## Busca

## Matemática Aplicada e Análise Numérica

Renormalized transport of inertial particles.

*Marco Martins Afonso*, Universidade do Porto.

## Resumo

We study how an imposed fluid flow — laminar or turbulent — modifies the transport properties of inertial particles (e.g. aerosols, droplets or bubbles), namely their terminal velocity, effective diffusivity, and concentration following a point-source emission.

Such quantities are investigated by means of analytical and numerical computations, as functions of the control parameters of both flow and particle; i.e., density ratio, inertia, Brownian diffusivity, gravity (or other external forces), turbulence intensity, compressibility degree, space dimension, and geometric/temporal properties.

The complex interplay between these parameters leads to the following conclusion of interest in the realm of applications: any attempt to model dispersion and sedimentation processes — or equivalently the wind-driven surface transport of floaters — cannot avoid taking into account the full details of the flow field and of the inertial particle.

## $QM^3$ Matéria Quântica & Matemática

Resurgence, Superconductors and Renormalons.

*Tomás Reis*, University of Geneva.

## Resumo

In this talk I will cover the recent work of M. Mariño and I (https://arxiv.org/abs/1905.09569, https://arxiv.org/abs/1905.09575) about an application of resurgence to superconductive quantum many-body systems. I will start by introducing the core idea of resurgence. Then, I will overview how to use the TBA to find the perturbative series of the ground-state of the Gaudin-Yang model (and other integrable models) to all orders. Finally, I will show how a resurgence analysis of such series connects to superconductivity and renormalon effects, leading to a concrete conjecture linking the Borel-summability of the perturbative series to the superconductor energy gap.

## Relatividade Matemática

Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes.

*Amol Sasane*, London School of Economics.

## Resumo

The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely the de Sitter universe in flat Friedmann-Lemaître-Robertson-Walker (FLRW) form, and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, decay rates for the solution are obtained. Also, a previously established decay rate of the time derivative of the solution to the wave equation, in an expanding de Sitter universe in flat FLRW form, is improved, proving Rendall's conjecture. A similar improvement is also given for the wave equation in the cosmological region of the RNdS spacetime.

## Análise, Geometria e Sistemas Dinâmicos

A Mini-course in large deviations (I).

*Tertuliano Franco*, Universidade Federal da Bahia.

## Resumo

Large deviations has importance and applications in different areas, as Probability, Statistics, Dynamical Systems, and Statistical Mechanics. In plain words, large deviations corresponds to finding and proving the (exponentially small) probability of observing events not expected by the law of large numbers. In this mini-course we introduce the topic including a discussion on the general statement of large deviations and the some of the usual challenges when facing the upper/lowerbound large deviations.

## Teoria de Cordas

Supersymmetric line operators and their spectral problem.

*Michele Cirafici*, University of Trieste.

## Resumo

I will discuss BPS invariants associated with quantum line operators in certain supersymmetric quantum field theories. Such operators can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR they are described by representation theory data. I will discuss the associated BPS spectral problem and the relevant indices.

Note: unusual date

## Análise, Geometria e Sistemas Dinâmicos

A Mini-course in large deviations (II).

*Tertuliano Franco*, Universidade Federal da Bahia.

## Resumo

Large deviations has importance and applications in different areas, as Probability, Statistics, Dynamical Systems, and Statistical Mechanics. In plain words, large deviations corresponds to finding and proving the (exponentially small) probability of observing events not expected by the law of large numbers. In this mini-course we introduce the topic including a discussion on the general statement of large deviations and the some of the usual challenges when facing the upper/lower bound large deviations.

## Álgebra

Dirac's theorem for random regular graphs.

*António Girão*, University of Birmingham.

## Resumo

In 1952, Dirac proved that any graph on n vertices with minimum degree $n/2$ contains a Hamiltonian cycle, i.e. a cycle which passes through every vertex of the graph exactly once. We prove a resilience version of Dirac’s Theorem in the setting of random regular graphs. More precisely, we show that, whenever $d$ is sufficiently large compared to $\epsilon \gt 0$, a.a.s. the following holds: let $G_0$ be any subgraph of the random $n$-vertex $d$-regular graph $G_{n,d}$ with minimum degree at least $(1/2 + \epsilon)d$. Then, $G_0$ is Hamiltonian. This proves a conjecture of Ben-Shimon, Krivelevich and Sudakov. Our result is best possible: firstly, the condition that $d$ is large cannot be omitted, and secondly, the minimum degree bound cannot be improved. This is joint work with Padraig Condon, Alberto Espuny Díaz, Daniela Kuhn and Deryk Osthus.

## Análise, Geometria e Sistemas Dinâmicos

A Mini-course in large deviations (III).

*Tertuliano Franco*, Universidade Federal da Bahia.

