Thu 25 Apr 15:00: Machine Learning and Dynamical Systems Meet in Reproducing Kernel Hilbert Spaces with Insights from Algorithmic Information Theory
Since its inception in the 19th century, through the efforts of Poincaré and Lyapunov, the theory of dynamical systems has addressed the qualitative behavior of systems as understood from models. From this perspective, modeling dynamical processes in applications demands a detailed understanding of the processes to be analyzed. This understanding leads to a model, which approximates observed reality and is often expressed by a system of ordinary/partial, underdetermined (control), deterministic/stochastic differential or difference equations. While these models are very precise for many processes, for some of the most challenging applications of dynamical systems, such as climate dynamics, brain dynamics, biological systems, or financial markets, developing such models is notably difficult. On the other hand, the field of machine learning is concerned with algorithms designed to accomplish specific tasks, whose performance improves with more data input. Applications of machine learning methods include computer vision, stock market analysis, speech recognition, recommender systems, and sentiment analysis in social media. The machine learning approach is invaluable in settings where no explicit model is formulated, but measurement data are available. This is often the case in many systems of interest, and the development of data-driven technologies is increasingly important in many applications. The intersection of the fields of dynamical systems and machine learning is largely unexplored, and the objective of this talk is to show that working in reproducing kernel Hilbert spaces offers tools for a data-based theory of nonlinear dynamical systems.
In the first part of the talk, we introduce simple methods to learn surrogate models for complex systems. We present variants of the method of Kernel Flows as simple approaches for learning the kernel that appear in the emulators we use in our work. First, we will discuss the method of parametric and nonparametric kernel flows for learning chaotic dynamical systems. We’ll also explore learning dynamical systems from irregularly sampled time series and from partial observations. We will introduce the methods of Sparse Kernel Flows and Hausdorff-metric based Kernel Flows (HMKFs) and apply them to learn 132 chaotic dynamical systems. We draw parallels between Minimum Description Length (MDL) and Regularization in Machine Learning (RML), showcasing that the method of Sparse Kernel Flows offers a natural approach to kernel learning. By considering code lengths and complexities rooted in Algorithmic Information Theory (AIT), we demonstrate that data-adaptive kernel learning can be achieved through the MDL principle, bypassing the need for cross-validation as a statistical method. Finally, we extend the method of Kernel Mode Decomposition to design kernels in view of detecting critical transitions in some fast-slow random dynamical systems.
Then, we introduce a data-based approach to estimating key quantities which arise in the study of nonlinear autonomous, control, and random dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems – with a reasonable expectation of success – once the nonlinear system has been mapped into a high or infinite dimensional Reproducing Kernel Hilbert Space. We develop computable, non-parametric estimators approximating controllability and observability energies for nonlinear systems. We apply this approach to the problem of model reduction of nonlinear control systems. It is also shown that the controllability energy estimator provides a key means for approximating the invariant measure of an ergodic, stochastically forced nonlinear system. Finally, we show how kernel methods can be used to approximate center manifolds, propose a data-based version of the center manifold theorem, and construct Lyapunov functions for nonlinear ODEs.
- Speaker: Boumediene Hamzi
- Thursday 25 April 2024, 15:00-16:00
- Venue: Centre for Mathematical Sciences, MR2.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 25 Apr 15:00: Machine Learning and Dynamical Systems Meet in Reproducing Kernel Hilbert Spaces with Insights from Algorithmic Information Theory
Since its inception in the 19th century, through the efforts of Poincaré and Lyapunov, the theory of dynamical systems has addressed the qualitative behavior of systems as understood from models. From this perspective, modeling dynamical processes in applications demands a detailed understanding of the processes to be analyzed. This understanding leads to a model, which approximates observed reality and is often expressed by a system of ordinary/partial, underdetermined (control), deterministic/stochastic differential or difference equations. While these models are very precise for many processes, for some of the most challenging applications of dynamical systems, such as climate dynamics, brain dynamics, biological systems, or financial markets, developing such models is notably difficult. On the other hand, the field of machine learning is concerned with algorithms designed to accomplish specific tasks, whose performance improves with more data input. Applications of machine learning methods include computer vision, stock market analysis, speech recognition, recommender systems, and sentiment analysis in social media. The machine learning approach is invaluable in settings where no explicit model is formulated, but measurement data are available. This is often the case in many systems of interest, and the development of data-driven technologies is increasingly important in many applications. The intersection of the fields of dynamical systems and machine learning is largely unexplored, and the objective of this talk is to show that working in reproducing kernel Hilbert spaces offers tools for a data-based theory of nonlinear dynamical systems.
