Upcoming Seminars
To receive notification of current SMRI seminars and other relevant seminars at the University of Sydney and affiliate organisations, please subscribe to the weekly seminar email update.
SMRI Afternoon Teas take place on Thursday afternoons at 2pm on the Quadrangle Terrace, accessed through A14-04-L4.36 (in the SMRI Common Room in case of bad weather).
One School Seminar
Blackbox Optimisation Algorithms
Lindon Roberts, School of Mathematics and Statistics, University of Sydney
Time and date: 13:00–14:00 AEDT, Thursday 12 October
Location: Carslaw 375 and online via Zoom (registration link)
Abstract: Numerical optimisation—being able to find maxima/minima of functions—is an important part in numerical analysis, with many applications across different disciplines. This problem becomes much harder if only limited information about the functions is available—no analytic expression and/or no exact function values available, for example. In this case, specialised techniques known as ‘blackbox optimisation’ must be used. In this talk, I will give an overview of some useful techniques for blackbox optimisation and some recent work on improving the scalability of these techniques using tools from random matrix theory.
About Our Seminars
SMRI hosts a number of seminar series, and recordings of most SMRI seminars are available on the SMRI YouTube channel. The main streams include the following:
SMRI Seminars
This seminar series gives visitors and staff members the opportunity to explain the context and aims of their work. 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 under “Past Seminars” below and in the SMRI Seminar YouTube playlist.
To receive notifications of upcoming seminars in this series (excludes other seminar series), please subscribe to the weekly SMRI Seminar email update.
SMRI What is … ? Seminar
Each talk in this series is about an idea, concept or method that the speaker has found surprising, useful or intriguing, and which they would like to share with colleagues and students. The talk answers a question of the form “What is…?” and is directed at a broad audience of non-experts and experts alike. There is ample time for discussion, comments and questions. This talk may also serve as a prelude to a more technical talk in a specialised seminar series.
Seminar information and recordings can be found under “Past Seminars” below and in the ‘What is…?’ Seminar YouTube playlist.
Algebra Seminars co-presented by SMRI
Algebra Seminars (2022 onwards), and former SMRI Algebra and Geometry Online (SAGO) seminars are specialised research talks by international researchers in algebra and geometry.
Seminar information and recordings can be found under “Past Seminars” below and in the SAGO YouTube playlist (2020-2021 talks).
Related talks will now be hosted under the University of Sydney Algebra Seminar series, for which SMRI occasionally organises online talks.
One School Seminar
This seminar series aims to facilitate sharing and learning about the research of our fellow staff members. Early and mid-career researchers will present a broader context of their work which should be accessible and relatable to the entire School community. Seminars will be held in-person, followed by a friendly gathering and refreshments in the SMRI common room or out on the terrace (weather permitting). Everyone is warmly invited.
D-Modules and Representation Theory (SMRI Course, Semester Two 2023)
Semester Two, 2023 course presented by Dragan Milicic, Geordie Williamson and others: D-Modules website
D-modules provide an algebraic language for studying systems of linear partial differential equations. In some sense, the idea goes back to Riemann: rather than studying some complicated function directly, study the equations which it satisfies and try relate these equations on different spaces. D-modules have found major applications in representation theory, algebraic analysis, algebraic geometry and mathematical physics.
This course will introduce the basics of the theory of algebraic D-modules (following some famous notes of Bernstein). The localisation theorem of Beilinson and Bernstein will be discussed in detail. We will then move on to other applications in representation theory. Namely, we hope to explain how certain old results of Harish-Chandra and Langlands become quite transparent in the language of D-modules.
Seminar information and recordings can be found below and in the D-Modules YouTube playlist.
Modular Representation Theory (SMRI Course, Semester One 2023)
Course organised by Geordie Williamson and Chris Hone: Modular Representation Theory website.
Seminar information and recordings can be found below and in the YouTube playlist.
Machine Learning for the Working Mathematician (SMRI Course, Semester One 2022)
Machine Learning for the Working Mathematician website
The Machine Learning for the Working Mathematician seminar is an introduction to ways in which machine learning (and in particular deep learning) has been used to solve problems in mathematics, organised by Joel Gibson, Georg Gottwald, and Geordie Williamson.
We aim for a toolbox of simple examples, where one can get a grasp on what machine learning can and cannot do. We want to emphasise techniques in machine learning as tools that can be used by working mathematics researchers, rather than a source of problems in themselves. The first six weeks or so will be introductory, and the second six weeks will feature talks from experts on applications.
View the YouTube playlist.
Mathematical Challenges in AI (SMRI Course, Semester Two 2023)
Mathematical Challenges in AI website
This series is the successor of Machine Learning for the Working Mathematician.
The main focus will be to explore the mathematical problems that arise in modern machine learning. For example, we aim to cover:
1) Mathematical problems (e.g. in linear algebra and probability theory) whose resolution would assist the design, implementation and understanding of current AI models.
2) Mathematical problems or results resulting from interpretability of ML models.
3) Mathematical questions posing challenges for AI systems.
Our aim is to attract interested mathematicians to what we see as a fascinating and important source of new research directions.
View the YouTube playlist.
Other SMRI Courses
Visitors regularly give lecture series and mini courses at SMRI.
- Hilbert schemes (September–December 2020). Speakers: Anthony Henderson, Emily Cliff, Joe Baine, Anthony Licata, Joshua Ciappara, Peter McNamara
- Langlands correspondence and Bezrukavnikov’s equivalence (March 2019–July 2020, recordings April–July 2020). Speaker: Geordie Williamson
Other seminar series organised by SMRI & staff in the School of Mathematics and Statistics
- Informal Friday Seminars: the IFS is a working group meeting at SMRI
- Sydney Dynamics Group seminars
- Asia-Pacific Analysis and PDE Seminar series
- Australian Geometric Topology Webinar series
- (GT)2 Graduate Talks in Geometry and Topology at the University of Sydney, supported by MATRIX and AMSI
- Recent Progress in Mathematics and Statistics
- Seminars of the School of Mathematics and Statistics can be viewed on the School’s upcoming Seminars & Conferences page
AMSI-MSRI Winter School 2022
SMRI Director Geordie Williamson was an invited speaker at the AMSI-MSRI Winter School, hosted over two weeks (20 June–1 July 2022) at the University of Queensland. He presented five lectures on Kazhdan-Lusztig Polynomials: Representation, Geometry and Combinatorics.
The Winter School full playlist can be viewed on YouTube.
Past Seminars
2023 Seminars
Abstracts and links to YouTube recordings (board talks are not recorded)
Renjie Feng (University of Cambridge): A quick introduction to random matrices and extreme gap problems
Date: Thursday 21 September
Abstract: Random matrices are studied in various mathematical areas, including statistics, high-energy physics, statistical physics, number theory, (quantum) information theory, numerical analysis, integrable systems, string theory, and more. I will first introduce two types of random matrices and discuss classical results such as the semicircle law and the Tracy-Widom law. Then I will provide several examples in statistical physics and representation theory where the Tracy-Widom law surprisingly
emerges. Finally, I will present our recent findings regarding extreme gap problems in classical random matrices and propose several conjectures.
Zoe Wyatt (University of Cambridge): Stability problems in general relativity
Date: Thursday 31 August
Abstract: Einstein’s theory of general relativity makes spectacular predictions, like gravitational waves, about our universe. For the mathematician, the analysis of the hyperbolic Einstein equations is one of the most powerful ways to understand conceptual questions of the theory. In this talk, I will explain some of the contributions of mathematics to general relativity, highlighting a recent joint work showing the stability of Kaluza-Klein spacetimes. These are important models in supergravity and their stability is connected to claims of Penrose and Witten.
