Anomalies, black strings and the charged Cardy formula.

*Seyed Morteza Hosseini*, Kvali IPMU Tokyo.

## Resumo

We derive the general anomaly polynomial for a class of two-dimensional CFTs arising as twisted compactifications of a higher-dimensional theory on compact manifolds, including the contribution of its isometries. We then use the result to perform a counting of microstates for dyonic rotating supersymmetric black strings in $\operatorname{AdS}_5 \times S^5$ and $\operatorname{AdS}_7 \times S^4$. We explicitly construct these solutions by uplifting a class of four-dimensional rotating black holes. We provide a microscopic explanation of the entropy of such black holes by using a charged version of the Cardy formula.

Entanglement entropy in many-body eigenstates of local Hamiltonians.

*Lev Vidmar*, Jozef Stefan Institute and University of Ljubljana.

## Resumo

The eigenstate entanglement entropy is a powerful tool to distinguish integrable from generic quantum-chaotic Hamiltonians. In integrable models, the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) has a volume-law coefficient that generally depends on the subsystem fraction. In contrast, the volume-law coefficient is maximal (subsystem fraction independent) in quantum-chaotic models. In the seminar I will present an overview of our current understanding of bipartite entanglement entropies in many-body quantum states above the ground states, and contrast analytical predictions with numerical results for eigenstates of physical Hamiltonians.

Gradient boosting for extreme quantile regression.

*Sebastian Engelke*, University of Geneva.

## Resumo

Quantile regression relies on minimizing the conditional quantile loss, which is based on the quantile check function. This has been extended to flexible regression functions such as the quantile regression forest (Meinshausen, 2006) and the gradient forest (Athey et al., 2019). These methods break down if the quantile of interest lies outside of the range of the data. Extreme value theory provides the mathematical foundation for estimation of such extreme quantiles. A common approach is to approximate the exceedances over a high threshold by the generalized Pareto distribution. For conditional extreme quantiles, one may model the parameters of this distribution as functions of the predictors. Up to now, the existing methods are either not flexible enough (e.g., linear methods) or do not generalize well in higher dimensions (e.g., kernel based methods). We develop a new approach based on gradient boosting for extreme quantile regression that estimates the parameters of the generalized Pareto distribution in a flexible way even in higher dimensions. We discuss cross-validation of the tuning parameters and show how the importance of the different predictors can be measured. Our estimator outperforms classical quantile regression methods and methods from extreme value theory in simulations studies. We study an application to forecasting of extreme precipitation in statistical post-processing.

This is joint work with Jasper Velthoen, Clement Dombry and Juan-Juan Cai.

Gradient boosting for extreme quantile regression.

*Sebastian Engelke*, University of Geneva.

## Resumo

Quantile regression relies on minimizing the conditional quantile loss, which is based on the quantile check function. This has been extended to flexible regression functions such as the quantile regression forest (Meinshausen, 2006) and the gradient forest (Athey et al., 2019). These methods break down if the quantile of interest lies outside of the range of the data. Extreme value theory provides the mathematical foundation for estimation of such extreme quantiles. A common approach is to approximate the exceedances over a high threshold by the generalized Pareto distribution. For conditional extreme quantiles, one may model the parameters of this distribution as functions of the predictors. Up to now, the existing methods are either not flexible enough (e.g., linear methods) or do not generalize well in higher dimensions (e.g., kernel based methods). We develop a new approach based on gradient boosting for extreme quantile regression that estimates the parameters of the generalized Pareto distribution in a flexible way even in higher dimensions. We discuss cross-validation of the tuning parameters and show how the importance of the different predictors can be measured. Our estimator outperforms classical quantile regression methods and methods from extreme value theory in simulations studies. We study an application to forecasting of extreme precipitation in statistical post-processing.

This is joint work with Jasper Velthoen, Clement Dombry and Juan-Juan Cai.

Data, Decisions, and You: Making Causality Useful and Usable in a Complex World.

*Samantha Kleinberg*, Stevens Institute of Technology.

## Resumo

The collection of massive observational datasets has led to unprecedented opportunities for causal inference, such as using electronic health records to identify risk factors for disease. However, our ability to understand these complex data sets has not grown the same pace as our ability to collect them. While causal inference has traditionally focused on pairwise relationships between variables, biological systems are highly complex and knowing when events may happen is often as important as knowing whether they will. In the first half of this talk I discuss new methods that allow causal relationships to be reliably inferred from complex observational data, motivated by analysis of intensive care unit and other medical data. Causes are useful because they allow us to take action, but how there is a gap between the output of machine learning and what helps people make decisions. In the second part of this talk I discuss our recent findings in testing just how people fare when using the output of machine learning and how we can go from data to knowledge to decisions.

Stochastic Cucker-Smale model: collision-avoidance and flocking.

*Qiao Huang*, GFM, Universidade de Lisboa.

