Spring 2026
Time & Location: Typically talks will be in TBA at 3:00 pm on a Friday.
Organizers: Chen, Hongfei and Gkogkou, Aikaterini
January 16, 2026
Applied and Computational
Title: Soliton Gas: recent results in one and two dimensions
Speaker: Giacomo Roberti - Northumbria University Newcastle, UK (Host: Kenneth McLaughlin)
Abstract: The concept of integrable turbulence, introduced by Zakharov in 2009, provides a framework for describing random nonlinear dispersive waves governed by integrable equations, such as the Korteweg–de Vries (KdV) and the focusing nonlinear Schrödinger (fNLS) equations.
Within this framework, we focus on a specialized class of integrable turbulence dominated by solitons, known as a soliton gas, first introduced by Zakharov in 1971.
In recent years, there has been rapidly growing interest in soliton gas theory and its applications, as soliton gas dynamics have been shown to underpin a wide range of fundamental nonlinear wave phenomena, including modulational instability and the formation of rogue waves.
In this talk, we present recent results on one-dimensional soliton gases, with particular emphasis on the collision of monochromatic soliton gases, as well as recent extensions of the theory to two-dimensional soliton gases.
Time: 3:00 PM
Location: Gibson Hall 126
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April 03, 2026
Applied and Computational Math
Title: Understanding the Matching Layer in Retrieval-Augmented Generation
Speaker: Jeonghoon Kim - Microsoft Host: (Sang Eun Lee)
Abstract: Retrieval-Augmented Generation (RAG) has emerged as an important paradigm for improving large language model systems by grounding generation in external knowledge, and it is now widely used in modern AI applications. In practice, the quality of a RAG system often depends critically on its matching layer, which determines what evidence is retrieved and made available to the generator. This talk focuses on the matching layer through the lens of relevance, ranking, and retrieval quality. We begin with a brief overview of the RAG pipeline used in industry and then focus on how query–document relevance is modeled and computed. In particular, we trace the progression from discrete lexical retrieval methods such as BM25 to continuous semantic representations, and then to more advanced interaction and fusion methods. Finally, we discuss system-level constraints and practical challenges in deploying RAG systems.
Time: 3:00 PM
Location: Gibson Hall 126
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April 10, 2026
Applied and Computational Math
Title: Topological Data Analysis of Biological Aggregations
Speaker: Lori Ziegelmeier - Macalester College Host: (Hongfei Chen)
Abstract: A time-varying collection of metric spaces as formed, for example, by a moving school of fish or flock of birds, can contain a vast amount of information. There is often a need to simplify or summarize the dynamic behavior. Algebraic topology can provide a lens to understand complex data by studying its shape. One such method is a crocker plot, a 2-dimensional image that displays the topological information at all times simultaneously. We discuss how this method has shown promise in a variety of contexts: to perform exploratory data analysis, to choose between two models of collective motion, and to investigate parameter recovery via machine learning. We also empirically quantify the stability of crocker plots with respect to noise, random particle deletion, and finite-size effects in various self-propelled particle models that exhibit collective behavior and phase separation.
Time: 3:00 PM
Location: Gibson Hall 126
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April 17, 2026
Applied and Computational Math
Title: Biofilm Rheology: Properties, Applications, and Uncertainty
Speaker: Nick Cogan - Florida State University Host: (Fauci Lisa & Hongfei Chen)
Abstract: Biofilms—communities of bacteria encased in a self-produced extracellular matrix—exhibit unique mechanical properties that are essential to their formation, persistence, and adaptation to environmental conditions. These properties emerge dynamically as biofilms interact with their physical and chemical surroundings.
Recent advances have provided deeper insights into the structural composition of the biofilm matrix and the genetic regulation of its polymeric constituents. In this talk, we will examine longitudinal rheological observations of mutant biofilm strains to elucidate the role of specific polymer types within the matrix. Additionally, from a mathematical perspective, we will explore parametric uncertainty and forward uncertainty propagation, discussing their implications for previous studies and future research directions.
Time: 3:00 PM
Location: Gibson Hall 126
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