Radiality, asymptotic equidistribution on spheres and harmonic functions on infinite graphs. Prof. Wolfgang Woess.

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Fabio Zucca Curriculum Vitæ Current position Place and birthdate Italian English French Assistant Professor (Ricercatore), Dipartimento di Matematica "F.

1 Fabio Zucca Curriculum Vitæ Current position Place and birthdate Italian English French Assistant Professor (Ricercatore), Dipartimento di Matematica "F.Brioschi", Politecnico di Milano, Piazza Leonardo da Vinci, 32, I-20133, Milano.. Milan (Italy), October 5, 1969 Languages Native speaking Very good Good Master Degree Degrees Physics (Laurea in Fisica) cum laude date July 7, 1995 place thesis title Università degli Studi of Milan Studio di una classe di equazioni differenziali stocastiche utilizzate in ottica quantistica (Study of a class of stochastic differential equations used in quantum optics). Ph.D. Mathematics (Dottore di Ricerca in Matematica) date February 23, 2000 place thesis title Advisor Università degli Studi of Milan Radiality, asymptotic equidistribution on spheres and harmonic functions on infinite graphs. Prof. Wolfgang Woess.

2 Professional Experience Career 10/1995 Admitted with a 3 years fellowship to the Ph.D. program Functional Analysis and Applications at the International School for Advanced Studies (Trieste, Italy). 1/1996 Admitted with a 4 years fellowship to the Ph.D. program Dottorato di Ricerca in Matematica at the Università degli studi of Milan. 11/2000-8/ /2001-6/2002 9/2002- present fellowship for research collaboration, 2 years fellowship at the Università degli Studi of Milan on May 16, National Research Council (CNR) fellowship, 6 months fellowship in Functional Analysis and its Applications assigned on January 24, 2001 to be spent at the University of Cergy-Pointoise in collaboration with Prof. T. Coulhon. 3 months extension assigned by CNR on March 19, Assistant Professor (Ricercatore), at the Politecnico di Milano. Other Activities: { Member of the Mathematical Competition Committee of the Department of Mathematics of the Università degli Studi of Milan from 1996 to Among my duties: preparation of mathematical puzzles, lectures, lecture notes. Grants and awards 2001 Young researchers project 2001, Research grant manager Young researchers project 2002, Research grant manager Research award, from the Università degli Studi of Milan, department of Mathematics, for distinguished research activity in INDAM Projects 2007, Research grant manager of the project Interacting particles systems for biological populations and estimates of transition probabilities INDAM Projects 2009, Research grant manager of the project Probabilistic evolution models on graphs. Invited at 2001 Erwin Schrödinger Institute (ESI), February 18 February 23, Invited Professor at the Erwin Schrödinger Institute (ESI), Wien, Austria Erwin Schrödinger Institute (ESI), July 1 July 13, Invited Professor at the Erwin Schrödinger Institute (ESI), Wien, Austria.

3 2003 Université de Cergy-Pontoise, February 10 March 9, Invited Professor at the Département de Mathématique, Université de Cergy-Pontoise, France Universidade de São Paulo, August 26 September 5, Invited Professor at the Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil Technische Universität Graz, September 17 September 25, Invited Professor, at the Institut für Matematik, Technische Universität Graz, Austria Universidade de São Paulo, November 27 December 6, Invited Professor at the Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil Universidade de São Paulo, November 4 November 13, Invited Professor at the Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil. Visiting 1998 Università di Vienna, November Department of Mathematics, University of Wien, Wien, Austria Università di Vienna, January Department of Mathematics, University of Wien, Wien, Austria Technische Universität Graz, January Institut für Matematik, Technische Universität Graz, Austria University of Louisville, November Department of Mathematics, University of Louisville, Louisville, KY (USA) Technische Universität Graz, October Institut für Matematik, Technische Universität Graz, Austria Technische Universität Graz, July Institut für Matematik, Technische Universität Graz, Austria.

