Instituto de Ciencias Matematicas – ICMAT (Institute of Mathematical Sciences)JAE School of Mathematics

Severo Ochoa — ICMAT — JAE Summer School,June 27 – July 15, 2016

Kurusch Ebrahimi-Farda · Fernando Lledob

In most sciences one generation tears down what another has built andwhat one has established another undoes. In mathematics alone eachgenerations adds a new story to the old structure.– Hermann Hankel

The ICMAT organises every June/July the JAE School of Mathematics, as the mainpart of the JAE INTRO programme. The school addresses talented undergraduate andgraduate students who are interested in mathematics research. By creating a fruitfulenvironment amplifying interactions between expert researchers and highly motivatedstudents, the school aims at encouraging those attending to pursue a research career inthe field of mathematical sciences.

The Instituto de Ciencias Matematicas – ICMAT (Institute of Mathematical Sciences)is a joint research center of the Consejo Superior de Investigaciones Cientıficas - CSIC(Spanish National Research Council) and three Madrid universities: the UniversidadAutonoma de Madrid (UAM), the Universidad Carlos III de Madrid (UC3M), and theUniversidad Complutense de Madrid (UCM).

www.icmat.es

Address: C/ Nicolas Cabrera 13-15, Campus Cantoblanco UAM, 28049 Madrid.Telephone: (+34) 91 2999700 – http://www.icmat.es/facilities/howtoarrive

aICMAT-CSIC, bICMAT-UC3M

2 Kurusch Ebrahimi-Farda, Fernando Lledob

Organizing Committee

Kurusch Ebrahimi-Fard ICMAT - CSIC, Madrid, Spaine-mail: kurusch@icmat.es — WWW

Fernando Lledo ICMAT & Univ. Carlos III de Madrid, Madrid Spaine-mail: flledo@math.uc3m.es — WWW

Venue

Aula Naranja and ICMAT library

ICMAT – Aula NARANJAC/ Nicolas Cabrera, 13-15

Campus Universitario de Cantoblanco, UAM28049 Madrid, SPAIN

Lodging

Residencia ErasmoCalle de Erasmo de Rotterdam 5-7

Campus Universitario de Cantoblanco, UAM28049 Madrid, SPAIN

Lunch

Restaurante Plaza Mayor UAM

Severo Ochoa — ICMAT — JAE Summer School, June 27 – July 15, 2016 3

ICMAT – 41Residencia ERASMO – 32Plaza Mayor UAM – 26

4 Kurusch Ebrahimi-Farda, Fernando Lledob

Participants

Lecturers

1. Fernando Casas (IMAC, Castellon, Spain)

2. Eduardo Colorado (ICMAT-UC3M, Madrid)

3. Eva A. Gallardo-Gutierrez (ICMAT-UCM, Madrid)

& Pedro Tradacete Perez (ICMAT-UC3M, Madrid)

4. Mario Garcıa Fernandez (ICMAT-CSIC, Madrid)

& Luis Alvarez Consul (ICMAT-CSIC, Madrid)

5. Antonio Gomez-Corral (ICMAT-UCM, Madrid)

6. Dominique Manchon (CNRS, France)

7. Jesus Munarriz Aldaz (ICMAT-UAM, Madrid)

8. Fran Presas (ICMAT-CSIC, Madrid)

& Alvaro del Pino (ICMAT-CSIC, Madrid)