Franz Pedit (University of Massachusetts, Amherst): Minimal Lagrangian surfaces of high genus in CP2
Date: Thursday 24 August
Abstract: The study of properties of surfaces in space has historically been a fertile ground for advances in topology, analysis, geometry, Lie theory, and mathematical physics. The most important surface classes are those which arise form variational problems, for example, minimal surfaces which are critical points of the area functional. The Euler Lagrange equations are PDEs which serve as model cases for developments in geometric analysis. Often these equations exhibit large (sometimes infinite dimensional) symmetry groups which puts the theory into the realm of integrable systems, that is, PDEs which allow for an infinte hierarchy of conserved quantities. This theory has been studied extensively over the past 40 years and led to significant advances in the classification of (minimal, constant mean curvature, Willmore etc.) surfaces of genus one. The higher genus case has been more illusive and examples are usually constructed using non-linear perturbation theory and gluing techniques.
In this talk I will explain how one can use ideas from integrable systems to construct examples of high genus minmal Lagrangian surfaces without recourse to hard analysis.
This approach is more explicit than PDE existence results and one is able to obtain more quantitative information about the constructed examples, for instance, asymptotic area/energy estimates. I will also give a brief overview of the historical developments and the significance of minimal Lagrangian surfaces in mathematical physics.
Iva Halacheva (Northeastern University): What is a cactus group?
‘What is …?’ Seminar
Date: Thursday 3 August
Abstract: The braid group is a classical algebraic object with an intuitively natural presentation via stacking pictures of braided strands. One point of view which makes them interesting to topologists is the interpretation of braid groups as the fundamental groups of certain configuration spaces. Braid groups also play a central role in representation theory through the Yang-Baxter equation, where they capture the symmetries of quantum group representations. The cactus group is a close relative of the braid group whose properties are yet to be fully explored. Cactus groups can also be viewed as the fundamental groups of interesting topological spaces and have recently been linked to combinatorial structures associated with quantum groups. I will describe the construction of the cactus group and outline some of the settings in which it appears.
Peng Lu (University of Oregon): Conformal Bach flow
Date: Thursday 10 August
Abstract: We introduce conformal Bach flow and establish its well-posedness on closed manifolds. We also obtain its backward uniqueness. To give an attempt to study the long-time behavior of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi’s type $L^2$-estimate of derivatives of curvatures are derived.
To make the talk more accessible, we will spend some time to survey on high order parabolic curvature flow. This is a joint work with Jiaqi Chen of Xiamen University and Jie Qing of UCSC.
Jose Carrillo (University of Oxford): Nonlocal Aggregation-Diffusion Equations: fast diffusion and partial concentration
Date: Thursday 20 July
Abstract: We will discuss several recent results for aggregation-diffusion equations related to partial concentration of the density of particles. Nonlinear diffusions with homogeneous kernels will be reviewed quickly in the case of degenerate diffusions to have a full picture of the problem. Most of the talk will be devoted to discuss the less explored case of fast diffusion with homogeneous kernels with positive powers. We will first concentrate in the case of stationary solutions by looking at minimisers of the associated free energy showing that the minimiser must consist of a regular smooth solution with singularity at the origin plus possibly a partial concentration of the mass at the origin. We will give necessary conditions for this partial mass concentration to and not to happen. We will then look at the related evolution problem and show that for a given confinement potential this concentration happens in infinite time under certain conditions. We will briefly discuss the latest developments when we introduce the aggregation term. This talk is based on a series of works in collaboration with M. Delgadino, J. Dolbeault, A. Fernandez, R. Frank, D. Gomez-Castro, F. Hoffmann, M. Lewin, and J. L. Vazquez.
Bob Rink (Vrije Universiteit Amsterdam): What is the parametrization method in dynamical systems?
‘What is …?’ Seminar
Date: Thursday 11 May
Abstract: The parametrization method is a tool to compute invariant manifolds in dynamical systems, such as periodic orbits, (un-)stable manifolds, slow manifolds and invariant tori. The idea behind the method is simple: it works by (algorithmically) finding an embedding of the invariant manifold together with a representation of its dynamics in a coordinate chart. De La Llave et al realized that the method can nicely be combined with ideas from rigorous numerics, to provide computer-assisted proofs for the existence of invariant manifolds. Others, including myself, have used the method to compute high-precision approximations of the dynamics on the invariant manifolds. I will discuss both approaches, starting with the basics and finishing with an unpublished result on high-order phase reduction.
Speaker bio: Bob Rink is a professor of mathematical analysis at the Vrije Universiteit Amsterdam, The Netherlands. He obtained his PhD in 2003 from Utrecht University, after which he was an EPSRC postdoctoral fellow at Imperial College London. He came to the Vrije Universiteit Amsterdam in 2007, where he became full professor in 2016. His research is in various directions of dynamical systems, with a focus on network dynamics and bifurcation theory.
Robert Gray (University of East Anglia): Subgroups of inverse monoids via the geometry of their Cayley graphs
Date: Thursday 4 May
Abstract: In the 1960s Higman was able to characterize the finitely generated subgroups of finitely presented groups, that is, groups defined using a finite set of generators and finite set of defining relations. His result, which is called the Higman Embedding Theorem, is a key result in combinatorial group theory which makes precise the connection between group presentations and logic. In this talk I will present a result of a similar flavour, proved in recent joint work with Mark Kambites (Manchester), in which we characterise the groups of units of inverse monoids defined by presentation where all the defining relators are of the form w=1. I will explain what an inverse monoid is, the motivation for studying this class of inverse monoids, and also outline some of the geometric ideas that we developed in order to prove our results.
Speaker bio: Robert Gray is a Reader in Pure Mathematics and an EPSRC Research Fellow at the University of East Anglia in the UK. His research lies at the interface of algebra, logic, and theoretical computer science. A central theme in his recent research has been the study of certain fundamental algorithmic questions for infinite groups, monoids and inverse semigroups, using methods from infinite combinatorics, topology, geometry and theoretical computer science.
Jonathan James Wylie (City University of Hong Kong): Unexpected Behaviour in Dilute Granular Materials
Date: Thursday 27 April
Abstract: The phrase ‘granular material’ is used to describe a large number of discrete solid, macroscopic particles that lose energy whenever the particles collide. One might naively imagine that such systems would exhibit similar behaviour to traditional fluid and solid mechanics. However, we present two problems that superficially appear to be extremely simple but yield surprisingly rich dynamics that have no analogue in traditional mechanics. Firstly, we consider a dilute stream of particles that collides with an oblique planar wall. Secondly, we show several surprising phenomena that occur in an extremely simple system of a single frictionless, inelastic, spherical particle falling under gravity through a symmetric funnel.
Speaker bio: Jonathan Wylie obtained his PhD and was subsequently awarded a Junior Research Fellowship from King’s College, Cambridge. He then held research fellow positions in Woods Hole Oceanographic Institution and the University of Toronto before joining the City University of Hong Kong. His research interests include fluid mechanics, granular materials, ion transport and the mathematical modelling of geophysical systems.
Sándor Kovács (University of Washington): What is the parametrization method in dynamical systems?
‘What is …?’ Seminar
Date: Thursday 20 April
Abstract: Max Noether said that algebraic curves were created by God and algebraic surfaces by the Devil. Unfortunately, that description seems to be also valid for the moduli theory of these objects respectively. I will recall one of the first obstacles one faces when trying to extend the basic results of the moduli theory of curves to that of surfaces and then discuss how one may resolve the arising issue. Time permitting I will also explain the various stability conditions this problem and its resolution led to.