In the first part of the talk, we introduce simple methods to learn surrogate models for complex systems. We present variants of the method of Kernel Flows as simple approaches for learning the kernel that appear in the emulators we use in our work. First, we will discuss the method of parametric and nonparametric kernel flows for learning chaotic dynamical systems. We’ll also explore learning dynamical systems from irregularly sampled time series and from partial observations. We will introduce the methods of Sparse Kernel Flows and Hausdorff-metric based Kernel Flows (HMKFs) and apply them to learn 132 chaotic dynamical systems. We draw parallels between Minimum Description Length (MDL) and Regularization in Machine Learning (RML), showcasing that the method of Sparse Kernel Flows offers a natural approach to kernel learning. By considering code lengths and complexities rooted in Algorithmic Information Theory (AIT), we demonstrate that data-adaptive kernel learning can be achieved through the MDL principle, bypassing the need for cross-validation as a statistical method. Finally, we extend the method of Kernel Mode Decomposition to design kernels in view of detecting critical transitions in some fast-slow random dynamical systems.
Then, we introduce a data-based approach to estimating key quantities which arise in the study of nonlinear autonomous, control, and random dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems – with a reasonable expectation of success – once the nonlinear system has been mapped into a high or infinite dimensional Reproducing Kernel Hilbert Space. We develop computable, non-parametric estimators approximating controllability and observability energies for nonlinear systems. We apply this approach to the problem of model reduction of nonlinear control systems. It is also shown that the controllability energy estimator provides a key means for approximating the invariant measure of an ergodic, stochastically forced nonlinear system. Finally, we show how kernel methods can be used to approximate center manifolds, propose a data-based version of the center manifold theorem, and construct Lyapunov functions for nonlinear ODEs.
- Speaker: Boumediene Hamzi
- Thursday 25 April 2024, 15:00-16:00
- Venue: Centre for Mathematical Sciences, MR2.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Wed 24 Apr 14:00: Feature Learning in Two-layer Neural Networks: The Effect of Data Covariance
We study the effect of gradient-based optimization on feature learning in two-layer neural networks. We consider a setting where the number of samples is of the same order as the input dimension and show that, when the input data is isotropic, gradient descent always improves upon the initial random features model in terms of prediction risk, for a certain class of targets. Further leveraging the practical observation that data often contains additional structure, i.e., the input covariance has non-trivial alignment with the target, we prove that the class of learnable targets can be significantly extended, demonstrating a clear separation between kernel methods and two-layer neural networks in this regime.
- Speaker: Murat A. Erdogdu (University of Toronto)
- Wednesday 24 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Nicolas Boulle.
Wed 24 Apr 14:00: Feature Learning in Two-layer Neural Networks: The Effect of Data Covariance
We study the effect of gradient-based optimization on feature learning in two-layer neural networks. We consider a setting where the number of samples is of the same order as the input dimension and show that, when the input data is isotropic, gradient descent always improves upon the initial random features model in terms of prediction risk, for a certain class of targets. Further leveraging the practical observation that data often contains additional structure, i.e., the input covariance has non-trivial alignment with the target, we prove that the class of learnable targets can be significantly extended, demonstrating a clear separation between kernel methods and two-layer neural networks in this regime.