## Resumo

In this talk, we consider the Cucker-Smale flocking model involving both singularity and noise. We first show the local strong well-posedness for the system, in which the communication weight is locally Lipschitz beyond the origin. Then, for the special case that the communication weight has a strong singularity at the origin, we establish the global well-posedness by showing the finite time collision-avoidance. Finally, we study the large time behavior of the system when the communication weight is of zero lower bound. The conditional flocking emerges for the case of constant noise intensity, while the unconditional flocking emerges for various time-varying intensities and long-range communications.

Cyclotomic expansions of the $gl_N$ knot invariants.

*Anna Beliakova*, University of Zürich.

## Resumo

Newton’s interpolation is a method to reconstruct a function from its values at different points. In the talk I will explain how one can use this method to construct an explicit basis for the center of quantum $gl_N$ and to show that the universal $gl_N$ knot invariant expands in this basis. This will lead us to an explicit construction of the so-called unified invariants for integral homology 3-spheres, that dominate all Witten-Reshetikhin-Turaev invariants. This is a joint work with Eugene Gorsky, that generalizes famous results of Habiro for $sl_2$.

Floquet Engineering of Quantum Materials.

*Takashi Oka*, University of Tokyo.

Co-associative fibrations of $G_{2}$-manifolds and deformations of singular sets.

*Simon K. Donaldson*, Simons Center for Geometry and Physics Stony Brook and Imperial College London.

## Resumo

The first part of the talk will review background material on the differential geometry of $7$-dimensional manifolds with the exceptional holonomy group $G_{2}$. There are now many thousands of examples of deformation classes of such manifolds and there are good reasons for thinking that many of these have fibrations with general fibre diffeomorphic to a $K3$ surface and some singular fibres: higher dimensional analogues of Lefschetz fibrations in algebraic geometry. In the second part of the talk we will discuss some questions which arise in the analysis of these fibrations and their "adiabatic limits". The key difficulties involve the singular fibres. This brings up a PDE problem, analogous to a free boundary problem, and similar problems have arisen in a number of areas of differential geometry over the past few years, such as in Taubes' work on gauge theory. We will outline some techniques for handling these questions.

From Optimization Algorithms to Dynamical Systems and Back.

*René Vidal*, Mathematical Institute for Data Science, Johns Hopkins University.

## Resumo

Recent work has shown that tools from dynamical systems can be used to analyze accelerated optimization algorithms. For example, it has been shown that the continuous limit of Nesterov’s accelerated gradient (NAG) gives an ODE whose convergence rate matches that of NAG for convex, unconstrained, and smooth problems. Conversely, it has been shown that NAG can be obtained as the discretization of an ODE, however since different discretizations lead to different algorithms, the choice of the discretization becomes important. The first part of this talk will extend this type of analysis to convex, constrained and non-smooth problems by using Lyapunov stability theory to analyze continuous limits of the Alternating Direction Method of Multipliers (ADMM). The second part of this talk will show that many existing and new optimization algorithms can be obtained by suitably discretizing a dissipative Hamiltonian. As an example, we will present a new method called Relativistic Gradient Descent (RGD), which empirically outperforms momentum, RMSprop, Adam and AdaGrad on several non-convex problems.

This is joint work with Guilherme França, Daniel Robinson and Jeremias Sulam.

A anunciar.

*Svetlana Roudenko*, Florida International University.

Klein TQFT and real Gromov-Witten invariants.

*Penka Georgieva*, Sorbonne Université.

A simple model of entangled qubits: how it describes superconductors and black holes.

*Subir Sachdev*, Harvard University.

## Resumo

Long-range, multi-particle quantum entanglement plays a fundamental role in our understanding of many modern quantum materials, including the copper-based high temperature superconductors. Hawking's quantum information puzzle in the quantum theory of black holes also involves non-local entanglement. I will describe a simple model of randomly entangled qubits which has shed light on these distinct fields of physics.

A anunciar.

*Thibaut Delcroix*, Université de Montpellier.

A anunciar.

*Sanjeev Arora*, Princeton University.

Geometric phases and the separation of the world.

*Michael Berry*, University of Bristol.

## Resumo

The waves that describe systems in quantum physics can carry information about how their environment has been altered, for example by forces acting on them. This effect is the geometric phase. It also occurs in the optics of polarised light, where it goes back to the 1830s; and it gives insight into the spin-statistics relation for identical quantum particles. The underlying mathematics is geometric: the phenomenon of parallel transport, which also explains how falling cats land on their feet, and why parking a car in a narrow space is difficult. Incorporating the back-reaction of the geometric phase on the dynamics of the changing environment exposes the unsolved problem of how strictly a system can be separated from a slowly-varying environment, and involves different mathematics: divergent infinite series.

A anunciar.

*Dusa McDuff*, Columbia University.

A anunciar.

*Manuel Scotto*, Instituto Superior Técnico and CEMAT.

A anunciar.

*Manuel Scotto*, Instituto Superior Técnico and CEMAT.