9. David Rıos Insua (AXA-ICMAT, Madrid)

Students

1. Alfaya Sanchez, David

2. Alonso Lorenzo, Izar

3. Alonso Nicolas, Sandra

4. Andres Miclea, Ruben

5. Armesto Garcıa, Diego

6. Barcena Petisco, Jon Asier

7. Barrero Santamarıa, Miguel

8. Bartoli Duncan, Claudia

9. Benıtez Pulido, Jose Angel

10. Berbel Lopez, Miguel Angel

11. Bernaola Alvarez, Nikolas

12. Canto Llorente, Javier

13. Cazorla Garcıa, Pedro Jose

14. Coltraro Ianniello, Franco

15. Fernandez Besoy, Blanca

16. Galdeano Solans, Mateo

17. Gallardo Arroyo, Carlos

18. Gallego Alcala, Vıctor Adolfo

19. Garcıa Marti, Dolores

20. Garcıa Rasines, Daniel

21. Gimenez Conejero, Roberto

22. Giordano Car, Alexander Michael

23. Gonzalez Molina, Raul

24. Kopylov, Nikita

25. Lleret, Manuel

26. Llinares Romero, Adrian

27. Lopez Alvarez, Diego

28. Martın Merchan, Lucıa

29. Martınez Agui, Francisco Javier

30. Martınez Bamio, David

31. Mota Sanchez, Eduardo

32. Nisar, Zubair

33. Noriega Rodrıguez, Diego

34. Paez Guillan, Marıa Pilar

35. Pal, Arpan

36. Paredero Gil, Daniel

37. Pelaez, Rebeca

38. Perez Fernandez, Victor

39. Ranz, Samuel

40. Rodrıguez Ramırez, Luis Alberto

41. Rubio Sanchez, Alicia

42. Ruiz Lanau, Ana

43. Saez Maestro, Eva

44. Salmeron Garrido, Jose Antonio

45. San Miguel Malaney, Alberto

46. Sanchidrian, Carlos

47. Santos Malpica, Ivan

48. Suarez, Ricardo

49. Trillo Fernandez, David

50. Uzal Couselo, Jose Manuel

51. Violan Arıs, Dıdac

Severo Ochoa — ICMAT — JAE Summer School, June 27 – July 15, 2016 5

Schedule

Registration on Monday, 09:00.

WEEK 1 (27/06/ – 01/07/2016):

Schedule Mon. Tue. Wed. Thu. Fri.JAE2016 27/06/ 28/06/ 29/06/ 30/06/ 01/07/

09:30 - Manchon Manchon Manchon Manchon Manchon- 10:25

10:30 - Manchon Manchon Manchon Manchon Manchon- 11:30

11:30 Coffee Coffee Coffee Coffee Coffee

12:00 - Gomez-C. Gomez-C. Gomez-C. Gomez-C. Gomez-C.- 12:55

13:00 - Gomez-C. Gomez-C. Gomez-C. Gomez-C. Gomez-C.- 14:00

14:00 Lunch Lunch Lunch Lunch Lunch

16:00 - Casas Casas Casas Casas Casas- 16:55

17:00 - Casas Casas Casas Casas Casas- 18:00

Lectures 1st Week (27/06/ – 01/07/2016)

Dominique Manchon — Lectures on combinatorial Hopf algebras and renormalisation

Antonio Gomez-Corral — Modelos Estocasticos y Aplicaciones

Fernando Casas — An Introduction to Geometric Numerical Integration

6 Kurusch Ebrahimi-Farda, Fernando Lledob

WEEK 2 (04-08/07/2016):

Schedule Mon. Tue. Wed. Thu. Fri.JAE2016 04/07/ 05/07/ 06/07/ 07/07/ 08/07/

09:30 - Munarriz Munarriz Munarriz Munarriz Munarriz- 10:25

10:30 - Munarriz Munarriz Munarriz Munarriz Munarriz- 11:30

11:30 Coffee Coffee Coffee Coffee Coffee

12:00 - Gallardo & Gallardo & Gallardo & Gallardo & Gallardo &- 12:55 Tradacete Tradacete Tradacete Tradacete Tradacete

13:00 - Gallardo & Gallardo & Gallardo & Gallardo & Gallardo &- 14:00 Tradacete Tradacete Tradacete Tradacete Tradacete

14:00 Lunch Lunch Lunch Lunch Lunch

16:00 - Colorado Colorado Colorado Colorado Colorado- 16:55

17:00 - Colorado Colorado Colorado Colorado Colorado- 18:00

Lectures 2nd Week (04-08/07/2016)

Eduardo Colorado — Solutions to some variational PDEs as critical points of theirEuler-Lagrange functionals

Jesus Munarriz Aldaz — Concentracion de medida

Eva A. Gallardo-Gutierrez — Recent approaches to the Invariant Subspace Problem& Pedro Tradacete Perez

Severo Ochoa — ICMAT — JAE Summer School, June 27 – July 15, 2016 7

WEEK 3 (11-15/07/2016):

Schedule Mon. Tue. Wed. Thu. Fri.JAE2016 11/07/ 12/07/ 13/07/ 14/07/ 15/07/

09:30 - Garcıa F. & Garcıa F. & Garcıa F. & Garcıa F. & Garcıa F. &

- 10:25 Alvarez C. Alvarez C. Alvarez C. Alvarez C. Alvarez C.

10:30 - Garcıa F. & Garcıa F. & Garcıa F. & Garcıa F. & Garcıa F. &

- 11:30 Alvarez C. Alvarez C. Alvarez C. Alvarez C. Alvarez C.

