Zurich colloquium in mathematics

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Date / Time

Speaker

Title

Location

26 March 2024
16:30-18:15

Isabelle Gallagher

Details

Title	On the dynamics of dilute gases
Speaker, Affiliation	Isabelle Gallagher,
Date, Time	26 March 2024, 16:30-18:15
Location	KO2 F 150
Abstract	Abstract: The evolution of a gas can be described by different models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. On the one hand Lanford showed in 1974 that the Boltzmann equation appears as a law of large numbers in the low density limit of a gas of hard spheres, at least for very short times. On the other hand, fluid mechanics equations such as the Navier-Stokes equations can be derived from the Boltzmann equation in the limit of when the mean free path tends to zero. Reconciling both approaches in order to derive fluid mechanics equations from Newton's laws for the system of particles is to this day an open question. In this talk we shall explain these different limiting procedures, their difficulties and some recent advances in Hilbert's program.

On the dynamics of dilute gasesread_more

KO2 F 150

23 April 2024
16:30-17:30

Prof. Dr. Sarah Zerbes
ETH Zurich, Switzerland

Details

Title	Elliptic curves, L-functions and Fermat’s last theorem
Speaker, Affiliation	Prof. Dr. Sarah Zerbes, ETH Zurich, Switzerland
Date, Time	23 April 2024, 16:30-17:30
Location	KO2 F 150
Abstract	L-functions are one of the central objects of study in number theory. There are many beautiful theorems and many more open conjectures linking their values to arithmetic problems. The most famous example is the conjecture of Birch and Swinnerton-Dyer, which is one of the Clay Millenium Prize Problems. I will discuss some recent progress on these conjectures using tools called `Euler systems’. I will also revisit the question of using Euler systems in the proof of Fermat’s last theorem.

Elliptic curves, L-functions and Fermat’s last theoremread_more

KO2 F 150

21 May 2024
16:30-18:15

Enrique Zuazua

Details

Title	Control and Machine Learning
Speaker, Affiliation	Enrique Zuazua,
Date, Time	21 May 2024, 16:30-18:15
Location	KO2 F 150
Abstract	In this lecture, we will discuss recent results from our group that explore the relationship between control theory and machinevlearning, specifically supervised learning and universal approximation. We will take a novel approach by considering the simultaneous control of systems of Residual Neural Networks (ResNets). Each item to be classified corresponds to a different initial datum for the ResNet's Cauchy problem, resulting in an ensemble of solutions to be guided to their respective targets using the same control. We will introduce a nonlinear and constructive method that demonstrates the attainability of this ambitious goal, while also estimating the complexity of the control strategies. This achievement is uncommon in classical dynamical systems in mechanics, and it is largely due to the highly nonlinear nature of the activation function that governs the ResNet dynamics. This perspective opens up new possibilities for developing hybrid mechanics-data driven modeling methodologies. Throughout the lecture, we will also address some challenging open problems in this area, providing an overview of the exciting potential for further research and development.

Control and Machine Learningread_more

KO2 F 150

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