Speaker bio: Sándor Kovács is a Professor of Mathematics at the University of Washington. He received his BS degree at Eötvös University in his native country of Hungary, and his PhD at the University of Utah. He held positions at MIT and the University of Chicago before moving to the University of Washington. He received the National Science Foundation’s Faculty Early Career Development Award, the American Mathematical Society’s Centennial Research Fellowship, an Alfred P. Sloan Foundation Research Fellowship, and two Simons Foundation Fellowships, one of which he is currently holding. He is a Fellow of the American Mathematical Society.
Nathan Duignan (University of Sydney): Perspectives on Dynamical Systems and Their Application to Nuclear Fusion
One School Seminar
Date: Thursday 6 April
Abstract: Historically, research of dynamical systems involved finding quantitative, explicit solutions to the defining differential equations. This was an almost purely analytic perspective of dynamical systems. <br>Over the past century, many fields of Mathematics have brought a new perspective on dynamical systems. With these new perspectives has come new fruits; insights and qualitative information about solutions to the system. <br>In this talk I will show how a combination of a geometric, topological, and algebraic perspective of dynamical systems has allowed me (and friends) to make new progress toward nuclear fusion confinement.
Jie Yen Fan (University of Sydney): Mimicking: martingales with matching marginals
One School Seminar
Date: Thursday 30 March
Abstract: Motivated by questions from finance, we are interested in constructing new processes from existing ones while preserving certain desired properties. In particular, starting from a martingale, we construct new martingales that have the same marginal distributions as the original process. We call this mimicking. This allows us to develop alternative (and hopefully better) models for asset price while retaining the (European) option prices. In this talk, I will give an overview of mimicking and some examples
Greg Yang (Microsoft Research Lab): The unreasonable effectiveness of mathematics in large scale deep learning
Date: Thursday 23 March
Abstract: Recently, the theory of infinite-width neural networks led to the first technology, mu Transfer, for tuning enormous neural networks that are too expensive to train more than once. For example, this allowed us to tune the 6.7 billion parameter version of GPT-3 using only 7% of its pretraining compute budget, and with some asterisks, we get a performance comparable to the original GPT-3 model with twice the parameter count. In this talk, I will explain the core insight behind this theory. In fact, this is an instance of what I call the *Optimal Scaling Thesis*, which connects infinite-size limits for general notions of “size” to the optimal design of large models in practice, illustrating a way for theory to reliably guide the future of AI. I’ll end with several concrete key mathematical research questions whose resolutions will have incredible impact on how practitioners scale up their NNs.
Speaker bio: Greg Yang is a researcher at Microsoft Research in Redmond, Washington. He joined MSR after he obtained Bachelor’s in Mathematics and Master’s degrees in Computer Science from Harvard University, respectively advised by ST Yau and Alexander Rush. He won the Hoopes prize at Harvard for best undergraduate thesis as well as Honourable Mention for the AMS-MAA-SIAM Morgan Prize, the highest honour in the world for an undergraduate in mathematics. He gave an invited talk at the International Congress of Chinese Mathematicians 2019.
Simon Foucart (Texas A&M University): Nonstatistical Learning Theory: the View from Optimal Recovery
Applied Mathematics Seminar
Date: Thursday 2 March
Abstract: For a function observed through point evaluations, is there an optimal way to recover it or merely to estimate a dependent quantity? I will give affirmative answers to variations of this data-focused question, especially under the assumption that the function belongs to a model set defined by approximation capabilities.
In fact, I will uncover computationally implementable linear recovery maps that are optimal in the worst-case setting.
I will present some recent and ongoing works extending the theory in several directions, with particular emphasis put on observations that are inexact—adversarially or randomly.
Michael Griebel (University of Bonn): Generalized sparse grid methods and applications
Date: Wednesday 8 March
Abstract: High-dimensional problems appear in various mathematical models. Their numerical approximation involves the well-known curse of dimension, which renders any direct discretization obsolete. One approach to circumvent this issue, at least to some extent, is the use of generalized sparse grid methods, which can exploit additional smoothness properties if present in the underlying problem.
In this talk, we will discuss the main principles and basic features of generalized sparse grids and show their application in such diverse areas as econometrics, fluid dynamics, quantum chemistry, uncertainty quantification and machine learning.
Marc Burger (ETH Zürich): On the Real Spectrum Compactification of Character Varieties
Algebra Seminar
Date: Friday 10 March
Abstract: For a finitely generated group F and a real algebraic semisimple group G, the set of conjugacy classes of G-representations of F is naturally a real semi algebraic set, called the G-character “variety” of F. For instance when F is the fundamental group of a closed surface then, depending on G, certain connected components of the G-character variety of F consist entirely of injective representations with discrete image: these are the so called “higher Teichmueller spaces”.
The real spectrum of areal algebraic set provides then a compactification of all its semialgebraic subsets and leads to interesting compactifications of higher Teichmueller spaces.
I will describe some of the properties of these compactifications and relate them to other known compactifications.
This is part of an ongoing project with Alessandra Iozzi, Anne Parreau and Beatrice Pozzetti.
D-Modules and Representation Theory: Semester Two 2023 SMRI Course
Links to YouTube recordings
Week One: Introduction
Date: Friday 11 August
Presenter: Geordie Williamson
Week Two: Sheaves of differential operators
Week Three: Connections and Functors
Date: Friday 25 August
Presenter: Geordie Williamson
Week Four: Pullbacks, lefts and rights
Date: Friday 1 September
Part One presented by Geordie Williamson
Part Two presented by Chris Hone
Week Five: Borel-Weil-Bott and Localisation
Date: Friday 8 September
Presenter: Dragan Milicic
Week Six: The Localisation Theorem
Date: Friday 15 September
Presenter: Dragan Milicic
Week Seven: Borel-Weil-Bott and Localisation
D-Modules workshop day 1
Date: Tuesday 26 September
Session 1: Dougal Davis 1
Abstract: In these talks, we will explain some very recent results on mixed Hodge modules and the unitary dual of a real reductive Lie group. (With a little luck, the ink will have dried and there will be a preliminary version on the arXiv by the time the workshop starts.) The main idea behind our work is to upgrade Beilinson-Bernstein localisation from D-modules to mixed Hodge modules, following a proposal made by Schmid and Vilonen over 10 years ago. When it applies, this endows everything in sight with a canonical filtration, the Hodge filtration, which we prove has some extremely nice properties, such as cohomology vanishing and global generation. In the context of real groups, we also prove that the Hodge filtration “sees” exactly which representations are unitary. We hope that this will lead to new progress on the very old problem of determining the unitary dual of a real group. We’ll do our best to put this problem in context, explain what our theorems say, and give the main ideas behind the proof.
Session 2: Dragan Milicic 1
D-Modules workshop day 2
Date: Wednesday 27 September
Session 1: Dougal Davis 2
Modular Representation Theory: Semester One 2023 SMRI Course
Links to YouTube recordings
Week One
Date: Thursday 23 February
Presenter: Chris Hone
Week Two
Date: Thursday 2 March
Presenter: Chris Hone
Week Three
Date: Wednesday 8 March
Presenter: Chris Hone
Week Four
Date: Thursday 16 March
Presenter: Chris Hone
Week Five
Date: Thursday 23 March
Presenter: Geordie Williamson
Week Six
Date: Thursday 30 March
Presenter: Chris Hone
Week Seven
Date: Thursday 6 April
Presenter: Geordie Williamson
Week Eight
Date: Thursday 20 April
Presenter: Geordie Williamson
Week Nine
Date: Thursday 27 April
Presenter: Geordie Williamson
Week Ten
Date: Thursday 4 May
Presenter: Geordie Williamson
Week Eleven
Date: Thursday 11 May
Presenter: Chris Hone
Week Twelve
Date: Thursday 18 May
Presenter: Geordie Williamson
Week Thirteen
Date: Thursday 1 June
Presenter: Geordie Williamson
Week Fourteen
Date: Thursday 8 June
Presenter: Nick Bridger
2023 Mathematical challenges in AI Seminars
Abstracts and links to YouTube recordings
Greg Yang (xAI): The unreasonable effectiveness of mathematics in large scale deep learning
Date: Wednesday 13 September
Abstract: Recently, the theory of infinite-width neural networks led to the first technology, muTransfer, for tuning enormous neural networks that are too expensive to train more than once. For example, this allowed us to tune the 6.7 billion parameter version of GPT-3 using only 7% of its pretraining compute budget, and with some asterisks, we get a performance comparable to the original GPT-3 model with twice the parameter count. In this talk, I will explain the core insight behind this theory. In fact, this is an instance of what I call the *Optimal Scaling Thesis*, which connects infinite-size limits for general notions of “size” to the optimal design of large models in practice. I’ll end with several concrete key mathematical research questions whose resolutions will have incredible impact on the future of AI.
