### Mathematical approaches to complex systems: Statistical mechanics and partial differential equations

6 – 7 July 2017, at Faculdade de Ciências da Universidade de Lisboa, room 6.2.33 [⤴]

Na sequência da workshop da Arrábida com o mesmo nome, haverá uma extensão de dois dias, dedicada a estudantes e público em geral, em que os mesmos temas serão tratados de modo acessível e pedagógico.

#### 5ª-feira, 6 de Julho de 2017

10:00 – 11:00 • M. LOSS (Georgia Tech, USA)*The Kac master equation: Propagation of chaos, derivation of Boltzmann equation and approach to equilibrium*

11:30 – 12:30 • M. PULVIRENTI (Univ. of Rome la Sapienza, Italy)*The mechanism of chaos for classical particle systems: Propagation in time of statistical independence, scaling limits and kinetic equations (Vlasov, Boltzmann, Landau)*

14:30 – 15:30 • M. INFUSINO (Univ. Konstanz, Germany)

To be announced

15:30 – 17:30 • Workshop discussions

#### 6ª-feira, 7 de Julho de 2017

10:00 – 11:00 • E. CARLEN (Rutgers University, USA)*Introduction to operator inequalities, non-commutative probability and quantum statistical mechanics*

11:30 – 12:30 • R. ESPOSITO (Univ. of Rome Tor Vergata, Italy)*Hydrodynamic limit of steady non equilibrium solutions to the Boltzmann equation*

14:30 – 17:30 • Workshop discussions

Comissão Organizadora: E. Carlen, M. C. Carvalho, J. L. Vasquez e R. Vilela Mendes

### Optimization 2017

6 – 8 September 2017, at Faculdade de Ciências, Universidade de Lisboa

Plenary Speakers: Immanuel Bomze (Universität Wien), Marco Campi (Università degli Studi di Brescia), Donald Goldfarb (Columbia University), Jacek Gondzio (University of Edinburgh), Martine Labbé (Université Libre de Bruxelles), Giovanni Rinaldi (IASI Roma, CNR)

### Workshop Day on Biomathematics

**March 31 ^{st}, 2017 **| Faculty of Sciences | University of Lisbon

From 3 p.m. until 6 p.m. | Room 6.2.33 | Building C6

In preparation for the **ECMTB 2018** and the Year of the Mathematical Biology, we invite for a workshop day on Biomathematics to take place in FCUL, University of Lisbon on March 31^{st}, 2017.

**Invited Speakers**

15:00–15:30 **Maíra Aguiar**, (CMA FCT) NOVA University of Lisbon | (CMAFCIO FCUL) Lisbon University, "The impact of the newly licensed dengue vaccine in endemic countries"

15:30–16:00 **Fabio Chalub**, (CMA FCT) NOVA University of Lisbon, "Regularity and time-inhomogeneity in the Wright-Fisher dynamics"

16:00–16:30 **Mats Gyllenberg**, University of Helsinki, "Invasion into dimorphic populations under Atkinson-Allen dynamics"

16:30–17:00 **Anna Marciniak-Czochra**, (IWR) University of Heidelberg, "Mathematical modeling of heterogeneity and clonal selection in acute leukemias"

17:00–17:30 **Luigi Preziosi**, Politecnico di Torino, "An overview of mathematical models for cell migratio"

17:30–18:00 **Nico Stollenwerk**, (CMAFCIO FCUL) Lisbon University, "Chaos via Torus destruction in models of Dengue Fever and predator-prey systems, implications for data analysis"

Event partially funded by the Portuguese Mathematical Society [⤴].

### 8th International Network Optimization Conference (INOC 2017)

26 – 28 February 2017, in Lisboa - Portugal

Keynote Speakers: William Cook (University of Waterloo), Alexander Martin (University of Erlangen-Nürnberg), Rolf H. Möhring (Technical University of Berlin), Alexander Schrijver (University of Amsterdam)

### Workshop “Long-range Coupled Polymers: Analysis and Simulation”

5 – 11 February 2017, at Academia das Ciências de Lisboa - Portugal

Wolfgang Bock (Technical University Kaiserslautern), Jinky Bornales (Mindanao State University), Samuel Eleutério (University of Lisbon), Torben Fattler (Technical University Kaiserslautern), Satoru Itoh (Institute for Molecular Sciences, Okazaki), Hisashi Okumura (Institute for Molecular Sciences, Okazaki), Maria João Oliveira (Universidade Aberta), Ludwig Streit (ACL, Portugal and University of Bielefeld), Herry P. Suryawan (University of Zurich), Rui Vilela Mendes (Academia das Ciências de Lisboa), Elmar Westphal (Forschungszentrum Jülich)*, Roland Winkler (Forschungszentrum Jülich) * To be confirmed