4 Interessi scientifici Systems of random walks, I am studying local and global survival for systems of interacting random walks (as the frog model) on graphs. Interacting particle systems, I am working on models for biological systems with non-compact configuration space. I am interested on the asymptotic behavior of the system, in particular on the existence of stationary distributions. I am also studying some epidemic models with immunization. I am interested in the study of local, strong local and global survival, phase transitions and critical parameters. Asymptotic estimates, One of my research fields is the study of asymptotic behavior of the transition probabilities of random walks; among the applications there are the so-called subgaussian estimates. Large scale behavior of Random walks, I introduced a new type problem and a new classification for random walks on graphs. My next aim is to apply this new classification to some fractal-like graphs. Heat Kernels, I worked on these topics in collaboration with Prof. Coulhon (University of Cergy Pointoise, France) and Prof. Grigor yan (Imperial College, UK). In particular we obtained a discrete analogous of the Integral Maximum Principle and some applications.

5 Recent communications 1997 Stochastic Partial Differential Equations and Applications, Levico Terme, Italia, 1/7/97 1/11/97, Poster: On Stochastic Differential Equations and Semigroups of Probability Operators in Quantum Probability V Convegno Nazionale di Fisica Statistica, Parma, Italia, 6/21/00 6/23/00, Poster: Equidistribution of random walks on spheres Random Walks and Statistical Physics, Vienna, Austria, 2/19/01 3/2/01, Talk: Equidistribution of random walks on spheres Convegno Nazionale di Analisi Armonica 2001, Sorrento, Italia, 5/28/01 5/31/01, Talk: The mean value property for harmonic functions on graphs and trees Processi Stocastici, Calcolo Stocastico ed Applicazioni, Pisa, Italia, 9/13/01 9/14/01, Talk: Equidistribution of random walks on spheres First Cornell Summer School In Probability, Ithaca, NY, USA, 7/10/05 7/23/05, Talk: The discrete integral maximal principle and estimates of transition probabilities Workshop on Interacting Particle System, Milano, Italia, 19/22/07 19/23/07, Talk: Ecological equilibrium for restrained random walks th Cornell Summer School In Probability, Ithaca, NY, USA, 6/23/08 7/4/08, Talk: Weak and strong survival for branching random walks on weighted graphs st Workshop Stochastic Modeling, Ribeirão Preto, Brazil, 8/27/08 8/29/08, (invited plenary speaker) - Talk: Survival for branching random walks th Cornell Summer School In Probability, Ithaca, NY, USA, 7/19/10 7/30/10, Talk: Approximating critical parameters of branching random walks Focussed meeting: the shape of branching random walk and related topics, Technische Universität Graz, Graz, Austria, 7/9/12 7/13/12, Talk: Can frogs survive locally? th Brazilian School Of Probability, Recife, Brazil, 8/6/12 8/11/12, Talk: Can frogs survive locally? th SPA conference, Boulder, CO, USA, 7/29/13 8/2/13, Talk: Fixed points of generating functions and strong local survival of Branching Random Walks Groups, graphs and random walks, Cortona, Italy, 6/2/14 6/6/14, (invited speaker) - Talk: Fixed points of generating functions and strong local survival of Branching Random Walks.

6 2014 4th Workshop Stochastic Modeling, São Carlos, Brazil, 11/5/14 11/7/14, (invited plenary speaker) - Talk: Fixed points of generating functions and strong local survival of Branching Random Walks. Recent seminars 1996 Milano, Department of Mathematics, 12/17/1996, Random walks on graphs with a strong isoperimetric inequality Milano, Department of Mathematics, 4/16/1997 & 4/23/1997, Introduction to Combinatorics Milano, Department of Mathematics, 17/12/2001, Generic differentiability for convex functions on Banach spaces Cergy-Pontoise, Département de Mathématique, 12/17/2001, Strong and weak mean value properties on trees Milano, Politecnico di Milano, Department of Mathematics, 7/11/2002, Equidistribution of random walks on spheres Cergy-Pontoise, Département de Mathématique, 3/3/2003, Discrete integral maximal principle and applications Milano, Politecnico di Milano, Department of Mathematics, 5/5/2003, Il principio del massimo integrale discreto ed applicazioni alle stime di probabilita di transizione dei random walk Siena, Università degli Studi, Dipartimento di Ingegneria dell Informazione, 9/21/2004, Funzioni armoniche sui grafi: cosa ci dicono sul comportamento delle passeggiate aleatorie? Una panoramica Bologna, Università degli Studi, Department of Mathematics, 4/14/2005, The Discrete integral maximal principle and its applications São Paulo, Brazil, University of São Paulo, Instituto de Matemática e Estatística, 9/1/2008, Survival for branching random walks Graz, Austria, Technische Universität Graz, Institut für Matematik, 9/17/2008, Survival for branching random walks Louisville, KY (USA), University of Louisville, Department of Mathematics, 11/14/2008, Survival for branching random walks Verona, Università degli Studi, Department of Mathematics, 1/26/2009, Survival for branching random walks Graz, Austria, Technische Universität Graz, Institut für Matematik, 10/8/2009, Patchy restrained processes and other models.