11:30 Coffee Coffee Coffee Coffee Coffee

12:00 - Rıos Rıos Rıos Rıos Rıos- 12:55

13:00 - Rıos Rıos Rıos Rıos Rıos- 14:00

14:00 Lunch Lunch Lunch Lunch Lunch

16:00 - Presas & Presas & Presas & Presas & Presas &- 16:55 del Pino del Pino del Pino del Pino del Pino

17:00 - Presas & Presas & Presas & Presas & Presas &- 18:00 del Pino del Pino del Pino del Pino del Pino

Lectures 3rd Week (11-15/07/2016)

Fran Presas & Alvaro del Pino — Generating functions in contact topology

David Rıos — Juegos y Decisiones – Matematicas para ayuda a la toma de decisiones

Mario Garcıa Fernandez — Una introduccion a la geometrıa generalizada& Luis Alvarez Consul

8 Kurusch Ebrahimi-Farda, Fernando Lledob

An Introduction to Geometric Numerical Integration(in Five Lectures)

Fernando Casas, Dept. de Matematiques and IMAC, Univ. Jaume I, Spain

Geometric Numerical Integration constitutes nowadays a branch of numerical analysis of dif-ferential equations which aims to provide numerical approximations incorporating qualitativefeatures of the solution of the continuous system being discretized, in particular its geometricproperties. The motivation for developing such structure-preserving algorithms arises indepen-dently in areas of research as diverse as celestial mechanics, molecular dynamics, control theory,particle accelerators physics, and numerical analysis.

Although diverse, the systems appearing in these areas have one important common feature.They all preserve some underlying geometric structure which influences the qualitative nature ofthe phenomena they produce. In geometric numerical integration these properties are built intothe numerical method, which gives the method an improved qualitative behavior, but also allowsfor a significantly more accurate long-time integration than with general-purpose methods.

In addition to the construction of new numerical algorithms, an important aspect of geo-metric integration is the explanation of the relationship between preservation of the geometricproperties of a numerical method and the observed favorable error propagation in long-timeintegration. In the analysis of the methods a number of techniques from different areas of math-ematics, pure and applied, come into play, including Lie groups and Lie algebras, formal seriesof operators, differential and symplectic geometry, etc.

In this short course, we will introduce the main themes, techniques and applications ofgeometric numerical integration, which much emphasis on illustrating them by using simple in-tegrators on well-known physical examples. Program codes will be provided and several exerciseswill also be proposed.

References

1. S. Blanes and F. Casas, A Concise Introduction to Geometric Numerical Integration, CRCPress (2016).

2. K. Feng and M. Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, ZheijangPubl. United Group - Springer (2010).

3. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration, 2nd Ed., Springer(2006).

4. A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett and A. Zanna, Lie-group methods, Acta Numerica9 (2000), 215-365.

5. B. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics, Cambridge University Press(2004).

6. R.I. McLachlan and R. Quispel, Splitting methods, Acta Numerica 11 (2002), 341-434.

Severo Ochoa — ICMAT — JAE Summer School, June 27 – July 15, 2016 9

Solutions to some variational PDEs as critical pointsof their Euler-Lagrange functionals

Eduardo Colorado1, ICMAT-UC3M

The aim of this short course is to show some techniques from the Calculus of Variationsapplied to some nonlinear problems. More precisely, we will show some recent results withapplications in nonlinear optics, Hartree fock Theory for Bose-Einstein condensates, Fluid Me-chanics as for example the interactions of gravity water waves, etc.

For the general theory one can see the following references [3, 2, 6, 5], etc. And for the morespecific problems we will show, see [1, 4].

References

1. A. Ambrosetti, E. Colorado, “Bound and ground states of coupled nonlinear Schrodingerequations”. C. R. Math. Acad. Sci. Paris 342 (2006), no. 7, 453-458.

2. A. Ambrosetti, A. Malchiodi, “Perturbation Methods and Semilinear Elliptic Problems onRn”. Progress in Math, vol. 240, Birkhuser, 2005.

3. H. Brezis, “Functional analysis. Theory and applications”. Collection of Applied Mathemat-ics for the Master’s Degree Masson, Paris, 1983. ISBN: 2-225-77198-7.

4. E. Colorado, “On the existence of bound and ground states for a system of coupled nonlinearSchrodinger-KdV equations”. Adv. Nonlinear Anal., DOI: 10.1515/anona-2015-0181, 2016.