The Organizing Committee: W. Bock, M. J. Oliveira, L. Streit, R. Vilela Mendes

## Ciência, política e sociedade

**in memoriam Jean-Pierre Contzen**

3 February 2017, at Academia das Ciências de Lisboa - Portugal

MANHÃ**9:00 – 9:15** *Abertura*: Presidente da ACL**8:15 – 10:45** *Testemunhos sobre J. P. Contzen*

• Hervé Hasquin, Secretário Perpétuo, ARB

• Arantes e Oliveira, ACL**10:45 – 11:00** Intervalo

• Moderador: R. Vilela Mendes, ACL**11:00 – 12:00** Ludwig Streit, “*Complexity, globalization, acceleration and what about democracy?*”**12:00 – 12:30** Jorge Braga de Macedo, “*Discussão e comentários*”**12:30 – 13:00** Discussão geral aberta à assistência

ALMOÇO 13:00 – 14:30

TARDE: *Dedicada ao tema da biodiversidade e cooperação com os países em vias de desenvolvimento*

• Moderador: Rui Malhó, ACL**14:30 – 16:00**

• Dominic Moran, “*Valuing biodiversity: a brief history*”

• Nuno Ferrand, ACL, "*Discussão e comentários*"**16:00 – 16:45** Painel "*Science and business for development*"**16:45** *Encerramento*, Ministro da Ciência, Tecnologia e Ensino Superior

**8th Workshop Dynamical Systems Applied to Biology and Natural Sciences**

31 January – 3 February 2017, at Universidade de Évora - Portugal

Plenary Talks: Maíra Aguiar (Lisbon University), Malay Banerjee (Indian Institute of Technology), Konstantin Blyuss (Universty of Sussex), Julyan Cartwright (Universidad de Granada), Bernard Cazelles (Ecole Normale Supérieure - UMMISCO - CNRS), Laurent Coudeville (Sanofi Pasteur), Ulrike Feudel (Universität Oldenburg), Istvan Kiss (Universty of Sussex), Bob W. Kooi (Free University of Amsterdam), Mats Gyllenberg (University of Helsinki)

**6th Winter School on Network Optimization**

16 – 20 January 2017, in Estoril - Portugal

Lecturers: Ángel Corberán (Univ. Valencia), Arie Koster (RWTH Aachen Univ.), Gerhard Reinelt (Univ. Heidelberg), Giovanni Rinaldi (IASI), José Valério de Carvalho (Univ. Minho)

## 2016

**COLLOQUIUM: The Legacy of Claude Shannon**

13 December 2016, 16:00, at Instituto Superior Técnico, Universidade de Lisboa

*Minicourse*

**An introduction to impredicative ordinal notation systems**

**DAVID FERNÁNDEZ-DUQUE**

UNIVERSITÉ PAUL SABATIER (Toulouse)

First session: November 2 (Wednesday), 6pm - 7:30pm, room 6.2.33

Second session: November 3 (Thursday), 3:30pm - 5pm, room 6.2.33

In this course we will give an introduction to ordinal notation systems based on collapsing cardinals in the style of Buchholz. Although familiarity with proof-theoretic ordinals is assumed, the course will work gradually, beginning with a quick review of predicative notation systems and introducing some intermediate systems along the way. The course will be divided in two sessions. Session 1: We introduce a general notion of ordinal notation system and show how the usual presentations for $\varepsilon_0$ and $\Gamma_0$ fall into this framework. We discuss the behavior of an uncountable ordinal within a notation system and introduce collapsing functions, culminating in a notation system for the Bachmann-Howard ordinal $\psi(\varepsilon_{\Omega+1})$. Session 2: We establish some important properties of $\psi(\varepsilon_{\Omega+1})$, including its computability. We motivate the role of multiple cardinals by considering collapsing functions with two uncountable cardinals. We then show how these techniques are extended to collapsing infinitely many cardinals. Time permitting, we discuss how larger sets (e.g., an inaccessible) can be used to construct even larger proof-theoretic ordinals.

**E=MC3 2016, a Spring-to-Summer event: three mini courses on Dynamics and Differential Equations**

Alessandra Celletti, March 29-30; Fabio Zanolin, July 11-15; Mark Levi, Sept 5-9

FCUL, Lisbon, 31 Aug-2 Sept 21 2016

**7th International Conference on Computational Logistics
(ICCL’16)**

**“Road to logistics excellence”**

September 7-9, 2016 in Lisbon, Portugal

**Journées sur les Arithmétiques Faibles (Weak Arithmetics Days)**

FCUL, Lisbon, 6-7 June 2016

**H-mesures and variants**

A short course by Nenad Antonic, April 18-21-22, 15:00-17:00.