Speaker bio: Greg Yang is a researcher at xAI. He obtained Bachelor’s in Mathematics and Master’s degrees in Computer Science from Harvard University, respectively advised by ST Yau and Alexander Rush. He won the Hoopes prize at Harvard for best undergraduate thesis as well as Honourable Mention for the AMS-MAA-SIAM Morgan Prize, the highest honour in the world for an undergraduate in mathematics. He gave an invited talk at the International Congress of Chinese Mathematicians 2019.
Sadhika Malladi (Princeton University): Mathematical Views on Modern Deep Learning Optimization
Date: Thursday 28 September
Abstract: This talk focuses on how rigorous mathematical tools can be used to describe the optimization of large, highly non-convex neural networks. We start by covering how stochastic differential equations (SDEs) provide a rigorous yet flexible model of how deep networks change over the course of training. We then cover how the SDEs yield practical insights into scaling training to highly distributed settings while preserving generalization performance. In the second half of the talk, we will explore the new deep learning paradigm of pre-training and fine-tuning large language models. We show that fine-tuning can be described by a very simplistic mathematical model, and insights allow us to develop a highly efficient and performant optimizer to fine-tune LLMs at scale. The talk will focus on various mathematical tools and the extent to which they can describe modern day deep learning.
YouTube recording to come
Neel Nanda (Deep Mind)
Date: Thursday 12 October
Abstract: TBA
2022 Machine Learning for the Working Mathematician Seminars
Abstracts and links to YouTube recordings (currently being reformatted, see drop-down below)
Week One
Week Two
Week Three
2022 Seminars
Abstracts and links to YouTube recordings (currently being reformatted, see drop-down below)
2021 Seminars
Abstracts and links to YouTube recordings (currently being reformatted, see drop-down below)
2020 Seminars
Abstracts and links to YouTube recordings (currently being reformatted, see drop-down below)
2022 Seminars
Alexandru Suciu, Northeastern University
Seminar title: Topological invariants of groups and tropical geometry
Date: Thursday 9 December
Francisco Crespo, Universidad del Bío-Bío
Seminar title: Relative equilibria in the full N-body problem
Date: Thursday 1 December
After determining the hamiltonian equations of motion, our approach identifies and uses the existence of translational and rotational symmetries of the N-body problem. In particular, we provide very compact equations characterizing relative equilibria solutions, which become linear by fixing the values of the invariants associated with the action of the symmetry group.
In the existing literature, relative equilibria have been classified into Lagrangian and non-Lagrangian, respectively, corresponding to whether the center of mass of all bodies is in the same plane. Our analysis determines what kind of configurations allow for each type of equilibrium and provides necessary conditions for non-Lagrangian equilibria.
Jeroen Schillewaert, University of Auckland
Seminar title: Constructing highly regular expanders from hyperbolic Coxeter groups
Date: Thursday 17 November
This talk is based on joint work with Marston Conder, Alexander Lubotzky and Francois Thilmany.
Changfeng Gui, University of Texas at San Antonio
Seminar title: Some New Inequalities in Analysis and Geometry
Date: Thursday 17 November
One such inequality, for example, incorporates the mass center deviation (from the origin) into the optimal inequality of Aubin on the sphere, which is for functions with mass centered at the origin. The main ingredient leading to the above inequalities is a novel geometric inequality: Sphere Covering Inequality.
Efforts have also been made to show similar inequalities in higher dimensions. Among the preliminary results, we have improved Beckner’s inequality for axially symmetric functions when the dimension $n=4, 6, 8$. Many questions remain open.
The talk is based on collaborations with Amir Moradifam, Sun-Yung Alice Chang, Yeyao Hu and Weihong Xie.
Rafał Kulik, University of Ottawa
Seminar title: Disjoint and sliding blocks estimators for heavy tailed time series
Date: Thursday 10 November
I will start with a mild introduction to extreme value theory, discussing probabilistic and statistical issues. This part will be accessible to a broader audience.
Then, I will talk about a more specific problem of statistical theory for cluster functionals and rare events. Two types of estimators are of a primary importance: disjoint and sliding blocks estimators. It has been conjectured that sliding blocks estimators are “better” (to be made precise in the talk). We proved in a recent series of papers that this is not the case and in fact both disjoint and sliding blocks estimators are asymptotically equivalent. This part will be aimed at probabilistic and statisticians.
I will conclude with recent directions in extreme value theory, such as extremes in high dimension, extremes of graphs and networks.
Matthew Conder, University of Auckland
Seminar title: Discrete two-generator subgroups of PSL(2,Q_p)
Date: Thursday 10 November
Here we completely classify discrete two-generator subgroups of PSL(2,Q_p) over the p-adic numbers Q_p by studying their action by isometries on the corresponding Bruhat-Tits tree. We give an algorithm to decide whether or not a two-generator subgroup of PSL(2,Q_p) is discrete, and discuss how this can be used to decide whether or not a two-generator subgroup of SL(2,Q_p) is dense. This is joint work with Jeroen Schillewaert.
Geordie Williamson, Sydney Mathematical Research Institute
Title: What can the working mathematician expect from deep learning?
Date: Wednesday 2 November
Finally, I will discuss what can be learned from the successful examples that I understand, and try to guess an answer to the question in the title. (Deep learning also raises interesting mathematical questions, but this talk won’t be about this.)
Garth Tarr, School of Mathematics and Statistics & Sydney Institute of Agriculture
Seminar title: Working with data
Date: Thursday 27 October
– Is the model you’ve selected uniquely “best”? [Spoiler: probably not]
– How can we develop methods that are resistant to data corruption?
– How can we take advantage of known structures in our data? For example, discover which groups in our data respond similarly to various inputs.
There are great funding opportunities associated with applied research. I’ve established a long-term association with Meat and Livestock Australia, particularly around predicting beef and sheep eating quality, which has spawned many projects. I’ll share some of my experiences of working with industry partners, interdisciplinary collaborators, and PhD students.
Bregje Pauwels, Sydney Mathematical Research Institute
Seminar title: Categories, approximation, representation theory and algebraic geometry
Date: Thursday 20 October
In this talk, I will try to convince you that you should use the tool of approximation in triangulated categories. Failing that, I will at least try to convince you that categories are everywhere, and their language is incredibly useful.
Will Donovan, Tsinghua University
Seminar title: Homological comparison of resolution and smoothing
Date: Friday 23 September
Biography: Will Donovan is currently an associate professor at Yau MSC, Tsinghua University, Beijing. He is also a member of the adjunct faculty at BIMSA, Yanqi Lake, Huairou, Beijing and a visiting associate scientist at Kavli IPMU, University of Tokyo. He received his PhD in Mathematics in 2011 from Imperial College London. His interests are algebraic geometry, noncommutative geometry, representation theory, string theory and symplectic geometry.