7 2011 São Paulo, Brazil, University of São Paulo, Instituto de Matemática e Estatística, 11/29/2011, Approximating critical parameters of branching random walks and applications São Paulo, Brazil, University of São Paulo, Instituto de Matemática e Estatística, 12/1/2011, Local survival for a frog model São Paulo, Brazil, University of São Paulo, Instituto de Matemática e Estatística, 11/11/2014, Branching random walks and multi-type contact-processes on the percolation cluster of Z d. Other congresses and summer schools 1996 Meeting On Real Analysis and Partial Differential Equations 20 years of Eugene Fabes in Cortona, Cortona, Italia, 5/30/96 6/1/ Random Walks and Discrete Potential Theory, Cortona, Italia, 7/22/97 7/28/ Research Workshop on Graph Theory and Statistical Mechanics, ICTP Trieste, Italy, 5/22/00 5/25/ Economic models with interacting agents, 7/20/2000 7/27/2000,, lectures held by Dott. R. Cont (Ecole Polytechnique di Palaiseau - France) at the Math. Dept. Università degli Studi of Milan Random Walks and Geometry, Vienna, Austria, 6/18/2001 7/13/ Analysis on Graphs and Metric Spaces, Paris, France, 6/26/2002 6/28/ International Conference on Group Theory: combinatorial, geometric, and dynamical aspects of infinite groups, Gaeta, Italy, 6/1/2003 6/6/ Discrete Random Walks: Theory and Applications in Combinatorics, Computational Biology, Computer Science, Probabilities, and Statistical Physics, Paris, France, 9/1/2003 9/5/ Stochastic Models in the Continuum, Florence, Italy, 6/14/2004 6/18/ Second Cornell Summer School In Probability, Ithaca, NY, USA, 6/26/2006 7/7/ Third Cornell Summer School In Probability, Ithaca, NY, USA, 6/18/2007 6/29/ th Cornell Summer School In Probability, Ithaca, NY, USA, 7/11/2011 7/22/2011.

8 Teaching Courses Teaching Assistant for the annual course in Mathematical Analysis II, for graduate students in Mathematics and in Physics at the Università degli Studi dell Insubria (Como, Italy) Teaching Assistant for the annual course in Mathematical Analysis II, for graduate students in Mathematics and in Physics at the Università degli Studi dell Insubria (Como, Italy) Teaching Assistant for the annual course in Mathematical Analysis I, for graduate students in Mechanical Engineering at the Politecnico di Milano-Bovisa (Italy). Teaching Assistant for the annual course in Mathematical Analysis II, for graduate students in Engineering at the department of Lecco of the Politecnico di Milano (Italy) Tutor for the annual course in Mathematical Analysis II, for graduate students in Computer Science at the Università degli Studi di Milano (Italy) Introductory course in Mathematics I, for graduate students in Statistics at the Università degli Studi di Milano - Bicocca. Tutor for the annual course in Mathematical Analysis II, for graduate students in Computer Science at the Università degli Studi di Milano (Italy) Teaching assistant for the courses in Statistics (2 classes), Teaching assistant for the courses in Statistics (2 classes), Teaching assistant for the course in Probability, Teaching courses in Statistics (2 classes), Teaching course in Matematics II: Mathematical Analysis B - Probability and Statistics, Teaching assistant for the course in Mathematics II: Mathematical Analysis B - Probability and Statistics, Teaching course in Matematics II: Mathematical Analysis B - Probability and Statistics, Teaching assistant for the course in Mathematics II: Mathematical Analysis B - Probability and Statistics,

