We will explain how certain linear PDEs can be "geometrized" into projective surfaces, and conversely. Then, results obtained in joint work with Matthew Ryan (arXiv:2602.12644) will be applied to gain new insights into geometry associated to Appell's hypergeometric functions, an important class of functions that generalize the well known Gauss hypergeometric function. 

The Langlands program is a broad and influential framework in modern mathematics that seeks to relate seemingly different areas such as number theory, representation theory, and geometry. While its full theory lies far beyond the undergraduate level, its geometric incarnation has led to remarkable interactions with modern theoretical physics. In this expository talk, I will present an accessible introduction to the philosophy of the Langlands program, with particular emphasis on geometric Langlands and its conceptual connection to gauge theory, dualities, and mirror symmetry. I will discuss how geometric objects such as bundles and moduli spaces enter the picture, and why these structures also play an important role in ideas coming from quantum field theory and string theory. This talk is intended as a broad conceptual overview for undergraduate students interested in the interface of pure mathematics and fundamental physics.

Quantum computing makes classical encryption methods such as RSA obsolete. In response to that, several quantum-resistant cryptographic schemes have been submitted to NIST (National Institute of Standards and Technology) to replace the current quantum-vulnerable cryptographic standards. The Matrix Equivalence Digital Signature (MEDS) is one of the many schemes submitted. However, certain more advanced MEDS-based signature schemes involve repetition of the secret key. This talk discusses the complexity of retrieving the secrete key when repetition of the secrete key is involved in MEDS. 

Many infectious diseases, such as influenza, show clear seasonal patterns, with outbreaks occurring at certain times of the year. But why do these patterns arise, and how can mathematics help us understand them? In this talk, I will discuss mathematical models used to study the spread of infectious diseases, focusing on how seasonal changes such as weather, behavior, and contact patterns influence transmission. I will then highlight the role of randomness in disease spread, showing how chance events can determine whether an outbreak grows or fades out, even under similar conditions. Together, these ideas illustrate how mathematical models provide useful tools for understanding, predicting, and informing responses to real-world public health challenges.