5. B. Dacorogna, “Direct methods in the calculus of variations”. Applied Mathematical Sci-ences, 78. Springer-Verlag, Berlin, 1989. ISBN: 3-540-50491-5.

6. M. Willem, “Minimax theorems. Progress in Nonlinear Differential Equations and theirApplications”. 24. Birkhuser Boston, Inc., Boston, MA, 1996. ISBN: 0-8176-3913-6.

1 Partially supported by Ministry of Economy and Competitiveness of Spain and FEDER funds underresearch project MTM2013-44123-P.

10 Kurusch Ebrahimi-Farda, Fernando Lledob

Recent approaches to the Invariant Subspace Problem

Eva A. Gallardo-Gutierrez, ICMAT-UCM andPedro Tradacete Perez, ICMAT-UC3M

The “invariant subspace problem” is among the most famous fundamental open problemsin Functional Analysis. The question is whether every bounded linear operator on a separableinfinite dimensional Hilbert space has non-trivial invariant subspaces. More generally, this iseven open for operators on reflexive Banach spaces. The aim of this course is to provide anintroduction to this problem starting from the basics and glimpsing on recent approaches to itsso far elusive solution.

Outline:

1. Introduction: Banach spaces and basic facts. Lomonosov’s theorem.2. Banach lattices. Positive and quasinilpotent operators.3. Almost invariant subspaces in reflexive Banach spaces.4. Hilbert spaces. Beurling theorem. More on quasinilpotent operators.5. Universal operators.

References

[AA ] Abramovich, Y. A.; Aliprantis, C. D. An invitation to operator theory. Graduate Studiesin Mathematics, 50. American Mathematical Society, Providence, RI, 2002. xiv+530 pp.

[AAB ] Abramovich, Y. A.; Aliprantis, C. D.; Burkinshaw, O. Invariant subspace theorems forpositive operators. J. Funct. Anal. 124 (1994), no. 1, 95–111.

[PT ] Popov, A. I.; Tcaciuc, A. Every operator has almost-invariant subspaces. J. Funct. Anal. 265(2013), no. 2, 257–265.

Severo Ochoa — ICMAT — JAE Summer School, June 27 – July 15, 2016 11

Una introduccion a la geometrıa generalizada

Mario Garcıa Fernandez ICMAT-CSIC, Madrid andLuis Alvarez Consul, ICMAT-CSIC, Madrid

La geometrıa generalizada fue introducida por Nigel Hitchin en 2003 en su estudio de formasdiferenciales en variedades. La idea basica es sustituir el espacio tangente (espacio de veloci-dades) a una variedad diferenciable por la suma del espacio tangente mas el espacio cotangente(espacio de momentos), y desarrollar las nociones habituales de geometrıa diferencial (campovectorial, metrica, conexion, tensor...) en este nuevo contexto.

El objetivo de este curso es dar una breve introduccion a esta tematica, con enfasis endos tipos de estructuras geometricas: metricas y estructuras complejas generalizadas. Estasnociones geometricas estan motivadas naturalmente en mecanica geometrica (cuantizacion desistemas mecanicos con ligaduras) y en varios contextos de la fısica teorica (supersimetrıa, teorıade cuerdas, supergravedad...), y continuan desarrollandose actualmente por varios grupos dematematicos y fısicos, siendo una fuente de problemas abiertos.

Bibliografıa:

– Marco Gualtieri: Generalized complex geometry. DPhil thesis, Oxford University, 2003.http://arxiv.org/abs/math/0401221

– Marco Gualtieri, Nigel Hitchin: Master Classes on Generalized Geometry. QGM, Aarhus(2011). http://qgm.au.dk/video/mc/geometry/

– Nigel Hitchin: Lectures on generalized geometry, 2010. http://arxiv.org/abs/1008.0973

12 Kurusch Ebrahimi-Farda, Fernando Lledob

Modelos Estocasticos y Aplicaciones

Antonio Gomez-Corral, ICMAT-UCM

IntroduccionEl curso esta orientado a la exposicion de los fundamentos de las cadenas de Markov, las

distribuciones PH y los procesos Markovianos de llegada, y de su aplicacion a la construcciony resolucion de modelos basicos en biologıa. En concreto, se analizaran en detalle los modelosclasicos SIS (susceptible-infective-susceptible) y SIR (susceptible-infective-removed) vinculadosa la propagacion de una epidemia entre los individuos de una poblacion homogeneamente mez-clada.