9 Teaching course in Matematics II: Mathematical Analysis B - Probability and Statistics, Teaching assistant for the course in Mathematics II: Mathematical Analysis B - Probability and Statistics, Teaching course in Mathematical Analysis II, Teaching assistant for the course in Mathematical Analysis II, Teaching course in Statistics, for graduate students in Biology at the University of Milano Bicocca. Teaching course in Analytical and statistical methods for engineers, Teaching assistant for the course in Probability and Statistics, Teaching course in Applied Statistics, Teaching assistant for the course in Applied Statistics, Teaching course in Statistics, Teaching assistant for the course in Statistics, Teaching course in Statistics, Teaching assistant for the course in Statistics, The main topics of these courses are: { Mathematics I: basic principles of mathematical logic, natural numbers, integers, rationale numbers and real numbers, equalities, inequalities, geometrical representations of polynomials of degree not greater than 2. { Mathematical Analysis I: combinatorics, sequences and series of real numbers, differential and integral calculus for functions of one real variable. { Mathematical Analysis II or Mathematical Analysis B: functions of several variables, sequences and series of functions, power series in the complex plane, differential equations, introduction to linear topological spaces and linear normed spaces and introduction to differential forms on euclidean multidimensional spaces. { Statistics, Applied Statistics or Probability and Statistics: elementary probability, random variables, point estimation, testing of statistical hypotheses.

10 Graduate students Studio della passeggiata aleatoria semplice sul pettine bidimensionale (Random walks on the 2-dimensional comb), Advisor, Student: Emanuele Fumagalli, ING MAT Simulazioni numeriche di branching random walks a due popolazioni interagenti (Numerical simulation for intercating 2-type Branching Random Walks), Advisor, Student: Antonio Scaravaggi, ING MAT Reading Course: Introduzione alle catene di Markov (Introduction to Markov chains), Advisor, Student: Gabriele Mazza, ING MAT Modello di una popolazione batterica soggetta a trattamento antibiotico (A model for a bacterial population under antibiotic treatment), Advisor, Student: Marco Nazzari - ING MAT, ING MAT.

11 Publications Preprints [1] F. Zucca, Moving closer: contractive maps on discrete metric spaces and graphs, preprint. [2] D. Bertacchi, F. Zucca, R. Ambrosini, The timing of life history events in presence of soft disturbances, preprint. Published papers (international journals) [3] D. Bertacchi, F. Zucca, S. Foresti, D. Mangioni, A. Gori, Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach, to appear on Math. Med. Biol. [4] D. Bertacchi, F. Zucca, Branching random walks and multi-type contact-processes on the percolation cluster of Z d, to appear on Ann. Appl. Probab. [5] D. Bertacchi, F. Zucca, Strong local survival of branching random walks is not monotone, Adv. Appl. Probab. 46 n. 2 (2014), [6] D. Bertacchi, F. P. Machado, F. Zucca, Local and global survival for inhomogeneous random walk systems on Z, Adv. Appl. Probab. 46 n. 1 (2014), [7] F. Zucca, Persistent and susceptible bacteria with individual deaths, J. Theor. Biol. 343 (2014), [8] D. Bertacchi, F. Zucca, Rumor processes in random environment on N and on Galton-Watson trees, J. Stat. Phys. 153 n.3 (2013), [9] D. Bertacchi, F. Zucca, Recent results on branching random walks, Statistical Mechanics and Random Walks: Principles, Processes and Applications, Nova Science Publishers, 2012, [10] D. Bertacchi, N. Lanchier, F. Zucca, Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions, Ann. Appl. Probab. 21 n.4 (2011), [11] F. Zucca, Survival, extinction and approximation of discrete-time branching random walks, J. Stat. Phys. 142 n. 4 (2011), [12] L. Belhadji, D. Bertacchi, F. Zucca, A self-regulating and patch subdivided population, Adv. Appl. Probab. 42 n.3 (2010), [13] D. Bertacchi, F. Zucca, Approximating critical parameters of branching random walks, J. Appl. Probab. 46 (2009), [14] D. Bertacchi, F. Zucca, Characterization of the critical values of branching random walks on weighted graphs through