- Speaker: Murat A. Erdogdu (University of Toronto)
- Wednesday 24 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Nicolas Boulle.
Thu 25 Apr 14:00: Machine Learning and Dynamical Systems Meet in Reproducing Kernel Hilbert Spaces with Insights from Algorithmic Information Theory
Since its inception in the 19th century, through the efforts of Poincaré and Lyapunov, the theory of dynamical systems has addressed the qualitative behavior of systems as understood from models. From this perspective, modeling dynamical processes in applications demands a detailed understanding of the processes to be analyzed. This understanding leads to a model, which approximates observed reality and is often expressed by a system of ordinary/partial, underdetermined (control), deterministic/stochastic differential or difference equations. While these models are very precise for many processes, for some of the most challenging applications of dynamical systems, such as climate dynamics, brain dynamics, biological systems, or financial markets, developing such models is notably difficult. On the other hand, the field of machine learning is concerned with algorithms designed to accomplish specific tasks, whose performance improves with more data input. Applications of machine learning methods include computer vision, stock market analysis, speech recognition, recommender systems, and sentiment analysis in social media. The machine learning approach is invaluable in settings where no explicit model is formulated, but measurement data are available. This is often the case in many systems of interest, and the development of data-driven technologies is increasingly important in many applications. The intersection of the fields of dynamical systems and machine learning is largely unexplored, and the objective of this talk is to show that working in reproducing kernel Hilbert spaces offers tools for a data-based theory of nonlinear dynamical systems.
In the first part of the talk, we introduce simple methods to learn surrogate models for complex systems. We present variants of the method of Kernel Flows as simple approaches for learning the kernel that appear in the emulators we use in our work. First, we will discuss the method of parametric and nonparametric kernel flows for learning chaotic dynamical systems. We’ll also explore learning dynamical systems from irregularly sampled time series and from partial observations. We will introduce the methods of Sparse Kernel Flows and Hausdorff-metric based Kernel Flows (HMKFs) and apply them to learn 132 chaotic dynamical systems. We draw parallels between Minimum Description Length (MDL) and Regularization in Machine Learning (RML), showcasing that the method of Sparse Kernel Flows offers a natural approach to kernel learning. By considering code lengths and complexities rooted in Algorithmic Information Theory (AIT), we demonstrate that data-adaptive kernel learning can be achieved through the MDL principle, bypassing the need for cross-validation as a statistical method. Finally, we extend the method of Kernel Mode Decomposition to design kernels in view of detecting critical transitions in some fast-slow random dynamical systems.
Then, we introduce a data-based approach to estimating key quantities which arise in the study of nonlinear autonomous, control, and random dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems – with a reasonable expectation of success – once the nonlinear system has been mapped into a high or infinite dimensional Reproducing Kernel Hilbert Space. We develop computable, non-parametric estimators approximating controllability and observability energies for nonlinear systems. We apply this approach to the problem of model reduction of nonlinear control systems. It is also shown that the controllability energy estimator provides a key means for approximating the invariant measure of an ergodic, stochastically forced nonlinear system. Finally, we show how kernel methods can be used to approximate center manifolds, propose a data-based version of the center manifold theorem, and construct Lyapunov functions for nonlinear ODEs.
