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:
Past seminars:
Thursday 6th August, 1-2pm
Title: SMRI Seminar, ‘The monopolist’s free boundary problem in the plane: an excursion into the economic value of private information’
Speaker: Professor Robert McCann, University of Toronto
Venue: SMRI Seminar Room (A12 Macleay Building, Room 301)
Abstract: The principal-agent problem is an important paradigm in economic theory for studying the value of private information: the nonlinear pricing problem faced by a monopolist is one example; others include optimal taxation and auction design. For multidimensional spaces of consumers (i.e. agents) and products, Rochet and Chone (1998) reformulated this problem as a concave maximisation over the set of convex functions, by assuming agent preferences are bilinear in the product and agent parameters. This optimisation corresponds mathematically to a convexity-constrained obstacle problem. The solution is divided into multiple regions, according to the rank of the Hessian of the optimiser.
If the monopolists costs grow quadratically with the product type we show that a partially smooth free boundary delineates the region where it becomes efficient to customise products for individual buyers. We give the first correct solution of the problem on square domains, and discover new transitions from unbunched to targeted and from targeted to blunt bunching as market conditions become more and more favourable to the seller.
Based on joint work with Kelvin Shuangjian Zhang, Cale Rankin, and Lucas O’Brien in various combinations: [1] Math. Models Methods Appl. Sci. 34 (2024) 2351-2394; [2] J. Convex Anal. (Rockafellar 90 Issue), 32 (2) (2025) 579-584; [3] arXiv 2303.04937; [4] arXiv 2412.15505; [5] arXiv 2603.14100.
Thursday 30th July, 1-2pm
Title: SMRI Seminar, ‘AI and mathematical modelling education’
Speaker: Dr Kerri Spooner, Auckland University of Technology
Venue: SMRI Seminar Room (A12 Macleay Building, Room 301)
Abstract: Artificial Intelligence (AI) is rapidly becoming an integral part of our daily lives. Within education, AI has the potential to provide new opportunities to support teaching, learning and assessment across disciplines. Within mathematics education, AI tools such as ChatGPT, Copilot and other generative AI systems are increasingly being used to generate explanations, solve problems, provide feedback, visualise concepts and support mathematical reasoning. These developments present both opportunities and challenges for mathematics education, and in particular mathematical modelling education, where students are expected to formulate, analyse, interpret and validate models of authentic real-world situations.
This presentation explores AI primarily as a technological tool that, given the right circumstances, has the potential to enhance the teaching and learning of mathematical modelling. AI has the potential to support many stages of the modelling cycle, including information gathering, problem formulation, mathematical representation, computation, interpretation, communication and critical reflection. At the same time, the use of AI raises important pedagogical questions concerning students’ development of mathematical thinking, modelling competencies, critical evaluation of AI-generated outputs, and the appropriate role of AI within modelling activities.
While AI can reduce routine cognitive load and broaden access to sophisticated mathematical techniques, effective modelling still requires students to make assumptions, justify modelling decisions, evaluate the validity of results and communicate conclusions within context. Consequently, AI should be viewed as a tool that augments, not replaces, the mathematical reasoning and critical judgement that underpin successful modelling. Developing AI literacy alongside modelling competency will therefore become an increasingly important goal for mathematical modelling education.
Drawing on emerging research and examples primarily within tertiary education, this presentation examines practical ways in which AI can be integrated into mathematical modelling pedagogy while maintaining authentic student engagement with the modelling process. Recommendations for educators seeking to incorporate AI responsibly into modelling education will be discussed. Opportunities and open research questions concerning the role of AI as an innovative educational technology for mathematical modelling will be presented.
Thursday 16th July, 1-2pm
Title: SMRI Seminar, ‘Researching & teaching ethics in mathematics’
Speaker: Dr Maurice Chiodo, University of Cambridge & Founder and Principal Investigator of the Ethics in Mathematics Project
Venue: SMRI Seminar Room (A12 Macleay Building, Room 301)
Abstract: The dedicated study and teaching of ethics in mathematics is a relatively new endeavour, brought about by a recent increase in awareness of the impact mathematics, mathematical work, and mathematicians can have on wider society. There are very few groups dedicated to this, one of which being the Ethics in Mathematics Project. In this talk Dr Chiodo will introduce ethics in mathematics and give an overview of the core, foundational principles and ideas behind the project, outlining the insights it has developed. He will discuss how these have been used in both a research and teaching setting, and in particular, how these lead to more knowledge creation and student learning. He will share the resources they have put together, and how others might also make use of them to create material relevant for their own particular settings and teaching environments. Ethics in mathematics has come a long way in the 10 years since the project was set up, and is now at the point where anyone can “pick it up, run with it, and teach it” without having to carry out their own foundational research.