12 infinite-type branching processes, J. Stat. Phys. 134 n. 1 (2009), [15] D. Bertacchi, F. Zucca, Critical behaviors and critical values of branching random walks on multigraphs, J. Appl. Prob. 45 n. 2 (2008), [16] F. Zucca, An inequality for correlated measurable functions, J. Ineq. Pure Appl. Math. 9 n. 1 (2008), Art. 3, 8pp. [17] D. Bertacchi, G. Posta, F. Zucca, Ecological equilibrium for restrained random walks, Ann. Appl. Probab. 17 n. 4 (2007), [18] T. Coulhon, A. Grigor yan, F. Zucca, The discrete integral maximum principle and its application, Tohoku Math. J. 57 n. 4 (2005), [19] F. Zucca, The Monty Hall problem and Napier s number, Crux Mathematicorum with Mathematical Mayhem 30 n. 3 (2004), [20] D. Bertacchi, F. Zucca, Classification on the average of random walks, J. Stat. Phys. 114 n. 3-4 (2004), [21] D. Bertacchi, F. Zucca, Uniform asymptotic estimates of transition probabilities on combs, J. Aust. Math. Soc. 75 (2003), [22] F. Zucca, Strong and weak mean value property on trees, Int. J. Pure Appl. Math. 6 n. 1 (2003), [23] F. Zucca, On some properties of transition operators, Extr. Math. 17 n. 2 (2002), [24] F. Zucca, The mean value property for harmonic functions on graphs and trees, Ann. Mat. Pura Appl. IV. Ser. 181 (2002) 1, [25] D. Bertacchi, F. Zucca, Equidistribution of random walks on spheres, J. Stat. Phys. 94 (1999), [26] A. Barchielli, A. M. Paganoni, F. Zucca, On Stochastic Differential Equations and Semigroups of Probability Operators in Quantum Probability, Stoc. Proc. and App. 73 (1998), [27] A. Barchielli, F. Zucca, On a class of Stochastic Differential Equations used in Quantum Optics, I Rendiconti del seminario Matematico e Fisico di Milano, vol. LXVI (1998), The paper was submitted April 23, 1997 and the book was released in The official date of the book is Published papers (italian journals) [28] F. Zucca, Vinca il migliore!, Periodico di Matematiche (Mathesis) Serie VII, Vol. 7, 2-3 (2000).

13 [29] F. Zucca, Una colonia di microbi eterna, Periodico di Matematiche (Mathesis) Serie VII, Vol. 6, 4 (1999), [30] F. Zucca, Uomini e Cappelli, Archimede 2 (1994), [31] F. Zucca, Il Solitario dei 4 Re, Archimede 3 (1992), Other papers and preprints [32] F. Zucca, A note on compact Markov operators, preprint. [33] F. Zucca, Continuità di una classe di funzioni, depositato presso la Procura della Repubblica e la Prefettura di Milano, preprint. [34] L. Valdettaro, F. Zucca, Calcolo delle Probabilità e Statistica Matematica, in preparation. [35] D. Bertacchi, F. Zucca, Introduzione all Analisi Combinatoria, appunti del ciclo di seminari tenuti nell ambito degli incontri per le gare matematiche (1998). [36] D. Bertacchi, A. Calogero, E. Ramazzina, F. Zucca, Il Teorema T1 e i Problemi di Dirichlet e Neumann su Domini Lipschitziani, appunti del ciclo di lezioni tenute at the Dipartimento di matematica dell Università di Milano dal Prof. E. Fabes (1996).

CURRICULUM VITÆ Mariapia Palombaro

Personal data CURRICULUM VITÆ Mariapia Palombaro May 2013 Name: Mariapia Palombaro Date of Birth: 12 August 1976 Place of Birth: Chieti (Ch), Italy Citizenship: Italian Civil Status: Married, one child