- Speaker: Boumediene Hamzi
- Thursday 25 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 25 Apr 14:00: Machine Learning and Dynamical Systems Meet in Reproducing Kernel Hilbert Spaces with Insights from Algorithmic Information Theory
Since its inception in the 19th century, through the efforts of Poincaré and Lyapunov, the theory of dynamical systems has addressed the qualitative behavior of systems as understood from models. From this perspective, modeling dynamical processes in applications demands a detailed understanding of the processes to be analyzed. This understanding leads to a model, which approximates observed reality and is often expressed by a system of ordinary/partial, underdetermined (control), deterministic/stochastic differential or difference equations. While these models are very precise for many processes, for some of the most challenging applications of dynamical systems, such as climate dynamics, brain dynamics, biological systems, or financial markets, developing such models is notably difficult. On the other hand, the field of machine learning is concerned with algorithms designed to accomplish specific tasks, whose performance improves with more data input. Applications of machine learning methods include computer vision, stock market analysis, speech recognition, recommender systems, and sentiment analysis in social media. The machine learning approach is invaluable in settings where no explicit model is formulated, but measurement data are available. This is often the case in many systems of interest, and the development of data-driven technologies is increasingly important in many applications. The intersection of the fields of dynamical systems and machine learning is largely unexplored, and the objective of this talk is to show that working in reproducing kernel Hilbert spaces offers tools for a data-based theory of nonlinear dynamical systems.
In the first part of the talk, we introduce simple methods to learn surrogate models for complex systems. We present variants of the method of Kernel Flows as simple approaches for learning the kernel that appear in the emulators we use in our work. First, we will discuss the method of parametric and nonparametric kernel flows for learning chaotic dynamical systems. We’ll also explore learning dynamical systems from irregularly sampled time series and from partial observations. We will introduce the methods of Sparse Kernel Flows and Hausdorff-metric based Kernel Flows (HMKFs) and apply them to learn 132 chaotic dynamical systems. We draw parallels between Minimum Description Length (MDL) and Regularization in Machine Learning (RML), showcasing that the method of Sparse Kernel Flows offers a natural approach to kernel learning. By considering code lengths and complexities rooted in Algorithmic Information Theory (AIT), we demonstrate that data-adaptive kernel learning can be achieved through the MDL principle, bypassing the need for cross-validation as a statistical method. Finally, we extend the method of Kernel Mode Decomposition to design kernels in view of detecting critical transitions in some fast-slow random dynamical systems.
Then, we introduce a data-based approach to estimating key quantities which arise in the study of nonlinear autonomous, control, and random dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems – with a reasonable expectation of success – once the nonlinear system has been mapped into a high or infinite dimensional Reproducing Kernel Hilbert Space. We develop computable, non-parametric estimators approximating controllability and observability energies for nonlinear systems. We apply this approach to the problem of model reduction of nonlinear control systems. It is also shown that the controllability energy estimator provides a key means for approximating the invariant measure of an ergodic, stochastically forced nonlinear system. Finally, we show how kernel methods can be used to approximate center manifolds, propose a data-based version of the center manifold theorem, and construct Lyapunov functions for nonlinear ODEs.
- Speaker: Boumediene Hamzi
- Thursday 25 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 16 May 15:00: Efficient Computation through Tuned Approximation
Numerical software is being reconstructed to provide opportunities to tune dynamically the accuracy of computation to the requirements of the application, resulting in savings of memory, time, and energy. Floating point computation in science and engineering has a history of “oversolving” relative to requirements or worthiness for many models. So often are real datatypes defaulted to double precision that GPUs did not gain wide acceptance in simulation environments until they provided in hardware operations not required in their original domain of graphics. However, driven by performance or energy incentives, much of computational science is now reverting to employ lower precision arithmetic where possible. Many matrix operations considered at a blockwise level allow for lower precision and, in addition, many blocks can be approximated with low rank near equivalents. This leads to smaller memory footprint, which implies higher residency on memory hierarchies, leading in turn to less time and energy spent on data copying, which may even dwarf the savings from fewer and cheaper flops. We provide examples from several application domains, including a look at campaigns in geospatial statistics and seismic processing that earned Gordon Bell Prize finalist status in, resp., 2022 and 2023.
- Speaker: David Keyes (KAUST)
- Thursday 16 May 2024, 15:00-16:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Hamza Fawzi.
