Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.

CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.

I will discuss the impact of nuisance parameters on the effectiveness of supervised classification in high energy physics problems, and techniques that may mitigate or remove their effect in the search for optimal selection criteria and variable transformations. The approaches discussed include nuisance parametrized models, modified or adversary losses, semi supervised learning approaches and inference-aware techniques.

This talk is concerned with the asymptotic analysis of a variational model of brittle damage, when the damaged zone concentrates into a set of zero Lebesgue measure, and, at the same time, the stiffness of the damaged material becomes arbitrarily small. In a particular non-trivial regime, concentration leads to a limit energy with linear growth as typically encountered in perfect plasticity. While the singular part of the limit energy can be easily described, the identification of the bulk part of the limit energy requires a subtler analysis of the interplay between concentration and oscillation properties of the displacements.

This is a joint work with F. Iurlano and F. Rindler.

Geometrical properties of Cheeger sets have been deeply studied by many authors since their introduction, as a way of bounding from below the first Dirichlet (p)-Laplacian eigenvualue. They represents the first eigenfunction of the Dirichlet (1)-Laplacian of a domain. In this talk we will introduce a recent property, studied in collaboration with Simone Ciani (Università degli studi di Firenze), concerning their contact surface with the ambient space. In particular we will show that the contact surface cannot be too small, with a lower bound on the dimension strictly related to the regularity of the ambient space. The talk will focus on the introduction of the problem. It will start with a brief explanation of its connection with the Dirichlet (p)-Laplacian eigenvalue problem. Then a brief sketch of the proof is given. Functional to the whole argument is the notion of removable singularity, as a tool for extending solutions of pdes under some regularity constraint.

In this talk, we will start by a review of the salient features of the so-called BMS symmetries, which appear as asymptotic symmetries of flat spacetimes, but turn out to be also present in the near-horizon region of black holes. We will then turn to quantum aspects of BMS symmetries in conformally flat spacetimes. After presenting asymptotic and conformal Killing vectors in $d$-dimensional Minkowski and several conformally flat spacetimes, we will show that the associated quantum charges for an arbitrary CFT satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call superdilations. At the end of the talk, we will discuss possible applications of these results for holography and black hole physics.

The dimer model is a model of uniform perfect matching and is one of the fundamental models of statistical physics. It has many deep and intricate connections with various other models in this fiel, namely the Ising model and the six-vertex model.

This model has received a lot of attention in the mathematics community in the past two decades. The primary reason behind such popularity is that this model is integrable, in particular, the correlation functions can be represented exactly in a determinental form. This gives rise to a rich interplay between algebra, geometry, probability and theoretical physics.

For graphs with very regular local structures, exact computations of the correlation functions are possible by Kasteleyn theory. R. Kenyon pioneered the development of the subject in this direction by proving that the fluctuations of the height function associated to the dimer model on the square lattice converges to the Gaussian free field (a conformally invariant Gaussian field). However, such computations seem only possible on graphs with special local structures, while the dimer model is supposed to have GFF type fluctuations in a much more general setting.

In this talk, I will give an overview of an ongoing project with N, Berestycki (U. Vienna) and B. Laslier (Paris-Diderot 7) where we establish a form of universality about the GFF fluctuation of the dimer model. Our approach does not use Kasteleyn theory, but uses a mapping known since Temperley-Fisher, which maps the dimer model to uniform spanning trees. Remarkably, as observed by Benjamini, the “winding” of the branches of this spanning tree exactly measures the height function of the dimers. We combine this approach with the developing universal scaling limit results of the uniform spanning trees, revolutionized by Schramm through the discovery of SLE. We show that the continuum “winding” of these continuum limiting spanning trees converge to the GFF and harness from this the universality of the scaling limit. A key input in identifying the limit is the so-called imaginary geometry developed by Miller and Sheffield. In a more recent work, we extend this universality partially to general Riemann surfaces as well.

This talk is based on the following preprints and some works in progress.

Pure model-based approaches are today often insufficient for solving complex inverse problems in imaging. At the same time, we witness the tremendous success of data-based methodologies, in particular, deep neural networks for such problems. However, pure deep learning approaches often neglect known and valuable information from physics.

In this talk, we will provide an introduction to this problem complex and then discuss a general conceptual approach to inverse problems in imaging, which combines deep learning and physics. This hybrid approach is based on shearlet-based sparse regularization and deep learning and is guided by a microlocal analysis viewpoint to pay particular attention to the singularity structures of the data. Finally, we will present several applications such as tomographic reconstruction and show that our approach outperforms previous methodologies, including methods entirely based on deep learning.

We all have to deal with the coronavirus epidemic. Many strategies have been put in place to try to contain the disease, with varying success.

I will present an SIR-type mathematical model to predict the state of the epidemic. The effect of distancing, isolation of exposed individuals and treatment of symptoms will be compared.

I will begin with a simple explanation of SIR models, then discuss a PDE model and its resolution.

This talk is based on joint work with M. Khovanov and Y. Kononov. By evaluating a topological field theory in dimension $2$ on surfaces of genus $0,1,2$, etc., we get a sequence. We investigate which sequences occur in this way depending on the assumptions on the target category.

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.