## Logic and Computation

Disjoint fibring of non-deterministic matrices.

*Sérgio Marcelino*, SQIG - Instituto de Telecomunicações.

## Abstract

*[Note the unusual week day and time of this seminar]*

We give a first definitive step towards endowing the general mechanism for combining logics known as fibring with a meaningful and useful semantics given by non-deterministic logical matrices (Nmatrices). We present and study the properties of two semantical operations: a unary operation of ω-power of a given Nmatrix, and a binary operation of strict product of Nmatrices with disjoint similarity types (signatures). We show that, together, these operations can be used to characterize the disjoint fibring of propositional logics, when each of these logics is presented by a single Nmatrix. As an outcome, we also provide a decidability and complexity result about the resulting fibred logic. We illustrate the constructions with a few meaningful examples.

Joint work with Carlos Caleiro.

## Geometria em Lisboa

On periodic points of symplectomorphisms on closed manifolds.

*Marta Batoréo*, Universidade Federal do Espírito Santo.

## Abstract

In this talk, we will discuss symplectomorphisms on closed manifolds with periodic orbits. We will present some results on the existence of (infinitely many) periodic orbits of certain symplectomorphisms on closed manifolds. Moreover, we will give a construction of a symplectic flow on a closed surface of genus $g$ greater than $1$ with exactly $2g-2$ fixed points and no other periodic orbits.

## Geometria em Lisboa

Contact topology of Gorenstein toric isolated singularities.

*Miguel Abreu*, Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Instituto Superior Técnico.

## Abstract

Links of Gorenstein toric isolated singularities are good toric contact manifolds with zero first Chern class. In this talk I will present some results relating contact and singularity invariants in this particular toric context. Namely,

- I will explain why the contact mean Euler characteristic is equal to the Euler characteristic of any crepant toric smooth resolution of the singularity (joint work with Leonardo Macarini).
- I will discuss applications of contact invariants of Lens spaces that arise as links of Gorenstein cyclic quotient singularities (joint work with Leonardo Macarini and Miguel Moreira).

## Functional Analysis, Linear Structures and Applications

Integral Graphs.

*Ali Mohammadian*, Institute for Research in Fundamental Sciences, Tehran, Iran.

## Abstract

A graph $G$ is called integral if all eigenvalues of its adjacency matrix, $A(G)$, consist entirely of integers. The nullity of $G$ is the nullity of $A(G)$, that is the multiplicity of $0$ as an eigenvalue of $A(G)$. In this talk, we are concerned with integral trees. These objects are extremely rare and very difficult to find. We first present a short survey on integral graphs. We show that for any integer $d \gt 1$, there are infinitely many integral trees of diameter $d$. We will also show that for any integer $k \gt 1$, there are only finitely many integral trees with nullity $k$.

## Partial Differential Equations

To be announced.

*Heinrich Freistühler*, University of Konstanz.

## 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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