Weak convergences are the foundations of most successful methods in the investigation of partial differential equations today. The approach known as <em>Tartar's programme</em> [15] proved particularly convenient for partial differential equations modelling physical laws; the basic assumption being that weak convergences of sequences of solutions model the transition from microscale to macroscale. We are particularly interested in mathematical objects being, in a generalised sense, accumulation points of weakly convergent sequences, such as defect measures or H-measures. H-measures are a microlocal analysis tool which has successfully been applied in a variety of applied analysis problems: in small amplitude homogenisation [16], in the theory of microstructure (problems with two or more potential wells) [10], in the study of propagation of oscillations and microlocal energy [17, 1], in controllability of partial differential equations [8], etc. The original H-measures are suited for the treatment of hyperbolic problems. Recently, different variants of the concept have been introduced, first allowing extension of the results to parabolic type problems [3, 5, 14], and later to problems of more general type.

Another successful application of H-measures is in the velocity averaging theory, as they enable generalisation of results obtained for constant coefficients (the homogeneous setting) to variable ones (the heterogeneous setting). First results of this kind are found in [9] for hyperbolic problems, while recent development of variant H-measures enabled generalisations to problems of various types [12], including other linear and even fractional differential equations. The notion of H-measures is given in the L2 framework, and the above results are constrained to solutions bounded in Lp, p>=2. By developping and applying appropriate tools, namely H-distributions [6], applications outside the L2 framework are also possible. Quite often, the nature of the problem requires a particular variant to be developed, prompting further research in constructing new objects.

[1] N. Antonic: H-measures applied to symmetric systems, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996) 6, 1133-1155

[2] N. Antonic, M. Lazar: A parabolic variant of H-measures, Ann. Univ. Ferrara Sez. VII Sci. Marc. 54 (2008) 2, 183-201

[3] N. Antonic, M. Lazar: H-measures and variants applied to parabolic equations, J.Math. Anal. Appl. 343 (2008) 1, 207-225

[4] N. Antonic, M. Lazar: Parabolic variant of H-measures in homogenization of a model problem based on Navier-Stokes equation, Nonlinear Anal. Real World Appl. 11 (2010) 6, 4500-4512

[5] N. Antonic, M. Lazar: Parabolic H-measures, J. Funct. Anal. 265 (2013) 7, 1190-1239

[6] N. Antonic, D. Mitrovic: H-distributions - an extension of H-measures to an Lp-Lq setting, Abstr. Appl. Anal. 2011 (2011), article ID 901084, 12 pages

[7] N. Antonic, M. Vrdoliak: Parabolic H-convergence and small amplitude homogenization, Appl. Anal. 88 (2009) 10-11, 1493-1508

[8] N. Burq, P. Gérard: Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes, C. R. Math. Acad. Sci. Paris, Série I, 325 (1997) 749-752

[9] P. Gérard: Microlocal defect measures, Comm. Partial Differential Equations 16 (1991) 1761-1794

[10] R. V. Kohn: The relaxation of a double-well energy, Contin. Mech. Thermodyn. 3 (1991) 193-236

[11] M. Lazar, D. Mitrovic: The velocity averaging for a heterogeneous heat type equation, Math. Commun. 16 (2011), 271-282

[12] M. Lazar, D. Mitrovic: Velocity averaging - a general framework, Dyn.Partial Differ. Equ. 9 (2012), 239-260

[13] M. Lazar, D. Mitrovic: On an extension of a bilinear functional on Lp(Rd) x E to a Bochner space with an application to velocity averaging, C. R. Math. Acad. Sci. Paris 351 (2013) 261-264

[14] E. Yu. Panov: Ultra-parabolic equations with rough coefficients. Entropy solutions and strong precompactness property, J. Math. Sci. (N. Y.) 159 (2009), 180-228

[15] L. Tartar: Compensated compactness and applications to partial differential equations, Non-linear Analysis and Mechanics: Heriott-Watt symposium, Vol IV, Res. Notes in Math. 39, Pitman, Boston, 1979, 136-212

[16] L. Tartar: H-measures and small amplitude homogenization, Random Media and Composites, R.V. Kohn & G.W. Milton eds, 89-99, SIAM, Philadelphia, 1989

[17] L. Tartar: H-measures, a new approach for studying homogenisation, oscillation and concentration effects in PDEs, Proc. Roy. Soc. Edinburgh Sect. A 115:3-4 (1990) 193-230

[18] L. Tartar: Oscillations and concentration effects in partial differential equations: why waves may behave like particles. XVII CEDYA: Congress on Differential Equations and Applications/VII CMA: Congress of Applied Mathematics (Spanish) (Salamanca, 2001), 179-219, Dep. Mat. Apl., Univ. Salamanca, Salamanca, 2001.

[19] L. Tartar: The general theory of homogenization, Springer, 2009

**Introduction to the algebraic theory of linear systems of differential equations**

A short course on D-Modules

**Luca Prelli (CMAFCIO)**

(March 17 and 22, April 5 and 7

**(Dynamical Systems Applied to Biology and Natural Sciences)**

2-5 February 2016, Universidade de Évora

**5th Winter School on Network Optimization**

11-15 January 2016, Hotel Sana, Estoril