**Information** about the courses Syllabus_2021_2022

**Information**about the courses Syllabus_2021_2022

**Information about acceptance of candidates to MAP-PDMA can be consulted** **HERE**

**For relevant dates, click here and here**

**Information About the First Semester**

**SEMINARS**

**Seminar #11: MAP-PDMA PhD Program 2022/2021 — January 14,**** 17****h15, Room 11.3.21, DMat-UA**

* Title: **Study of convex Semi-infinite Programming problems: general approaches, applications, and open problems**

* Speaker: Tatiana Tchemisova, CIDMA, Department of Mathematics, University of Aveiro

* Abstract: Problems of convex Optimization consist in search for extrema of convex functions in domains which are convex sets. Many times the success of the process of solution of such problems depends on the way how the feasible sets are described. The problems where the feasible sets are described with the help of a finite number of convex functions (constraint functions) belong to the convex Nonlinear Programming; such problems are rather well studied and there are solvers developed for them. In the case when the number of constraints is infinite, we deal with problems of Semi-infinite Programming.

In the talk, we present different approaches to solving convex SIP problems, and speak about the open questions and problems.

**Seminar #10: MAP-PDMA PhD Program 2022/2021 — January 14, 16h15, Room 11.3.21, DMat-UA**

* Title: **Compositional data: some challenges in the world of Multivariate Statistics**

* Speaker: Adelaide Freitas, CIDMA, Department of Mathematics, University of Aveiro

* Abstract: In the relative scale, 5% is a half of 10% and 45% forms a fraction of 0.9 of 50%. Obviously! However, in absolute scale, both comparisons produce the same difference. Whenever multivariate observations in a data set represent quantitative descriptions of the parts of some whole, conveying only relative information between parts, statistical techniques adequate to analyze compositional data should be used. Since compositional data are positive multivariate data with constant sum constraint, classic statistical methods (dealing with differences) can be not appropriate to be considered on them. Compositional data has emerged over the last years in numerous scientific fields. We illustrate some examples and list some difficulties to work with compositional data, namely in the area of exploratory multivariate statistics. We review some transformations proposed to overcumber the constraint imposed by the definition and discuss some challenges in the analysis of compositions of compositional data.

**Seminar #9: MAP-PDMA PhD Program 2021/2022 — December 17, 16h30**

* Place: via zoom, https://videoconf-colibri.zoom.us/j/86389857315

* Title: **Multivariate and multiscale complexity under long-range correlation: application in cardiovascular variability**

* Speaker: Ana Paula Rocha, CMUP, Department of Mathematics, University of Porto

* Abstract: An intrinsic feature of some physiological or econometric systems, is their dynamical complexity, resulting from the activity of several coupled mechanisms operating across multiple temporal scales. The cardiovascular system is one of such systems and specific complex characteristics such as long memory and volatility have been considered from a model based ARFIMA-GARCH parametric viewpoint. Entropy rate is another current measure of complexity. Recently, an efficient estimation of the linear multiscale entropy (MSE) was introduced using a state space formulation, able to attend the simultaneous presence of short-term dynamics and long-range correlations by using ARFI modeling. Given the interactions present in these systems, natural generalizations consider a multivariate approach with VARFI models. Within this framework, for Gaussian processes, we propose to estimate the Transfer Entropy, or equivalently Granger Causality, allowing to quantify the information flow and assess directed interactions accounting for long-range correlations.

The methods are applied in experimental and clinical cardiovascular stress situations, allowing to discriminate between health and disease and to assess disease severity. Moreover the developed measures appear to reflect the changes in the cardiovascular variability system dynamics.

**Seminar #8: MAP-PDMA PhD Program 2021/2022 — December 10, 16h30**

* Place: via zoom, https://videoconf-colibri.zoom.us/j/86389857315

* Title: **From Newton’s cooling law to turbulent filtration of non-Newtonian fluids through a porous medium**

* Speaker: Eurica Henriques, Dep. of Mathematics – University of Trás-os-Montes e Alto Douro (UTAD), Centre of Mathematics CMAT – University of Minho: Pole CMAT-UTAD

* Abstract: Differential equations govern several phenomena and their study gives rise to some answers and several other questions. In this seminar we go on a tour starting at Newton’s cooling law (an ordinary differential equation), stoping briefly at some well known partial differential equations (pde) and ending on a doubly nonlinear pde. We will present recent results concerning regularity aspects of the weak solutions to the doubly nonlinear pde

\begin{displaymath}

u_t-\textrm{div} \big(|u|^{m-1} |Du|^{p-2} Du\big)=0 , \qquad p>1

\end{displaymath}

**Seminar #7: MAP-PDMA PhD Program 2021/2022 — December 3, 16h30**

* Place: via zoom, https://videoconf-colibri.zoom.us/j/86389857315

* Title: **Pak-Stanley labeling of hyperplane arrangements**

* Speaker: Rui Duarte, CIDMA, Department of Mathematics, University of Aveiro

* Abstract: In the nineties Pak and Stanley introduced a construction in which every region of the *m*-Shi arrangement of hyperplanes is labeled with a *m*-parking function. In this talk we consider the same construction applied to the regions of the *m*-Catalan arrangement and to the regions of the Ish arrangement. We characterize the Pak-Stanley labels of the regions and of the relatively bounded regions of these arrangements. Finally, we present an algorithm for the inverse.

