This seminar series gives visitors and staff members the opportunity to explain the context and aims of their work. During semester, the SMRI seminar is usually on Thursdays from 1 pm — 2 pm, followed by afternoon tea. These research talks cover any field in the mathematical sciences, and should be presented in a way that is understandable and interesting to a broad audience. Seminar information and recordings can be found below and in the SMRI Seminar YouTube playlist.
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Upcoming:
SMRI Seminar
Patrice Koehl, UC Davis
Thursday 16th April 2026 at 1 pm, SMRI Seminar Room (A12 Macleay Room 301)
Abstract: TBA
Past:
SMRI Seminar, ‘Immune Dysregulation in COVID-19: What Can Mathematical Modeling Tell Us?‘
Hwayeon Ryu, Elon University
Thursday 26th March 2026
Abstract: Why do some people experience mild COVID-19 while others develop severe disease? A key part of the answer lies in how the immune system responds to viral infection. In this talk, I present a mathematical model of the interaction between SARS-CoV-2 and the immune system, focusing on the role of key immune components. While a well-coordinated immune response helps control the virus, its dysregulation can drive severe disease. Using simulations and sensitivity analysis, we explore how different immune responses lead to divergent outcomes and identify key mechanisms that shape disease progression. We also use the model to examine how potential interventions might alter these dynamics. This work highlights how mathematical modeling can provide insight into complex immune processes and inform our understanding of disease severity and potential treatment strategies. Watch on YouTube.
SMRI Seminar, ‘Mapping class groups and algebraic cycles‘
Richard Hain, Duke University
Thursday 12th March 2026
Abstract: The topology, geometry and arithmetic of moduli spaces of curves are well known to be intertwined. Many geometric properties of algebraic curves are reflected in the topology and geometry of the corresponding moduli space. In this talk I will give an overview of one aspect of this connection — namely results that relate algebraic cycles on powers C^n of a genus g curve C to the structure of the mapping class group of a closed surface of genus g. This is a subject with a rich history with roots in the work of Riemann and Abel in the 19th century.
I will review relevant background material, including the definition of and basic results about mapping class groups and algebraic cycles. I will explain why cycles that are defined for all curves, such as those defined by Ceresa and Gross–Schoen, are related to the Torelli subgroups of mapping class groups. If time permits, I will describe a new (higher) algebraic cycle defined for hyperelliptic curves that Wanlin Li and I have constructed. Watch on YouTube.
SMRI Seminar, ‘The Tait conjectures for classical, virtual, and welded knots‘
Hans Boden, McMaster University
Thursday 5th March 2026
Abstract: The Tait conjectures were originally posed in the 1900s but remained open for nearly 100 years. They were ultimately resolved in the late 1980s using the new (at the time) technology from quantum topology, namely the Jones polynomial. In a more recent development, Josh Greene found a geometric characterization of alternating knots as those that simultaneously bound positive and negative definite spanning surfaces, and he used this to give a new proof of the Tait conjectures. In this talk, I will survey some results obtained by adapting these methods to knots in thickened surfaces and virtual knots. Some of these results were derived from a previous productive visit to SMRI, and they represent a fruitful collaboration with Zsuzsi Dancso, Damian Lin, and Tilda Wilkinson-Finch. Watch on YouTube.
SMRI Seminar, ‘Learning Theory for Neural Operators’
Jakob Zech, Heidelberg University
Thursday 26th February, 2026
Abstract: In this talk, we present results on the approximability and data requirements necessary to learn surrogates of nonlinear mappings between infinite-dimensional spaces. Such surrogate models have a wide range of applications and can be used in uncertainty quantification and parameter estimation problems in fields such as classical mechanics, fluid mechanics, electrodynamics, and earth sciences. Our analysis shows that, for certain neural network architectures, empirical risk minimization based on noisy input-output pairs can overcome the curse of dimensionality. Additionally, we provide a numerical comparison to other approaches including classical constructive methods.
SMRI Seminar, ‘Cohomology of p-adic period domains’
David Hansen, National University of Singapore
Thursday 22nd January, 2026
Abstract: Since the pioneering work of Drinfeld, p-adic period domains have been a driving force behind many developments in nonarchimedean geometry. However, despite many advances, the basic question of computing their cohomology has remained completely open outside of a few very special cases treated by Drinfeld and Schneider-Stuhler over 30 years ago. In this talk I will present a general formula for the cohomology of these spaces. This formula is elementary, and it has several unusual features which suggest some very rich phenomenology. I will explain this formula and where it comes from, present several examples, and take the first steps towards unraveling the patterns this formula is hiding. Watch on YouTube.