## Quantum Computation and Information

On the Security of Semi-Quantum Key Distribution.

*Walter Krawec*, Universidade de Connecticut.

## Abstract

A semi-quantum key distribution protocol is presented and its proof of security is detailed.

## Functional Analysis, Linear Structures and Applications

On a simple proof of the boundedness of Bergman projection in various Banach spaces and some related questions.

*Alexey Karapetyants*, Southern Federal University, Rostov-na-Donu, Russia.

## Abstract

We give a simple proof of the boundedness of Bergman projection in various Banach spaces of functions on the unit disc in the complex plain. The approach of the paper is based on the idea of V. P. Zaharyuta, V. I. Yudovich (1962) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderon-Zygmund operators. We exploit this approach and treat the cases of variable exponent Lebesgue space, Orlicz space and variable exponent generalized Morrey space. In the case of variable exponent Lebesgue space the boundedness results is known, so in that case we provide a simpler proof. The other two cases are new. The major idea of this paper is to show that the approach can be applied to a wide range of function spaces. This opens a door in a sense for introducing and studying new function spaces of Bergman type in complex analysis.

We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollifying dilations.

This is a joint work with Stefan Samko and Humberto Rafeiro.

## Probability and Statistics

GARCH processes and the phenomenon of misleading and unambiguous signals.

*Manuel Cabral Morais*, Departamento Matemática - Instituto Superior Técnico.

## Abstract

In Finance it is quite usual to assume that a process behaves according to a previously specified target GARCH process. The impact of rumours or other events on this process can be frequently described by an outlier responsible for a short-lived shift in the process mean or by a sustained change in the process variance. This calls for the use of joint schemes for the process mean and variance, such as the ones proposed by Schipper (2001) and Schipper and Schmid (2001).

Since changes in the mean and in the variance require different actions from the traders/brokers, this paper provides an account on the probabilities of misleading and unambiguous signals (PMS and PUNS) of those joint schemes, thus adding valuable insights on the out-of-control performance of those schemes.

We are convinced that this talk is of interest to business persons/traders/brokers, quality control practitioners, and statisticians alike.

Joint work with:

Beatriz Sousa (MMA; CGD);

Yarema Okhrin (Faculty of Business and Economics, University of Augsburg, Germany);

Wolfgang Schmid (Department of Statistics, European University Viadrina, Germany)

References

Schipper, S. (2001). Sequential Methods for Detecting Changes in the Volatility of Economic Time Series. Ph.D. thesis, European University, Department of Statistics, Frankfurt (Oder), Germany.

Schipper, S. and Schmid, W. (2001). Control charts for GARCH processes. Nonlinear Analysis: Theory, Methods & Applications 47, 2049-2060.

## LisMath

Topological pressure and dimension.

*João Rijo*, Instituto Superior Técnico.

## Abstract

Introduction to the thermodynamic formalism, including the notions of topological entropy and topological pressure. Variational principle with sketch of the proof in the particular case of topological entropy. Description of some applications to the dimension theory of hyperbolic dynamics, after introducing the relevant notions of dimension theory and of repeller, with formulation (without proof) of the result giving the dimension of a conformal repeller via the topological pressure.

**Bibliography**

[1] L. Barreira, Dimension and Recurrence in Hyperbolic Dynamics, Birkhäuser, 2008.

[2] L. Barreira, Thermodynamic Formalism and Applications to Dimension Theory, Birkhäuser, 2011.

[3] L. Barreira, Ergodic Theory, Hyperbolic Dynamics and Dimension Theory, Springer, 2012.

[4] L. Barreira and C. Valls, Dynamical Systems, Springer, 2013.

## Partial Differential Equations

To be announced.

*Heinrich Freistühler*, University of Konstanz.

## Colloquium

O Poder dos Sistemas Analógico-Digitais.

*José Félix Costa*, IST - ULisboa.

## Abstract

Introduz-se um modelo de computação analógico-digital em que a componente digital é o modelo padrão (e.g. máquina de Turing) e a componente analógica é o resultado de uma medição, e.g. obtida através de sensor de grandeza física. A medição atua como oráculo e a troca de informação entre a componente digital e a componente analógica decorre no tempo intrínseco ao processo físico. As medições realizadas pelo acoplamento analógico-digital podem ser executadas através de diferentes protocolos, de estocástico a determinístico, nomeadamente fazendo variar a precisão da medição entre finita e infinita. Discute-se a natureza das medições que podem ser efetuadas pelos sistemas analógico-digitais. Estabelece-se que o poder computacional destes sistemas que operam num número polinomial de passos é o das classes computacionais $\mathit{BPP//}\log^{(k)}\!\

**See also**: https://www.math.tecnico.ulisboa.pt/~camado/ColoquioDM/Cartaz_ColloquiumMatematica_outubro17.pdf

## Analysis, Geometry, and Dynamical Systems

To be announced.

*Adriana Neumann*, Universidade Federal do Rio Grande do Sul.

## Analysis, Geometry, and Dynamical Systems

To be announced.

*David Krejciric*, Czech Technical University.

## Analysis, Geometry, and Dynamical Systems

To be announced.

*Daniel Rodrigues*, University of Groningen.

## Analysis, Geometry, and Dynamical Systems

A random particle system and nonentropy solutions of the Burgers equation on the circle.

*Alexandre Boritchev*, Institut Camille Jordan, Université Lyon 1.

## Abstract

We consider a particle system which is equivalent to a process valued on the space of nonentropy solutions of the inviscid Burgers equation. Such solutions are conjectured to be relevant for the study of the KPZ fixed point. We prove ergodicity and obtain some properties of the stationary measure.

Joint work with C.-E. Bréhier (Lyon) and M. Mariani (Rome).

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