Thu 16 May 15:00: Efficient Computation through Tuned Approximation
Numerical software is being reconstructed to provide opportunities to tune dynamically the accuracy of computation to the requirements of the application, resulting in savings of memory, time, and energy. Floating point computation in science and engineering has a history of “oversolving” relative to requirements or worthiness for many models. So often are real datatypes defaulted to double precision that GPUs did not gain wide acceptance in simulation environments until they provided in hardware operations not required in their original domain of graphics. However, driven by performance or energy incentives, much of computational science is now reverting to employ lower precision arithmetic where possible. Many matrix operations considered at a blockwise level allow for lower precision and, in addition, many blocks can be approximated with low rank near equivalents. This leads to smaller memory footprint, which implies higher residency on memory hierarchies, leading in turn to less time and energy spent on data copying, which may even dwarf the savings from fewer and cheaper flops. We provide examples from several application domains, including a look at campaigns in geospatial statistics and seismic processing that earned Gordon Bell Prize finalist status in, resp., 2022 and 2023.
- Speaker: David Keyes (KAUST)
- Thursday 16 May 2024, 15:00-16:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Hamza Fawzi.
Thu 02 May 14:00: Title to be confirmed
Abstract not available
- Speaker: Sina Mohammadtaheri
- Thursday 02 May 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 02 May 14:00: Title to be confirmed
Abstract not available
- Speaker: Sina Mohammadtaheri
- Thursday 02 May 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 25 Apr 14:00: Title to be confirmed
Abstract not available
- Speaker: Boumediene Hamzi
- Thursday 25 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 25 Apr 14:00: Title to be confirmed
Abstract not available
- Speaker: Boumediene Hamzi
- Thursday 25 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 11 Apr 14:00: The Algorithmic Transparency Requirement
Deep learning still has drawbacks in terms of trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obligations associated to trustworthiness have been proposed via regulatory guidelines, e.g., in the European AI Act. Therefore, a central question is to what extent trustworthy deep learning can be realized. Establishing the described properties constituting trustworthiness requires that the factors influencing an algorithmic computation can be retraced, i.e., the algorithmic implementation is transparent. We derive a mathematical framework which enables us to analyze whether a transparent implementation in a computing model is feasible. Finally, we exemplarily apply our trustworthiness framework to analyze deep learning approaches for inverse problems in digital computing models represented by Turing machines.
- Speaker: Adalbert Fono (LMU Munich)
- Thursday 11 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Thu 11 Apr 14:00: The Algorithmic Transparency Requirement
Deep learning still has drawbacks in terms of trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obligations associated to trustworthiness have been proposed via regulatory guidelines, e.g., in the European AI Act. Therefore, a central question is to what extent trustworthy deep learning can be realized. Establishing the described properties constituting trustworthiness requires that the factors influencing an algorithmic computation can be retraced, i.e., the algorithmic implementation is transparent. We derive a mathematical framework which enables us to analyze whether a transparent implementation in a computing model is feasible. Finally, we exemplarily apply our trustworthiness framework to analyze deep learning approaches for inverse problems in digital computing models represented by Turing machines.
- Speaker: Adalbert Fono (LMU Munich)
- Thursday 11 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Matthew Colbrook.
Fri 22 Mar 09:00: SCIENCE AND THE FUTURES OF MEDICINE One Day Meeting Check website for latest updates and booking information http://www.cambridgephilosophicalsociety.org
Recent advances in the sciences underpinning medicine, and their translation to clinical impact, are transforming our ability to understand and treat human diseases. This one-day meeting will explore emerging areas in which the convergence of fundamental science and translational opportunities promises to shape the futures of medicine.