YouTube video
Seminar notes [PDF]
Kari Vilonen, University of Melbourne
Seminar title: What is a Hodge module?
Date: Thursday 15 September
Biography: Kari Vilonen is a professor of mathematics at the University of Melbourne. His research is in geometric aspects of representation theory and the Langlands program. He has also worked on foundational questions on perverse sheaves and D modules including the microlocal point of view.
Jana de Wiljes, University of Potsdam
Seminar title: Sequential Bayesian Learning
Date: Thursday 8 September
Common reasons that make this problem so challenging are: ( i ) the underlying system is extremely complex (e.g., highly nonlinear) and chaotic (i.e., crucially dependent on the initial conditions), (ii) the associate state and/or parameter space is very high dimensional (e.g., worst case 10^8) (iii) Observations are noisy, partial in space and discrete in time.
In practice these obstacles are combated with a series of approximations (the most important ones being based on assuming Gaussian densities and using Monte Carlo type estimations) and numerical tools that work surprisingly well in some settings. Yet the mathematical understanding of the signal tracking ability of a lot of these methods is still lacking. Additionally, solutions of some of the more complicated problems that require simultaneous state and parameter estimation (including control parameters that can be understood as decisions/actions performed) can still not be approximated in a computationally feasible fashion. Here we will try to address the first layer of these issues step by step and discuss the next advances that need to be made in these many layered problems. More specifically a stability and accuracy analysis of a family of the most popular sequential data assimilation methods typically used in practice is presented. Then we will discuss how techniques from the world of machine learning can aid to overcome some of the computational challenges.
YouTube video
Henri Guenancia, Paul Sabatier University
Seminar title: On the invariance of plurigenera
Date: Friday 26 August
Kenneth Ascher, University of California, Irvine
Seminar title: What is a moduli space?
Date: Thursday 25 August
Biography: Kenneth Ascher is an assistant professor in the department of mathematics at the University of California Irvine. His research area is algebraic and arithmetic geometry, with specific focuses on moduli spaces of higher dimensional varieties and applications to questions in arithmetic. He received his PhD in 2017 from Brown University under the direction of Dan Abramovich , and was a postdoctoral fellow at the Massachusetts Institute of Technology and Princeton University.
YouTube video
Hans Boden, McMaster University
Seminar title: What is a virtual knot?
Date: Tuesday 31 May
Biography: Dr Hans U. Boden is a professor of mathematics at McMaster University in Canada. He is visiting the University of Sydney and SMRI from May 17 to June 11. His research interests are on the geometry and topology of manifolds, especially gauge theory and low-dimensional topology. In recent years, his work has focused on developing geometric methods to understand knotting and linking in 3-dimensional manifolds. While in Sydney, he will be working closely with Dr Zsuzsi Dancso on a collaborative project related to the Tait conjectures in knot theory.
Clara Grazian, University of Sydney
Seminar title: Finding structures in observations: consistent(?) clustering analysis
Date: Tuesday 10 May
Methodologies to perform inference on the number of clusters have often been proved to be inconsistent and introducing a dependence structure among the clusters implies additional difficulties in the estimation process. In a Bayesian setting, clustering in the situation where the number of clusters is unknown is often performed by using Dirichlet process priors or finite mixture models. However, the posterior distributions on the number of groups have been recently proved to be inconsistent.
This seminar aims at reviewing the Bayesian approaches available to perform via mixture models and give some new insights.
YouTube video
Jonathan Spreer, University of Sydney
Seminar title: Studying manifolds in Geometric Topology
Date: Tuesday 3 May
Geometric topology is the study of manifolds. But unlike in most other settings where manifolds occur, we are not primarily interested in their shapes, but in their properties that remain unchanged under continuous deformations.
I will explain how manifolds can be most conveniently represented; go over some methods to study these representations; and demonstrate how these methods can give rise to deterministic algorithms solving fundamental problems in the field.
The flavour of this research highly depends on an integer: the dimension of the manifolds under investigation. In this talk the flavour will be mostly three.
Pedram Hekmati, University of Auckland
Seminar title: What is a cohomological field theory?
Date: Tuesday 26 April
This talk will give an overview of these ideas and be aimed at a broad audience.
YouTube video
Monica Vazirani, University of California, Davis
Seminar title: From representations of the rational Cherednik algebra to parabolic Hilbert schemes via the Dunkl-Opdam subalgebra
Date: Thursday 14 April
We can also describe this simple module using the geometry of parabolic Hilbert schemes of points on plane curve singularities. The “tableau” basis that diagonalizes the Dunkl-Opdam subalgebra is the basis of equivariant homology that comes from torus fixed points.
This is joint work with Eugene Gorsky and José Simental.
Bio: Monica Vazirani is a professor at UC Davis. She received her PhD from UC Berkeley, after which she had an NSF postdoc she spent at UC San Diego and UC Berkeley, as well as postdoctoral positions at MSRI and Caltech. Dr. Vazirani’s research interests center on the representation theory of algebras related to the symmetric group and how to express algebraic phenomena via the combinatorics of partitions, tableaux, crystal graphs and parking functions.
YouTube video
Clément Canonne, University of Sydney
Seminar title: What is deterministic amplification?
Date: Tuesday 12 April
I will first discuss why one would want to do this, then how to achieve it naively, and — quite surprisingly — how we can do much better than this naive approach using expander graphs.
Bio: Clément Canonne is a Lecturer in the School of Computer Science of the University of Sydney; he obtained his Ph.D. in 2017 from Columbia University, before joining Stanford as a Motwani Postdoctoral Fellow, then IBM Research as a Goldstine Postdoctoral Fellow. His main areas of research are distribution testing (and, broadly speaking, property testing) and learning theory; focusing, in particular, on understanding the computational aspects of learning and statistical inference subject to various resource or information constraints.
YouTube video
Theodore Vo, Monash University
Seminar title: Canards, Cardiac Cycles, and Chimeras
Date: Tuesday 8 March
More specifically, we will use canard theory to analyse a canonical model of the electrical activity in a heart muscle cell. We demonstrate that pathological heart rhythms, called early afterdepolarisations, are canard-induced phenomena. We use this knowledge to explain the rich set of model behaviours, some of which have also been observed in experiments. Then, we explore a new class of canard-induced patterns in reaction-diffusion PDEs which exhibit coexisting domains of mutually synchronised oscillators and complementary domains of decoherent (asynchronous) oscillators.
YouTube video
Sang-hyun Kim, Korea Institute for Advanced Study
Seminar title: Optimal regularity of mapping class group actions on the circle
Date: Wednesday 2 March
Bio: Sang-hyun Kim works at Korea Institute for Advanced Study as Professor in the School of Mathematics since 2019. Before this, he worked at Seoul National University, KAIST, Tufts University, the University of Texas at Austin and MSRI. He received Ph.D in 2007 at Yale University under the supervision of Andrew Casson. His research interests focus on the interplay between geometric group theory and low–dimensional topology, particularly motivated by right-angled Artin groups and manifold diffeomorphism groups. He was selected as the Scientist of the Month by the Korean Ministry of Science and ICT in 2020.