A anunciar.

*Anna C. Gilbert*, Yale University.

Multiple zeta values in deformation quantization.

*Brent Pym*, McGill University.

## Resumo

In 1997, Kontsevich gave a universal solution to the deformation quantization problem in mathematical physics: starting from any Poisson manifold (the classical phase space), it produces a noncommutative algebra of quantum observables by deforming the ordinary multiplication of functions. His formula is a Feynman expansion whose Feynman integrals give periods of the moduli space of marked holomorphic disks. I will describe joint work with Peter Banks and Erik Panzer, in which we prove that Kontsevich's integrals evaluate to integer-linear combinations of multiple zeta values, building on Francis Brown's theory of polylogarithms on the moduli space of genus zero curves.

A anunciar.

*Sthitadhi Roy*, University of Oxford.

Neural Networks/Quantum Field Theory Correspondence.

*James Halverson*, Northeastern University.

A anunciar.

*Steve Simon*, University of Oxford.

A anunciar.

*Xavier Bresson*, Nanyang Technological University.

Universal Symmetries of Gerbes and Smooth Higher Group Extensions.

*Severin Bunk*, Univ. of Hamburg.

Persistence and Triangulation in Lagrangian Topology.

*Paul Biran*, ETH Zurich.

Making ML Models fairer through explanations, feature dropout, and aggregation.

*Miguel Couceiro*, Université de Lorraine.

## Resumo

Algorithmic decisions are now being used on a daily basis, and based on Machine Learning (ML) processes that may be complex and biased. This raises several concerns given the critical impact that biased decisions may have on individuals or on society as a whole. Not only unfair outcomes affect human rights, they also undermine public trust in ML and AI. In this talk, we will address fairness issues of ML models based on decision outcomes, and we will show how the simple idea of *feature dropout* followed by an *ensemble approach* can improve model fairness without compromising its accuracy. To illustrate we will present a general workflow that relies on explainers to tackle *process fairness*, which essentially measures a model's reliance on sensitive or discriminatory features. We will present different applications and empirical settings that show improvements not only with respect to process fairness but also other fairness metrics.

Liquid crystal director fields in three-dimensional non-Euclidean geometries.

*Rémy Mosseri*, LPTMC Sorbonne Université.

## Resumo

This work investigates nematic liquid crystals in three-dimensional curved space, and determines which director deformation modes are compatible with each possible type of non-Euclidean geometry. Previous work by Sethna et al. [1] showed that double twist is frustrated in flat space $\mathbb{R}^3$, but can fit perfectly in the hypersphere $\mathbb{S}^3$. Here, we extend that work to all four deformation modes (splay, twist, bend, and biaxial splay) and all eight Thurston geometries [2]. Each pure mode of director deformation can fill space perfectly, for at least one type of geometry. This analysis shows the ideal structure of each deformation mode in curved space, which is frustrated by the requirements of flat space.

- Sethna J. P., Wright D. C. and Mermin N. D., 1983 Phys. Rev. Lett. 51 467–70.
- J.-F. Sadoc, R. Mosseri and J. Selinger, New Journal of Physics 22 (2020) 093036.

Many more infinite staircases in symplectic embedding functions.

*Ana Rita Pires*, University of Edinburgh.

A anunciar.

*Ana Cristina M. Freitas*, Faculty of Sciences of the University of Porto and CMUP.

A anunciar.

*Ana Cristina M. Freitas*, Faculty of Sciences of the University of Porto and CMUP.

Causal Inference and Overparameterized Autoencoders in the Light of Drug Repurposing for SARS-CoV-2.

*Caroline Uhler*, MIT and Institute for Data, Systems and Society.

## Resumo

Massive data collection holds the promise of a better understanding of complex phenomena and ultimately, of better decisions. An exciting opportunity in this regard stems from the growing availability of perturbation / intervention data (drugs, knockouts, overexpression, etc.) in biology. In order to obtain mechanistic insights from such data, a major challenge is the development of a framework that integrates observational and interventional data and allows predicting the effect of yet unseen interventions or transporting the effect of interventions observed in one context to another. I will present a framework for causal structure discovery based on such data and highlight the role of overparameterized autoencoders. We end by demonstrating how these ideas can be applied for drug repurposing in the current SARS-CoV-2 crisis.

A anunciar.

*Jonathan Weitsman*, Northeastern University.

A anunciar.

*Thomas Strohmer*, University of California, Davis.

A anunciar.

*Alexandru Oancea*, Institut de Mathématiques de Jussieu, Sorbonne Université.

A anunciar.

*A. Pedro Aguiar*, Faculdade de Engenharia, Universidade do Porto.

A anunciar.

*Leonor Godinho*, Instituto Superior Técnico and CAMGSD.

Machine Learning of Robot Skills.

*Jan Peters*, Technische Universitaet Darmstadt.

Instituto Superior Técnico
Av. Rovisco Pais,
Lisboa,
PT