Programme
09.00-09.15 Introduction to meeting
09.15-10.15 Serena Nik-Zainal, Professor of Genomic Medicine and Bioinformatics, Department of Medical Genetics, School of Clinical Medicine, University of Cambridge – The contribution of genomics to precision medicine
10.15-11.15 Shyni Varghese, Professor of Biomedical Engineering, Mechanical Engineering and Materials Science and Orthopaedics, Duke University, USA - Tissue engineering
11.15-11.45 Morning Coffee
11.45- 12.45 Jan Hoeijmakers, Department of Molecular Genetics, Erasmus University, Rotterdam and Cologne, Princess Maxima Center for Pediatric Oncology, Oncode, Utrecht, both in the Netherlands and the CECAD , Cologne, Germany – DNA damage, cancer and aging, the unexpected impact of nutrition on medicine
12.45-13.45 Lunch
13.45-14.45 Paul Workman, Former CEO and President of the Institute of Cancer (ICR), London, Harrap Professor of Pharmacology and Therapeutics, Centre for Cancer Drug Discovery, ICR – Transforming small molecule cancer drug discovery for precision medicine
14.45-15.45 Iain Buchan, W.H. Duncan Chair in Public Health Systems, Associate Pro Vice Chancellor for Innovation, Public Health, Policy & Systems, University of Liverpool – How might artificial intelligence augment population health?
15.45-16.15 Afternoon Tea
16.15- 17.15 Alessio Ciulli, Professor of Chemical and Structural Biology and Director of the Centre for Targeted Protein Degradation, School of Life Sciences, University of Dundee – Proximity-inducing modalities in drug discovery: Protein degraders and beyond
17.15 Closing remarks
Check website for latest updates and booking information http://www.cambridgephilosophicalsociety.org
- Speaker: Organisers: Professor Ashok Venkitaraman, Dr James Fraser and Dr Nick Pugh
- Friday 22 March 2024, 09:00-17:15
- Venue: Cambridge University Engineering Department. Constance Tipper Lecture Theatre.
- Series: Cambridge Philosophical Society; organiser: Beverley Larner.
Wed 24 Apr 14:00: Title to be confirmed
Abstract not available
- Speaker: Murat A. Erdogdu (University of Toronto)
- Wednesday 24 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Nicolas Boulle.
Wed 24 Apr 14:00: Title to be confirmed
Abstract not available
- Speaker: Murat A. Erdogdu (University of Toronto)
- Wednesday 24 April 2024, 14:00-15:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Nicolas Boulle.
Mon 11 Mar 18:00: Using organoids to reveal what sets the human brain apart Check website for latest updates and booking information http://www.cambridgephilosophicalsociety.org
The human brain sets us apart as a species, yet how it develops and functions differently to that of other mammals is still largely unclear. This also makes it difficult to understand how disorders of the brain arise, and therefore how to treat them. To understand such a complex organ, we have developed cerebral organoids, or brain organoids, 3D brain tissues made from stem cells that mimic the fetal brain. Such organoids are allowing us to tackle questions previously impossible with more traditional approaches. Indeed, our recent findings provide insight into various factors that influence the developing brain, and how the human brain becomes so uniquely large enabling our special cognitive abilities.
Check website for latest updates and booking information http://www.cambridgephilosophicalsociety.org
- Speaker: Dr Madeline Lancaster, Group Leader in the Cell Biology Division, MRC Laboratory of Molecular Biology, University of Cambridge
- Monday 11 March 2024, 18:00-19:00
- Venue: Bristol-Myers Squibb Lecture Theatre, Department of Chemistry.
- Series: Cambridge Philosophical Society; organiser: Beverley Larner.
Wed 24 Apr 15:00: Title to be confirmed
Abstract not available
- Speaker: Murat A. Erdogdu (University of Toronto)
- Wednesday 24 April 2024, 15:00-16:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Nicolas Boulle.
Wed 24 Apr 15:00: Title to be confirmed
Abstract not available
- Speaker: Murat A. Erdogdu (University of Toronto)
- Wednesday 24 April 2024, 15:00-16:00
- Venue: Centre for Mathematical Sciences, MR14.
- Series: Applied and Computational Analysis; organiser: Nicolas Boulle.