YouTube video
Ivan Guo, Monash University
Seminar title: Stochastic Optimal Transport in Financial Mathematics
Date: Tuesday 22 February
YouTube video
2022 Machine Learning for the Working Mathematician Seminars
Lars Buesing, Columbia University
Title: Searching for Formulas and Algorithms: Symbolic Regression and Program Induction
Date: Thursday 2 June
YouTube video
Qianxiao Li, National University of Singapore
Title: Deep learning for sequence modelling
Date: Thursday 26 May
Gitta Kutyniok, Ludwig-Maximilians-Universität and University of Tromsø
Title: Deep Learning meets Shearlets: Explainable Hybrid Solvers for Inverse Problems in Imaging Science
Date: Thursday 19 May
In this talk, we will develop a conceptual approach towards inverse problems in imaging sciences by combining the model-based method of sparse regularization by shearlets with the data-driven method of deep learning. Our solvers pay particular attention to the singularity structures of the data. Focussing then on the inverse problem of (limited-angle) computed tomography, we will show that our algorithms significantly outperform previous methodologies, including methods entirely based on deep learning. Finally, we will also touch upon the issue of how to interpret the results of such algorithms, and present a novel, state-of-the-art explainability method based on information theory.
YouTube video
Daniel Halpern-Leinster, Cornell University
Title: Learning selection strategies in Buchberger's algorithm
Date: Thursday 12 May
YouTube video
Alex Davies, DeepMind
Title: A technical history of AlphaZero
Date: Thursday 4 May
YouTube video
Carlos Simpson, Université Côte d’Azur
Title: Machine learning for optimizing certain kinds of classification proofs for finite structures
Date: Thursday 28 April
YouTube video
Bamdad Hosseini, University of Washington
Title: Perspectives on graphical semi-supervised learning
Adam Zsolt Wagner, Tel Aviv University
Title: A simple RL setup to find counterexamples to conjectures in mathematics
Date: Thursday 7 April
YouTube video
Georg Gottwald & Geordie Williamson, University of Sydney
Title: Geometric Deep Learning II; Saliency + Combinatorial Invariance
Date: Thursday 31 March
Saliency + Combinatorial Invariance (Geordie Williamson): YouTube video
Geordie Williamson, University of Sydney
Title: Geometric Deep Learning; or never underestimate symmetry
Date: Thursday 24 March
Joel Gibson & Georg Gottwald, University of Sydney
Title: Recurrent Neural Nets; Regularisation
Date: Thursday 17 March
Georg Gottwald, University of Sydney
Title: How to think about machine learning
Date: Thursday 10 March
YouTube video
Joel Gibson, University of Sydney
Title: What can and can't neural networks do
Date: Thursday 3 March
YouTube video
Geordie Williamson, University of Sydney
Title: Basics of Machine Learning
Date: Thursday 24 February
YouTube video
2021 Seminars
Alexei Davydov, Ohio University
Seminar title: Condensation of anyons in topological states of matter and structure theory of E_2-algebras
Date: Monday 13 December
YouTube video
Shane Kelly, Tokyo Institute of Technology
Seminar title: Blowup formulas for nilpotent sensitive cohomology theories
Date: Thursday 2 December
A feature of these topologies which often turns out to be a bug is that the associated sheaves cannot see nilpotents. In this talk I will discuss a modification which can see nilpotents, and which still has long exact sequences for many blowups.
Bio: Shane Kelly is an Associate Professor at Tokyo Institute of Technology. His research area is algebraic K-theory and motivic homotopy theory, and more recently he is interested in applications to representation theory. His graduate studies were mostly based in Paris; in 2012 he received a PhD jointly from Université Sorbonne Paris Nord and The Australian National University under the joint supervision of Cisinski and Neeman, respectively.
Seminar notes (PDF)
Jack Morava, Johns Hopkins University
Seminar title: On the group completion of the Burau representation
Date: Thursday 11 November
∏i≠k(zi – zk) ∈
×of a finite collection of points of the plane defines the abelianization homomorphism
sending a braid to its number of overcrossings less undercrossings or writhe.
In terms of diffeomorphisms of the punctured plane, it defnes a kind of
`invertible topological quantum field theory’ associated to the Burau representation,
and in the classical physics of point particles the real part of
its logarithmic derivative is the potential energy of a collection of Coulomb
charges, while its imaginary part is essentially the Nambu-Goto area of a
loop of string in the three-sphere.
Its higher homotopy theory defines a very interesting a double-loop map
× Ω2S3 → 𝒫ic(S0)
to the category of lines over the stable homotopy ring-spectrum, related
to Hopkins and Mahowald’s exotic (E2) multiplication on classical integral
homology, perhaps related to the `anyons’ of nonclassical physics.
Bio: Jack Johnson Morava, of Czech and Appalachian descent, studied under Eldon Dyer and Sir Michael Atiyah, graduating with a PhD from Rice University in 1968, followed by an Academy of Sciences postdoc in Moscow with Yuri Manin and Sergei Novikov. He joined the Johns Hopkins faculty in 1979 where he was involved in the Japan-US mathematical institute, and from roughly 2003 to 2010 he worked half-time on the DARPA FunBio initiative. He retired in 2017 to live with his anthropological linguist wife in Charlottesville, Virginia and get some work done.
YouTube video
Vladimir Bazhanov, Australian National University
Seminar title: Quantum geometry of 3-dimensional lattices
Date: Tuesday 26 October
geometry and the theory of integrable systems, both classical and quantum. We will
study geometric consistency relations between angles of 3-dimensional (3D) circular
quadrilateral lattices — lattices whose faces are planar quadrilaterals inscribable
into a circle. We show that these relations generate canonical transformations of a
remarkable “ultra-local” Poisson bracket algebra defined on discrete 2D surfaces
consisting of circular quadrilaterals. Quantization of this structure allowed us to
obtain new solutions of the tetrahedron equation (the 3D analog of the Yang-Baxter
equation) as well as reproduce all those that were previously known. These solutions
generate an infinite number of non-trivial solutions of the Yang-Baxter equation and
also define integrable 3D models of statistical mechanics and quantum field theory. The
latter can be thought of as describing quantum fluctuations of lattice geometry.
YouTube video
Joel Kamnitzer, University of Toronto
Seminar title: Symplectic duality and (generalized) affine Grassmannian slices
Date: Thursday 21 October
The slices in the affine Grassmannian and truncated shifted Yangians can also be defined as special cases of the Coulomb branch construction of Braverman-Finkelberg-Nakajima. From this perspective, we find many insights. First, we can generalize affine Grassmannian slices to the case of non-dominant weights and arbitrary symmetric Kac-Moody Lie algebras. Second, we establish a link with modules for KLRW algebras. Finally, we defined a categorical g-action on the categories O, using Hamiltonian reduction.
Bio: Joel Kamnitzer is a Professor of Mathematics at the University of Toronto. His research concerns complex reductive groups and their representations, focusing on canonical bases, categorification, and geometric constructions. His 2005 Ph.D. thesis from UC Berkeley focused on the study of Mirkovic-Vilonen cycles in Affine Grassmannians. He received the 2011 Andre Aisenstadt Prize, a 2012 Sloan Research Fellowship, a 2018 E.W.R. Steacie Memorial Fellowship, a 2018 Poincare Chair, and the 2021 Jeffrey-Williams Prize.
YouTube video
Giles Gardam, University of Münster
Seminar title: Solving semidecidable problems in group theory
Date: Tuesday 5 October
Bio: Giles Gardam is a research associate at the University of Münster working in geometric group theory. He studied mathematics and computer science at the University of Sydney, receiving his Bachelor’s degree in 2012, and completed his doctorate at Oxford in 2017. He was then a postdoc at the Technion before starting at Münster in 2019.
YouTube video
Thursday 16 September
John Greenlees, Warwick University
Seminar title: The singularity category of C^*(BG) for a finite group G
is a very special graded commutative ring, but this comes out much more clearly if one uses
the cochains C^*(BG), which can be viewed as a commutative ring up to homotopy. For
example C^*(BG) is always Gorenstein (whilst this is not quite true for H^*(BG)).