*This is joint work with António Guedes de Oliveira (CMUP, Department of Mathematics, University of Porto)*

**Seminar #6: MAP-PDMA PhD Program 2021/2022 — November 26, 16h15**

* Place: via zoom, https://videoconf-colibri.zoom.us/j/86389857315

* Speaker: Thomas Kahl, Center of Mathematics, University of Minho

* Title: **Algebraic topology and concurrency theory**

* Abstract: It has been discovered relatively recently that concepts and methods from algebraic topology may be employed profitably in concurrency theory, the field of computer science that studies systems of simultaneously executing processes. A very expressive combinatorial-topological model of concurrency is given by higher-dimensional automata. In this talk, I will present a method to extract homological information from HDAs that is meaningful from a computer science point of view.

**Seminar #5: MAP-PDMA PhD Program 2021/2022 — November 26, 16h15**, **Room 11.3.21, DMat-UA**

* Speaker: Vera Afreixo, CIDMA, University of Aveiro

* Title: **Stable variable selection — an approach based on penalized regression procedures**

* Abstract: The challenge in finding a plausible method to apply in genomic data is due to its high dimensionality. Penalized regression methods were applied in a combined way with methods based on Akaike’s Information Criterion (AIC) to evaluate the importance of potential predictors and to contribute to stable variable selection.

**Seminar #4: MAP-PDMA PhD Program 2021/2022 — November 12, 16h30**

* Place: via zoom, https://videoconf-colibri.zoom.us/j/86389857315

* Speaker: Ana Jacinta Soares, Centre of Mathematics, University of Minho

* Title: **Modeling and applications in kinetic theory of mixtures**

* Abstract: In many problems arising in the interface of mathematics with engineering, natural and life sciences, one important aspect is the presence of diﬀerent scaling regimes of evolution. For example, when modeling biological systems, one should describe not only the global behaviour of the cellular populations but also the cellular dynamics and the biological expression of cells. In ﬂuid dynamics, many problems are described by a macroscopic approach, like Euler or Navier-Stokes, but a microscopic model is needed to describe transition regimes like gas-surface interactions. The kinetic theory is a branch of statistical mechanics that provides a detailed description of the gas at small scales. It allows to obtain the corresponding macroscopic analogue as the hydrodynamic limit of the kinetic equations. Thus, it oﬀers a very convenient approach to many diﬀerent problems.

In this seminar, I will present some interesting problems and applications of the kinetic theory to both ﬂuid dynamical processes and and biological systems.

**Seminar #3: MAP-PDMA PhD Program 2021/2022 — November 5, 16h15, Room 11.3.21, DMat-UA**

* Speaker: Domenico Catalano, CIDMA, University of Aveiro

* Title: **Hypermaps and their classification**

* Abstract: Maps are embeddings of graphs on compact surfaces generalized by hypermaps, replacing graphs by hypergraphs. There are three main approaches to investigate and partially classify hypermaps. Namely by studying hypermaps

• on the same surface or class of surfaces,

• with the same hypergraph or class of hypergraphs,

• with the same group or class of groups of symmetries.

After an introduction to the topic, I will give an idea how classifications of hypermaps can be achieved in each of the above three main ways.

**Seminar #2: MAP-PDMA PhD Program 2021/2022 — October 29, 16h00, Room 11.3.21, DMat-UA**

* Speaker: Dirk Hofmann, CIDMA, University of Aveiro

* Title: **It’s all about the maps**

* Abstract: Category theory is a relatively new area of mathematics which arose originally from the study of a relationship between geometry and algebra; by now it pervades almost all of modern mathematics. Intuitively, every discipline of mathematics can be organised in at least one category; furthermore, category theory encourages a shift of perspective: the focus is placed on the relations (maps or morphisms) between entities (spaces, groups, rings, . . . ) rather than emphasising the entities themselves. In this talk we give an introduction into the theory of categories and the vocabulary surrounding it. We pay special attention to what is is arguably the most successful categorical notion: that of an adjunction. If time permits, we will go one step further and follow Bill Lawvere’s important observation that “. . . the kinds of structures which actually arise in the practice of geometry and analysis are far from being ‘arbitrary’ . . . , as concentrated in the thesis that fundamental structures are themselves categories.”

**Seminar #1: MAP-PDMA PhD Program 2021/2022 — October 22, 16h00, Room 11.3.21, DMat-UA**

* Speaker: Ivan Beschastnyi, CIDMA, University of Aveiro

* Title: **Sub-Riemannian geometry and its applications**

Abstract: In this talk I will explain the basic notions of sub-Riemannian geometry. It is a geometry that models dynamical systems with constraints. Even though its formal definition arose fairly recently, in the end of the XX century, its roots go to antiquity and the isoperimetric problem. After the main definitions are be given, I will show some applications to robotics and neuroscience.