prescribing surface areas, framed as Monge-Ampère type equations and related elliptic partial differential equations on the sphere, and to present some characterizations of ellipsoids and Euclidean balls. The last part of the course turns to curvature flows as geometric parabolic partial differential equations. These equations are presented both as techniques for establishing the existence of convex bodies with prescribed curvature properties and as methods for proving geometric inequalities. The material, intended to be accessible to students with only basic prior knowledge of differential equations, serves as an entry point to more advanced topics in geometric analysis and PDEs in convex geometry. References have been kept to a minimum, limited to those that are both essential and of broader relevance, and from which the interested reader may pursue more specialized developments

Still on Stage! Engaging Children in Telling and Acting Out Stories to Impact Learning

This article focuses on story dictation and story acting in preschool classrooms, including tips for educators gleaned from own research and the research of others. The final version of the article appears in the spring 2026 issue of the journal Young Children celebrating 100 years of work by the National Association for the Education of Young Children (NAEYC)

On Certain Infinitesimal Homothetic Conditions in Affine Geometry

We prove new results in which the homothety between a smooth convex body with positive Gauss curvature and certain small parameter deformation of it implies that the convex body is an ellipsoid. We also introduce a new convex body determined by an affine invariant construction similar to that of the convex floating body

Files and Databases - Notes

Notes for Files and Database

Towards best practices in low-dimensional semi-supervised latent Bayesian optimization for the design of antimicrobial peptides

Generative deep learning techniques have demonstrated an impressive capacity for tackling biomolecular design problems in recent years. Despite their high performance, however, they still suffer from a lack of interpretability and rigorous quantification of associated search spaces, which are necessary to unlock their full potential for scientific inquiry beyond efficient design. An area in which they are of particular interest is in the design of antimicrobial peptides, which are a promising class of therapeutics to treat bacterial infections. Discovering and designing such peptides is difficult because of the vast number of possible sequences and comparatively small amount of experimental information. In this work, we perform an empirical} investigation of latent Bayesian optimization for searching through peptide sequence spaces, with a focus on antimicrobial peptides. We investigate (1) whether searching through a dimensionally-reduced variant of the latent design space may facilitate optimization, (2) how organizing latent spaces by differing amounts of more and less relevant information may improve the efficiency of arriving at an optimal peptide design, and (3) the interpretability of the spaces. We find that employing a dimensionally-reduced version of the latent space is more interpretable and can be advantageous, while the use of less-relevant but more easily-computable physicochemical properties is advantageous to latent space organization in certain contexts and the use of more-relevant but sparser properties associated with the latent Bayesian objective function is advantageous in others. This work lays crucial groundwork for biophysically-motivated peptide design procedures, with an especial focus on antimicrobial peptides

Database of Women, Gender, and Sexuality Programs in Canada

This database draws on available information on women, gender, and/or sexuality programs in Canadian universities. The dataset was collected between 2025-2026 and drew on information on Universities Canada in addition to departmental and program websites, calendars, and other publicly available information. The dataset includes core courses available on university program websites and details on whether experiential learning opportunities are available

Deploying and Evaluating a Conversational Agent Using LLMs for Academic Library Reference

This study has two aims. First, we sought to implement a RAG-based GenAI system capable of answering reference questions. Second, we aimed to develop an evaluation protocol to assess the chatbot by means of comparing implementations that use three different LLMs. An evaluation rubric was piloted to gauge its viability as an assessment tool. The RAG-based chatbot uses a two-step approach. First, in response to a query, the system retrieves relevant documents from a knowledge base. Each document is vectorized and matched by relevance. Second, retrieved data is combined with an LLM's generative capabilities to produce a context-aware response. Fourteen common questions representing different areas of the knowledge base were tested with the chatbot versions. The research team developed and then used an evaluation rubric to score the chatbots’ responses according to: accuracy, groundedness, elicitation, completeness, and further assistance. The rubric was also evaluated by calculating the standard deviation among reviewers’ scores. The RAG implementations were largely successful in restricting the chatbot’s responses to the knowledge base. The evaluation rubric was effective for assessing the models, highlighting each’s strengths and weaknesses. Despite the evaluation being subjective, the evaluators gave similar scores, with the greatest variation in the elicitation dimension. This study offers a technical description of a practical way to implement a RAG-based chatbot in a library setting as well as a protocol for evaluating such chatbots in multiple dimensions that hasn’t been discussed in previous literature

Files and Databases Class Notes

Class notes for a course in Files and Database

Court

COURT is a ceramic installation and written thesis that examines how space is held and what happens when that holding is tested. Space is understood as a lived and psychological condition shaped by bodies, objects, and systems of relation. Everyday operations such as stacking, storing, measuring, transporting, defending, and resting accumulate into infrastructures that guide patterns that dictate what can be maintained and what cannot. The project explores the fragility of infrastructures and the tension between individual and collective needs. Through an arrangement of ceramic spheres, COURT considers how meaning accumulates when a single form is repeatedly assembled into a larger co-dependent network. The installation appears stable yet remains at risk of collapse, revealing the ambivalence embedded in shared space

Postpartum Posttraumatic Growth: An Arts-Based Heuristic Inquiry

A significant amount of people who give birth are affected by traumatic birth experiences (TBE), but research shows that there is potential for achieving posttraumatic growth (PTG) following such events. There is growing evidence of art therapy’s efficacy within treatment for survivors of trauma, and promising research demonstrates the potential for art therapy interventions to facilitate and measure PTG. This arts-based heuristic inquiry explores what insights a student-researcher with lived TBE can gain about posttraumatic growth. The arts-based component of this project consists of five artworks and writings created through the Open Studio Process (OSP), and a painting made in the creative synthesis phase of the heuristic inquiry. The project uses Reflexive Thematic Analysis to analyze the data sets generated through the OSP. Key findings of this inquiry suggest that a) the OSP may facilitate and contain deliberate rumination about TBE, with potential to produce insight about PTG; and b) there was a struggle with notions of success and failure throughout all OSP rounds that were connected to deeply held core values and negative core beliefs. The results could inform possible future art therapy intervention research integrating the OSP, and possibly aspects of PTG, with exploration of TBE. The struggle with ideas of success and failure in childbirth carries significance for countertransference for art therapists with lived experience of TBE who work with clients who have given birth