This leads one to study C^*(BG) as if it was a commutative local Noetherian ring, though of
course one has to use homotopy invariant methods. The ring C^*(BG) is regular
if and only if G is p-nilpoent and so it is natural to look for ways of deciding where C^*(BG) lies
on a the spectrum between regular and Gorenstein rings. For a commutative Noetherian ring,
one considers the singularity category D_{sg}(R) (the quotient of finite complexes of finitely
generated modules by finitely generated projectives). This is trivial if and only if R is regular,
so is the appropriate tool. The talk will describe how to define this for C^*(BG), show it has
good basic properties and describe the singularity category in the simplest case it is not
trivial (when G has a cyclic Sylow p-subgroup).
YouTube video
3, 9, 16 24 & 31 August
Vladimir Bazhanov, Australian National University
Course title: Yang-Baxter maps
The topic lies on the intersection of the theory of quantum groups and discrete integrable equations.
YouTube playlist
Thursday 26 August
Hankyung Ko, Uppsala University
Seminar title: A singular Coxeter presentation
YouTube video
Thursday 19 August
Lauren Williams, Harvard University
Seminar title: Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations
It has interesting physical properties (e.g. boundary-induced phase transitions) and also beautiful mathematical properties. The inhomogeneous TASEP is a Markov chain of weighted particles hopping on a ring, in which the probability that two particles interchange depends on the weight of those particles. If each particle has a distinct weight, then we can think of this as a Markov chain on permutations. In many cases, the steady state probabilities can be expressed in terms of Schubert polynomials. Based on joint work with Donghyun Kim.
Speaker bio: Lauren Williams is the Robinson professor of mathematics at Harvard and the Seaver Professor at the Harvard Radcliffe Institute. Her research is in algebraic combinatorics. Williams received her BA in mathematics from Harvard College in 2000, and her PhD from MIT in 2005. Subsequently, she was a postdoc at UC Berkeley and Harvard, then a faculty member at UC Berkeley from 2009 to 2018, before returning to Harvard in 2018. She is the recipient of a Sloan Research Fellowship, an NSF CAREER award, the AWM-Microsoft research prize, and is an Honorary member of the London Mathematical Society.
YouTube video
Thursday, 5 August
Xuhua He, Chinese University of Hong Kong
Seminar title: Tits groups of Iwahori-Weyl groups and presentations of Hecke algebras
In this talk, I will discuss a generalization of the notion of the Tits group T to a reductive p-adic group G. Such T, if exists, gives a nice lifting of the Iwahori-Weyl group of G. I will show that the Tits group exists when the reductive group splits over an unramified extension of the p-adic field and will provide an example in the ramified case that such a Tits group does not exist. Finally, as an application, we will provide a nice presentation of the Hecke algebra of the p-adic group G with ln-level structure.
This talk is based on the recent joint work with Ganapathy.
Speaker bio: Xuhua He is the Choh-Ming Professor of Mathematics at the Chinese University of Hong Kong. He works in pure mathematics. His research interests include Arithmetic geometry, Algebraic groups, and representation theory. He received his Bachelor’s degree in mathematics from Peking University in 2001 and a Ph.D. degree from MIT in 2005 under the supervision of George Lusztig. He worked as a member at the Institute for Advanced Study during 2005-2006 and Simons Instructor at Stony Brook University during 2006-2008. He worked at the Hong Kong University of Science and Technology during 2008-2014 as an assistant Professor and associated Professor, and then moved to the University of Maryland during 2014-2019 as a Full Professor of Mathematics before joining CUHK in 2019. He received the Morningside Gold Medal of Mathematics in 2013, the Xplorer Prize in 2020 and is an invited sectional speaker of the International Congress of Mathematicians in 2018.
YouTube video
Friday, 23 July
Shrawan Kumar, University of North Carolina
Seminar title: Root components for tensor product of affine Kac-Moody Lie algebra modules
Seminar notes: PDF document
YouTube video
Thursday, 8 July
Ulrich Thiel, University of Kaiserslautern
Seminar title: Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution
Thursday, 24 June 2021
Gus Lonergan, A Priori Investment Management LLC
Seminar title: Geometric Satake over KU
About the speaker: Gus Lonergan is the Chief Mathematician at A Priori Investment Management LLC. He was previously a L.E. Dickson Instructor in the mathematics department at the University of Chicago. He is interested in representation theory.
Lonergan completed his PhD at MIT under Roman Bezrukavnikov; the thesis was an attempt to understand mod p phenomena in algebraic topology in the context of geometric representation theory. He attended Cambridge University for his undergraduate and master’s degree. He plays a little music on the side.
YouTube video
Thursday, 17 June 2021
Magdalena Boos, Ruhr University Bochum
Seminar title: Advertising symmetric quivers and their representations
YouTube video
Thursday, 10 June 2021
Behrouz Taji, University of Sydney
Seminar title: Projective families of varieties through birational geometry and Hodge theory
Seminar slides: PDF document
Wednesday, 9 June 2021
Paul Zinn-Justin, University of Melbourne
Seminar title: Generic pipe dreams, conormal matrix Schubert varieties and the commuting variety
Thursday, 3 June 2021
Uri Onn, Australian National University
Seminar title: Base change and representation growth of arithmetic groups
YouTube video
Thursday, 20 May 2021
Stephan Tillmann, University of Sydney
Seminar title: On the space of properly convex projective structures
I will outline joint work with Daryl Cooper concerning the space of holonomies of properly convex real projective structures on manifolds whose fundamental group satisfies a few natural properties. This generalises previous work by Benoist for closed manifolds. A key example, computed with Joan Porti, is used to illustrate the main results.
YouTube video
13 May 2021
Reinout Quispel, La Trobe University
Seminar title: How to discover properties of differential equations, and how to preserve those properties under discretization
The first part will be introductory, and will address the question:
Given an ordinary differential equation (ODE) with certain physical/geometric properties (for example a preserved measure, first and/or second integrals), how can one preserve these properties under discretization?
The second part of the talk will cover some more recent work, and address the question:
How can one deduce hard to find properties of an ODE from its discretization?
Bio: Reinout Quispel was an undergraduate at the University of Utrecht (the Netherlands) for nine years, before obtaining a PhD on the discretization of soliton theory from Leiden University in 1983. He moved to Australia for a three-year position in 1986 and is still there 35 years later. His main areas of expertise are in integrable systems and in the geometric numerical integration of differential equations. He was awarded the Onsager Professorship and Medal by the Norwegian University of Science and Technology (NTNU) in 2013.
YouTube video
6 May 2021
Shun-Jen Cheng, Institute of Mathematics, Academia Sinica
Seminar title: Representation theory of exceptional Lie superalgebras
In the second part of the talk we shall discuss the representation theory of these Lie superalgebras and explain the irreducible character problem in the BGG category. Our main focus will be on our computation of the irreducible characters for two of the exceptional Lie superalgebras. This part is based on recent joint works with C.-W. Chen, L. Li, and W. Wang.
YouTube video
22 April 2021
Marcy Robertson, University of Melbourne
Seminar title: Expansions, completions and automorphisms of welded tangled foams
This classification allows us to connect these “welded tangled foams” to the Kashiwara-Vergne conjecture in Lie theory. In work in progress, we show that the group of homotopy automorphisms of the (rational completion of) the wheeled prop of welded foams is isomorphic to the group of symmetries KV, which acts on the solutions to the Kashiwara-Vergne conjecture. Moreover, we explain how this approach illuminates the close relationship between the group KV and the pro-unipotent Grothendieck–Teichmueller group.