Thursday 25th June, 1-2 pm
Title: SMRI Seminar, ‘AI and Humanity’s Longest Conversation’
Speaker: Geordie Williamson, The University of Sydney
Venue: The Quad General Lecture Theatre (K2.05)
Abstract: Mathematics has been called humanity’s longest conversation. Observations of Euclid, Pythagoras, Euler and Poincaré still occupy the minds of mathematicians today. This conversation has experienced shocks and challenges, including the crisis of foundations in the early 20th century, and the first computer assisted proofs in the second half of the 20th century. We are currently in the midst of another shock, with the rise of formal proof and the first signs of AI systems helping to produce research-level mathematics. This raises questions of fundamental importance: How should mathematicians respond to AI? Will AI systems help (or hinder) our understanding of the mathematical world? Williamson will discuss some recent developments at the interface of mathematics and AI, with the aim of having a clearer picture of this unique point in the history of mathematics.
Thursday 11th June, 1-2pm
Title: SMRI Seminar, ‘Schubert calculus via puzzles’
Speaker: Allen Knutson, Cornell University
Venue: SMRI Seminar Room (A12 Macleay Building, Room 301)
Abstract: “Littlewood-Richardson numbers” come up in many places: the representation theory of the symmetric group and general linear groups, spectral problems involving Hermitian matrices, and intersection theory on the Grassmannian. The last problem admits many independent (and combinable) generalizations, all of which have formulæ for the intersection numbers, but only a few of which have manifestly positive formulæ. I’ll discuss the “puzzle” formalism for most of the sharpest positive formulae, due to me and Terry Tao and further developed with Paul Zinn-Justin. Time permitting, I’ll connect the rule to geometric representation theory of quantized loop algebras.
Thursday 4th June, 1pm (part 1) & 3pm (part 2)
Title: SMRI Seminar, ‘Periods and Irrationality’
Speaker: Frank Calegari, The University of Chicago
Venue: SMRI Seminar Room (A12 Macleay Building, Room 301)
Abstract: We give a broad introduction to methods (old and new) to understand the arithmetic properties of “periods”, a broad class of numbers (which we will define in the talk) including many of the most familiar constants in mathematics.
Thursday 30th April 2026
Title: SMRI Seminar, ‘Physical measures, intermittent dynamics and random walks’
Speaker: Ian Melbourne, University of Warwick
Abstract: The classical Birkhoff ergodic theorem discusses almost sure convergence of time averages to space averages. (It is a generalisation of the strong law of large numbers in probability theory.) However, in examples the almost sure convergence is often on a set of zero volume in phase space.
A physical measure is one where convergence of time averages to space averages holds for continuous observables on a set of positive volume. Equivalently, a physical measure is one that is the weak* limit of empirical measures on a set of positive volume.
We consider systems with no physical measure and characterise the weak* limits and distributional limits of empirical measures in such situations. Examples include intermittent maps, random walks on the integers and random walks on Y-shaped regions (imagine the integers with 3 (several) directions and 3 (several) points at infinity). As far as we know, our results are new even for the simple symmetric random walk on the integers.
This is joint work with Douglas Coates and Amin Talebi. Watch on YouTube.
Thursday 16th April 2026
Title: SMRI Seminar, ‘A physicist’s view on the assignment and optimal transport problems’
Speaker: Patrice Koehl, UC Davis
Abstract: Optimal transport (OT) has become a discipline by itself that offers solutions to a wide range of theoretical problems in probability and mathematics. Despite its appealing theoretical properties, solving the OT problem involves the resolution of a linear program whose computational cost can quickly become prohibitive whenever the size of the problem exceeds a few hundred points. The recent introduction of entropy regularization, however, has led to the development of fast algorithms for solving an approximate OT problem. The successes of those algorithms have resulted in a popularization of the applications of OT in several applied fields including geometry, machine learning, and in data sciences in general. Problems remain, however, as to the numerical convergence of those regularized approximations towards the actual OT solution. In addition, the physical meaning of this regularization is unclear. In this talk, I will describe a novel approach to solving the discrete balanced and unbalanced OT problems using techniques adapted from statistical physics. I will illustrate applications of this framework to the problem of image comparison as well as to the problem of comparing three dimensional shapes.
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.
Thursday 22nd January, 1-2pm
Title: SMRI Seminar, ‘Cohomology of p-adic period domains’
Speaker: David Hansen, National University of Singapore
Venue: SMRI Seminar Room (A12 Macleay Building, Room 301)
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.