## Resumo

Large deviations has importance and applications in different areas, as Probability, Statistics, Dynamical Systems, and Statistical Mechanics. In plain words, large deviations corresponds to finding and proving the (exponentially small) probability of observing events not expected by the law of large numbers. In this mini-course we introduce the topic including a discussion on the general statement of large deviations and the some of the usual challenges when facing the upper/lower bound large deviations.

## Probabilidades e Estatística

Monitoring Image Processes.

*Wolfgang Schmid*, European University Viadrina, Department of Statistics, Frankfurt, Germany.

## Resumo

In recent years we observe dramatic changes in the way in which quality features of manufactured products are designed and inspected. The modeling and monitoring problems obtained by new inspection methods and fast multi-stream high-speed sensors are quite complex. These measurement tools are used in emerging technologies like, e.g., additive manufacturing. It has been shown that in these fields other types of quality characteristics have to be monitored. It is mainly not the mean, the variance, the covariance matrix or a simple profile which reflects the behavior of the quality characteristics but the shape, surfaces and images, etc. This is a new area for SPC. Note that more complicated characteristics arise in other fields of applications as well like, e.g., the monitoring of optimal portfolio weights in finance. Since in the last years many new approaches have been developed in the fields of image analysis, spatial statistics and for spatio-temporal modeling a huge amount of tools are available to model the underlying processes. Thus the main problem lies on the development of monitoring schemes for such structures.

In this talk new procedures for monitoring image processes are introduced. They are based on multivariate exponential smoothing and cumulative sums taking into account the local correlation structure. A comparison is given with existing methods. Within an extensive simulation study the performance of the analyzed methods is discussed.

The presented results are based on a joint work with Yarema Okhrin and Ivan Semeniuk.

## Análise, Geometria e Sistemas Dinâmicos

A short KPZ story.

*Alessandra Occelli*, Instituto Superior Técnico.

## Resumo

The aim of this talk is to present a few models in the Kardar–Parisi–Zhang (KPZ) universality class, a class of stochastic growth models that have been widely studied in the last 30 years. We will focus in particular on last passage percolation (LPP) models. They provide a *physical* description of combinatorial problems, such as Ulam's problem, in terms of zero temperature directed polymers; but also a geometric interpretation of an interacting particle system, the totally asymmetric simple exclusion process (TASEP); and of a system of queues and servers. Moreover, in the large time limit, they share statistical features with certain ensembles of random matrices.

## $QM^3$ Matéria Quântica & Matemática

The geometry and topology of free fermions.

*Bruno Mera*, Security and Quantum Information Group of Instituto de Telecomunicações.

## Análise, Geometria e Sistemas Dinâmicos

KPZ universality for last passage percolation models.

*Alessandra Occelli*, Instituto Superior Técnico.

## Resumo

In this seminar we consider last passage percolation on $\mathbb{Z}^2$, a model in the Kardar–Parisi–Zhang (KPZ) universality class. We will investigate the universality of the limit distributions of the last passage time for different settings. In the first part we analyze the correlations of two last passage times for different ending points in a neighbourhood of the characteristic. For a general class of random initial conditions, we prove the universality of the first order correction when the two observation times are close. In the second part we consider a model of last passage percolation in half-space and we obtain the distribution of the last passage time for the stationary initial condition.

## Geometria em Lisboa

A anunciar.

*Michela Zedda*, Università di Parma.

## $QM^3$ Matéria Quântica & Matemática

A anunciar.

*Angelo Carollo*, University of Palermo.

## Teoria de Cordas

$3d$ Modularity.

*Francesca Ferrari*, SISSA Trieste.

## Resumo

We find and propose an explanation for a large variety of modularity-related symmetries in problems of $3$-manifold topology and physics of $3d$ $N=2$ theories, where such structures a priori are not manifest.

## Geometria em Lisboa

A anunciar.

*Bruno Colbois*, Université de Neuchâtel.

## $QM^3$ Matéria Quântica & Matemática

A anunciar.

*Alex Bullivant*, University of Leeds.

## Teoria de Cordas

An SLE approach to four dimensional black hole microstate entropy.

*Paolo Benincasa*, Niels Bohr Institute.

## Resumo

We model the Bekenstein-Hawking entropy of a four dimensional extremal black hole in terms of classifying particles moving in its near horizon $AdS_2$ geometry. We use the framework of SLE curves in $AdS_2$ to classify these particle trajectories in terms of their boundary conditions.

## Relatividade Matemática

Mode stability for the Teukolsky equation on extremal Kerr black hole spacetimes.

*Rita Teixeira da Costa*, University of Cambridge.

## Resumo

We prove that there are no exponentially growing modes nor modes on the real axis for the Teukolsky equation on extremal Kerr black hole spacetimes. While the result was previously known for subextremal spacetimes, we show that the proof for the latter cannot be extended to the extremal case as the nature of the event horizon changes radically in the extremal limit.

Finally, we explain how mode stability could serve as a preliminary step towards understanding boundedness, scattering and decay properties of general solutions to the Teukolsky equation on extremal Kerr black holes.