Bio: Marcy Robertson obtained her PhD in Algebraic Topology from the University of Illinois at Chicago in 2010. From there she worked in Canada, France and her native United States before settling down in Australia 2015. She is now a Senior Lecturer of Pure Mathematics at the University of Melbourne.
YouTube video
15 April 2021
Yury Stepanyants, University of Southern Queensland
Seminar title: The asymptotic approach to the description of two dimensional soliton patterns in the oceans
The suggested approach is equally applicable to a wide class of non-integrable equations too. As an example, the asymptotic theory is applied to the description of wave patterns in the 2D Benjamin-Ono equation describing internal waves in the infinitely deep ocean containing a relatively thin one of the layers.
Bio: Yury Stepanyants graduated in 1973 with the HD of MSc Diploma from the Gorky State University (Russia) and started to work as the Engineer with the Research Radiophysical Institute in Gorky. He proceeded his career with the Institute of Applied Physics of the Russian Academy of Sciences (Nizhny Novgorod) from 1977 to 1997. In 1983 Yury obtained a PhD in Physical Oceanography, and in 1992 he obtained a degree of Doctor of Sciences in Geophysics. After immigration in Australia in 1998, Yury worked for 12 years as the Senior Research Scientist with the Australian Nuclear Science and Technology Organisation in Sydney. Since July 2009 he holds a position of Full Professor at the University of Southern Queensland in Toowoomba, Australia. Yury has published more than 100 journal papers, three books, several review papers and has obtained three patents.
YouTube video
8 April 2021
Adam Piggott, Australian National University & Murray Elder, University of Technology Sydney
Seminar title: Recent progress on the effective Mordell problem
Elder Abstract: The growth function of a finitely generated group is a powerful and well-studied invariant. Gromov’s celebrated theorem states that a group has a polynomial growth function if and only if the group is ‘virtually nilpotent’. Of interest is a variant called the ‘geodesic growth function’ which counts the number of minimal-length words in a group with respect to some finite generating set. I will explain progress made towards an analogue of Gromov’s theorem in this case.
I will start by defining all of the terms used in this abstract (finitely generated group; growth function; virtual property of a group; nilpotent) and then give some details of the recent progress made. The talk is based on the papers arxiv.org/abs/1009.5051, arxiv.org/abs/1908.07294 and arxiv.org/abs/2007.06834 by myself, Alex Bishop, Martin Brisdon, José Burillo and Zoran Šunić.
YouTube video
18 March 2021
Jared M. Field, University of Melbourne
Seminar title: Gamilaraay Kinship Dynamics
Indeed, the Gamilaraay system dynamically trades off kin avoidance to minimise incidence of recessive diseases against pairwise cooperation, as understood formally through Hamilton’s rule.
Bio:Jared Field completed his undergraduate studies at the University of Sydney in Mathematics and French literature, before reading for a DPhil in Mathematical Biology at Balliol College, Oxford. He is now a McKenzie Fellow in the School of Mathematics and Statistics at the University of Melbourne, with broad interests at the intersection of mathematics, evolution and ecology.
26 February 2021
Monica Nevins, University of Ottawa
Seminar title: Recent progress on the effective Mordell problem
In this talk, I will aim to share the spirit of, and open questions in, the representation theory of G, through the lens of restricting these representations to maximal compact open subgroups.
Our point of departure: the Bruhat-Tits building of G, a 50-year-old combinatorial and geometric object that continues to reveal secrets about the structure and representation theory of G today.
YouTube video
2020 Seminars
9 December 2020
Minhyong Kim, University of Warwick
Seminar title: Recent progress on the effective Mordell problem
genus at least two have only finitely many rational points. This can be understood as
the statement that most polynomial equations (in a precise sense)
f(x,y)=0
of degree at least 4 have at most finitely many solutions. However, the effective
version of this problem, that of constructing an algorithm for listing all rational
solutions, is still unresolved. To get a sense of the difficulty, recall how long it
took to prove that there are no solutions to
x^n+y^n=1
other than the obvious ones. In this talk, I will survey some of the recent progress on
an approach to this problem that proceeds by encoding rational solutions into arithmetic
principal bundles and studying their moduli in a manner reminiscent of geometric gauge
theory.
YouTube video
18 November 2020
Aidan Sims, University of Wollongong
Seminar title: Homotopy of product systems, K-theory of k-graph algebras, and the Yang-Baxter equations
Each k-graph can be described in terms of a coloured graph, called its skeleton, and some factorisation rules that describe how 2-coloured paths pair up into commuting squares. C*-algebras of k-graphs generalise Cuntz-Krieger algebras, and have been the subject of sustained interest essentially because questions about crossed products of C*-algebras by higher-rank free abelian groups are hard, and k-graph algebras constitute a comparably tractable class of examples that could point the way to general theorems.
A particularly obstinate question in this vein is that of determining the K-theory of a k-graph algebra, or even just whether the K-theory depends on the factorisation rules, or only on the skeleton. I’ll outline some joint work with James Fletcher and Elizabeth Gillaspy that uses a homotopy argument to establish a surprising link between this question and the question of connectedness (or otherwise) of the space of solutions to a Yang-Baxter-like equation. I won’t assume any background about C*-algebras, k-graphs, or the Yang-Baxter equations, and all are welcome—and people who might know about connectedness (or otherwise) of the spaces of solutions to Yang-Baxter-like equations are especially welcome!
11 November 2020
David Robertson, University of New England
Seminar title: Piecewise full groups of homeomorphisms of the Cantor set
They first appeared in the work of Giordano, Putnam and Skau in the context of Cantor minimal systems. Recently they have received significant attention as a source of new examples of finitely generated infinite simple groups. I will present a number of results about these groups obtained in joint work with Alejandra Garrido and Colin Reid.
28 October, 4 November 2020
James Borger and Lance Gurney, Australian National University
Series title: The geometric approach to cohomology
YouTube videos
26 October 2020
Peng Shan, Tsinghua University
Seminar title: Coherent categorification of quantum loop sl(2)
YouTube video
21 October 2020
Anthony Licata, Australian National University
Seminar title: Stability conditions and automata
8 October 2020
Shamgar Gurevich, University of Wisconsin, Madison
Seminar title: Harmonic analysis on GLₙ over finite fields
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank.
Rank suggests a new organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s “philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge collection) of “Large” representations.
This talk will discuss the notion of rank for the group GLₙ over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for random walks.
This is joint work with Roger Howe (Yale and Texas A&M). The numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).
4 August 2020
Sam Raskin, University of Texas at Austin
Seminar title: Tate’s thesis in the de Rham setting
YouTube video
6 July 2020
Eugen Hellmann, University of Münster
Seminar title: On the derived category of the Iwahori–Hecke algebra
YouTube video
25 June 2020
Victor Ostrik, University of Oregon
Seminar title: Incompressible symmetric tensor categories
YouTube video
3 June 2020
David Ben-Zvi, University of Texas at Austin
Seminar title: Boundary conditions and hamiltonian actions in geometric Langlands
YouTube video
26 February–11 March 2020
Tom Bridgeland, University of Sheffield
Series title: Introduction to derived categories of coherent sheaves
30 January 2020
Nancy Reid, University of Toronto
Colloquium title: In praise of small data
Bio: Nancy Reid is University Professor and Canada Research Chair in Statistical Theory and Applications at the University of Toronto. Her research interests include statistical theory, likelihood inference, design of studies, and statistical science in public policy. Her main research contributions have been to the field of theoretical statistics. Professor Reid is a Fellow of the Royal Society, the Royal Society of Canada, the American Association for the Advancement of Science, and a Foreign Associate of the National Academy of Sciences. In 2014 she was appointed Officer of the Order of Canada.