Classification theory is a branch of model theory that tries to
classify the models in a given class by finding various dimensions.
Concrete examples of such are the transcendence degree of an algebraically
closed field or the linear dimension of a vector space.

When turning to structures from analysis (e.g. Banach spaces, operators,
etc.) new phenomena arise. One is that things looks better if studied 'up
to perturbation'. In this talk I will talk about what happens when one
attempts classificatio theory 'up to perturbation': which model
theoretical methods work, which don't, which ones would I like to attain.

The Maxwell equations form the basis of the classical electromagnetic theory. In addition to these famous four equations, we need the constitutive relations, which connect the fields and flux densities to each other by the material parameters, permittivity and permeability. It is very natural to assume that these material parameters are in most cases positive. However, if we allow them to go negative, we face new exciting physical phenomena that have attracted mathematicians, physicists and engineers alike. For example, double-negative materials allow backward wave propagation and negative refraction enabling sub-wavelength focusing of a light beam. If only the electric permittivity is negative, such interfaces can support plasmonic resonances that are sub-wavelength oscillations of electron density excited by the incident light. Noble metals can manifest negative permittivity at visible and ultraviolet frequencies. However, the possibility of constructing double-negative materials has become closer to reality only recently alongside the research of artificial metamaterials.

The word "gerbe" is an odd one-it is not a furry little animal, nor a hip slang word used to indicate your disrespect towards someone. In fact, it derives instead from a french word in common use and got absorbed by English language. The Oxford English dictonary gives "something resembling a sheaf of wheat" and "something resembling a sheaf" is quite close to the mathematical meaning of the word. In this talk I plan to give a short insight in the theory of gerbes and its connection to cohomology. 

In this talk, I will discuss how I came to know and like hyperbolic geometry. I will discuss a few results which I think are absolutely striking such as Poincaré's reflection theorem and Mostow rigidity. Time permitting, I will say a few words about Sullivan's dictionary and discuss some parallel ideas in complex dynamics.

"Digital Speech Processing" refers to the study of a speech signal. Namely, these signals are processed in a digital representation, as for example, synthesis, analysis, enhancement, compression and recognition may refers to this process.

In this talk we are interested on solving the core problem known as "Glottal Inverse Filtering" (GIF). Commonly this problem can be modelled by convolving a pressure function (input signal) with an impulse response function (filter). Our approach is done in a deterministic setup based on the dbl-RTLS (double regularised total least squares) approach introduced recently. Additionally we review briefly the methodology and we give the first numerical realisations, based on an alternating minimisation procedure.

Bootstrap percolation on the random graph G_{n,p} is a process of spread of “activation” on a given realization of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at least r ≥ 2 active neighbours become active as well.

The graph G_{n,p} has n vertices and every pair of vertices has an edge with probability p independently of the other edges.

The parameters of the model are, besides r (fixed) which I will take to be 2 along the presentation and n (tending to ∞), the size a = a of the initially active set and the probability p = p of the edges in the graph.

The model exhibits a sharp phase transition: depending on the parameters of the model the final size of activation, of size A^∗, with a high probability is either n − o or it is o.

This is a joint work with Svante Janson, Tomasz Luczak and Tatyana Turova.

This talk is intended for a general audience.

Juggling patterns provide hands-on examples of both affine permutations (periodic setting) and coupled renewal processes (random setting). I will first give a short illustration of the basics and then survey some past and ongoing research from a thermodynamical formalism point of view.

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that aims to recover the internal conductivity/permittivity of a body via current and voltage measurements taken at its surface. Images are then formed from the reconstructed conductivity/permittivity distribution(s) for diagnostic and evaluative purposes.   In the 2D geometry, EIT is clinically useful for chest and brain imaging, and applications extend to nondestructive evaluation and underground prospecting.   The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very sensitive to noise, and requires the use of regularized solution methods such as D-bar methods.  D-bar methods, based on tailor-made scattering transforms, regularize EIT through nonlinear low-pass filters.  Key tools for the methods involve complex geometrical optics solutions, the Faddeev Green’s function, scattering transforms, and D-bar equations.   Advantages of D-bar algorithms include parallelization, low frequency limits in the scattering parameter, and as the methods are non-iterative, no concerns regarding convergence to local minima.   In this introductory talk, a conceptual overview of D-bar methods for the EIT problem is given.  Reconstructions of complex admittivities (conductivities and permittivities) from experimental EIT data are presented, and the partial data case is explored.

Dependence logic is a new logical framework in which various notions of dependence and independence can be formalized and studied. I will introduce the basics of dependence logic and discuss some recent work related to the complexity theoretic aspects of it. I will also shed some light on the connections dependence logic has to areas such as database theory and probability theory.

A good lemma is worth a thousand theorems. I will make a case for this by considering the Schwarz lemma. In particular, I will illustrate uses of Schwarz lemma in connection with complex dynamics and quasiconformal mappings. A key notion here is that of a holomorphic motion.

I will briefly tell what modular forms are, and why they are useful. I will then motivate the research of exponential sums related to modular forms. Finally, I will explain some applications, namely, I will explain the idea behind the solution of Linnik's problem using modular forms, and conclude with the recent application in coding theory.

In the talk we discuss some results on characterizing the traces of functions from Sobolev spaces, Besov spaces and Triebel-Lizorkin spaces to Ahlfors regular subsets of the Euclidean space.

This talk will start with some basic examples of dynamical systems, illustrating that complexity and randomness can be generated by simple deterministic rules. We will examine the sometimes surprising results when one perturbs certain systems in the one-dimensional setting. Towards the end I shall present some recent results of mine concerning the dynamics of the exponential family in the complex plane. The talk will be suitable for a non-specialist audience.

Many numerical problems in science, engineering, finance, and statistics are solved through Monte Carlo methods. For instance, the computations required in Bayesian analysis have become viable using efficient random sampling algorithms. Within the Monte Carlo techniques, the Markov Chain Monte Carlo (MCMC) algorithms are very powerful tools and widely used for Bayesian inference. This talk provides a brief (and basic) "journey" through the MCMC world.

Quantum walks have attracted a lot of attention during recent years due to their surprising limit behavior. In this talk I will introduce quantum walks on the line with a temporal randomization. Looking at each individual step we find that all processes appear to be classical. However, we will show that the time correlations are non-classical and differ depending on the randomization.

I will give a brief introduction to conformal invariance phenomena in two-dimensional statistical physics. Conformal invariance is a property of various quantities associated to the model (expectations, probabilities, probability measures on random curves etc.) to behave nicely under conformal maps. Based on several simple examples, I will explain modern tools to study this phenomenon, such as discrete complex analysis and Schramm-Loewner evolution. Time permitting, I will discuss my joint results with Dmitry Chelkak and Clément Hongler concerning the Ising model.