Programa tentativo

1. Elementos basicos de cadenas de Markov2. Distribuciones de tipo fase (PH) y procesos Markovianos de llegada 3. Distribuciones cuasi-

estacionarias3. Aplicaciones a modelos de epidemias: modelo SIS y modelo SIR

Bibliografıa basica

– L.J.S. Allen (2003) An Introduction to Stochastic Processes with Applications to Biology.Pearson Prentice Hall.

– E. Cinlar (1975) Introduction to Stochastic Processes. Prentice-Hall, Inc.– V.G. Kulkarni (1995) Modeling and Analysis of Stochastic Systems. Chapman & Hall.– G. Latouche and V. Ramaswami (1999) Introduction to Matrix Analytic Methods in Stochas-

tic Modeling. ASA-SIAM Series on Statistics and Applied Probability.

Severo Ochoa — ICMAT — JAE Summer School, June 27 – July 15, 2016 13

Lectures on combinatorial Hopf algebras and renormalisation

Dominique Manchon, CNRS, France

The objects we now call Hopf algebras appeared in 1941 in an algebraic topological context[3], and quickly became a subject of research in themselves (see e.g. [8]). The interest for themincreased greatly in the Eighties of last century, when quantum groups [4], inspired from latticemodels in statistical mechanics, furnished a family of nontrivial examples appearing as defor-mations of universal enveloping algebras.

Besides the nowadays very active field of research opened by the discovery of quantumgroups, combinatorial Hopf algebras have also been intensively studied. They occupy a particu-lar place among Hopf algebras, due to the fact that they can be studied by induction procedureswith respect to a suitable grading or filtration. Together with the concept or renormalisation[2, 6], they have found numerous applications since the turn of the century, from quantum fieldtheory to analysis and number theory.

This series of lectures will start with the basic definitions and examples: we will explain indetail how a finite group gives rise to two canonical Hopf algebras, and how these two basicexamples are related by duality. Tensor algebras and universal enveloping algebras will also beintroduced. Other more recent examples of combinatorial Hopf algebras will be addressed: shuf-fle and quasi-shuffle Hopf algebras, Hopf algebras of rooted trees, quasi-symmetric functions,Hopf algebras of Feynman graphs, etc. The Connes-Kreimer renormalisation procedure will bealso reviewed, as well as the important notion of pre-Lie algebra [7] closely related to that ofcombinatorial Hopf algebra [5].

The lectures will first closely follow [6] and partly [1, 8], and then address more recent topicsif time permits. No prior knowledge of the theory is requested: the prerequisites are limited toelementary linear algebra. Some familiarity with basic group theory is useful, but the necessarynotions will be recalled.

References

1. P. Cartier, A primer of Hopf algebras, Frontiers in Number Theory, Physics, and Geometry,Vol. II, On Conformal Field Theories, Discrete Groups and Renormalization, P. Cartier,P. Moussa, B. Julia, P. Vanhove Eds., Springer (2007), 537–615. Publ. Math. IHES (2006).

2. A. Connes, D. Kreimer, Hopf algebras, renormalization and noncommutative geometry,Comm. in Math. Phys. 199 (1998), 203–242.

3. H. Hopf, Uber die Topologie der Gruppen-Mannigfaltigkeiten und ihrer Verallgemeinerun-gen, Ann. Math. 42, 22–52 (1941).

4. C. Kassel, Quantum Groups, Springer (1995).5. J.-L. Loday, M Ronco, Combinatorial Hopf algebras, Alain Connes 60th birthday volume,

Clay Mathematics Proceedings, Vol. 11, (2010), Amer. Math. Soc.6. D. Manchon, Hopf algebras in renormalisation, Handbook of Algebra 5, (2008), 365–427,

M. Hazewinkel Ed. See also arXiv:math/0408405 [math.QA].7. D. Manchon, A short survey on pre-Lie algebras, E. Schrodinger Institut Lectures in Math.

Phys., Eur. Math. Soc, A. Carey Ed. (2011).8. M. E. Sweedler, Hopf Algebras, Benjamin (1969).

14 Kurusch Ebrahimi-Farda, Fernando Lledob

Concentracion de medida

Jesus Munarriz Aldaz, ICMAT-UAM, Madrid

El tema de la concentracion de medida, en su formulacion mas elemental, se pregunta dondeesta la mayor parte de la masa (medida) en dimensiones altas. Por ejemplo, para una bolaeuclıidea, la mayor parte de la masa esta cerca del borde. Pero tambien esta cerca del ecuador.Mas generalmente, una funcion Lipschitz definida en una bola, es en cierto sentido, aproximada-mente constante.

Este curso tendra un nivel bastante elemental y sera autocontenido. No hay requisitos previosmas alla del calculo en varias variables.

Bibliografıa

Hay innumerables archivos colgados en internet sobre el tema. Mencionamos, por ejemplo:

1) Concentration of measure inequalities Lecture notes, de Gabor Lugosi.

2) Measure concentration lecture notes, de A Barvinok.

3) Por supuesto, el blog de Terence Tao contiene informacion sobre la concentracion demedida, y sobre todo lo demas.

4) Concentration of measure. Nathanal Berestycki and Richard Nickl with an appendix byBen Schlein. University of Cambridge.

5) La siguiente referencia es un libro, y no unas notas de internet: Ledoux, Michel.The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89.American Mathematical Society, Providence, RI, 2001. x+181 pp. ISBN: 0-8218-2864-9.

Severo Ochoa — ICMAT — JAE Summer School, June 27 – July 15, 2016 15

Generating functions in contact topology

Fran Presas, ICMAT-CSIC, Madrid andAlvaro del Pino, ICMAT-CSIC, Madrid

Symplectic geometry (and its odd-dimensional counterpart, contact geometry) first devel-oped as the natural language for the Hamiltonian formalism of mechanics; indeed, much of thecurrent research still focuses on problems of a dynamical nature. On the other hand, it is alsoone of the central ingredients in the study of Mirror Symmetry.

One of the reasons why symplectic geometry is mathematically meaningful is that the groupsof contact and symplectic transformations present a certain “rigidity” that goes beyond algebraictopology. The course will introduce generating function theory as a way of “discretizing” theseinfinite dimensional groups in order to capture their properties. We will focus on the case ofLegendrian submanifolds as a concrete example of the general philosophy.

– Lecture 1: Crash course on Morse theory [Mi].– Lecture 2: Basics in Contact Topology [Ge, MS].– Lecture 3: Legendrian knots. Classical invariants. Review of classical results [Ge].– Lecture 4: Legendrian homology I. [Th]– Lecture 5: Legendrian homology II. [Th]

[Mi ] Milnor, J. Morse theory. Based on lecture notes by M. Spivak and R. Wells. Annals ofMathematics Studies, No. 51 Princeton University Press, Princeton, N.J. 1963 vi+153 pp.

[Ge ] Geiges, H. An introduction to contact topology. Cambridge Studies in Advanced Mathe-matics, 109. Cambridge University Press, Cambridge, 2008. xvi+440 pp.

[MS ] McDuff, D; Salamon, D. Introduction to symplectic topology. Second edition. OxfordMathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1998.x+486 pp.

[Th ] Theret, D. Utilisation des fonctions generatrices en geometrie sympletique globale. Thesede doctorat de l’Universite Paris VII.

16 Kurusch Ebrahimi-Farda, Fernando Lledob

Juegos y DecisionesMatematicas para ayuda a la toma de decisiones

David Rıos Insua, AXA-ICMAT, CSIC y Real Academia de Ciencias

IntroduccionEn el curso haremos una introduccion a modelos matematicos que nos permiten apoyar la

toma de decisiones en situaciones con uno o varios decisores. Se cubren algunos aspectos de-scriptivos, se hace una introduccion a los principales aspectos normativos y se pone el enfasis enlos aspectos prescriptivos. Las ideas se ilustran con ejemplos de seguridad. Se presentan algunosproblemas abiertos.

Contenidos

– Introduccion al analisis de decisiones y a la teorıa de juegos.– Analisis de Decisiones– Aspectos descriptivos de la toma de decisiones individuales– Estructuracion de problemas– Modelizacion de creencias.– Modelizacion de preferencias.– Maximizacion de la utilidad esperada.– Aplicaciones en analisis de riesgos.– Teorıa de Juegos– Aspectos descriptivos de la toma de decisiones por grupos.– Juegos no cooperativos.– Juegos cooperativos.– Analisis de riesgos adversarios.– Aplicaciones.– Algunos problemas abiertos.

Referencias

– S. French, D. Rıos Insua (2000) Statistical Decision Theory, Arnold.– D. Rıos Insua, F. Ruggeri, M. Wiper (2012) Bayesian Analysis of Stochastic Process Models,

Wiley.– D. Banks, J. Rıos, D. Rıos Insua (2015) Adversarial Risk Analysis, Taylor Francis.

Software

– GeNIe. Descargar de https://dslpitt.org/genie/ Seccion Downloads.– R. Descargar de http://www.r-project.org/ Seccion Download.