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.. E-mail: fabio.zucca@polimi.it 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.
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. 11/2000-8/2002 10/2001-6/2002 9/2002- present fellowship for research collaboration, 2 years fellowship at the Università degli Studi of Milan on May 16, 2000.. 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, 2002. 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 2009. Among my duties: preparation of mathematical puzzles, lectures, lecture notes. Grants and awards 2001 Young researchers project 2001, Research grant manager. 2002 Young researchers project 2002, Research grant manager. 2002 Research award, from the Università degli Studi of Milan, department of Mathematics, for distinguished research activity in 2001.. 2007 INDAM Projects 2007, Research grant manager of the project Interacting particles systems for biological populations and estimates of transition probabilities. 2009 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, 2001 - Invited Professor at the Erwin Schrödinger Institute (ESI), Wien, Austria. 2001 Erwin Schrödinger Institute (ESI), July 1 July 13, 2001 - Invited Professor at the Erwin Schrödinger Institute (ESI), Wien, Austria.
2003 Université de Cergy-Pontoise, February 10 March 9, 2003 - Invited Professor at the Département de Mathématique, Université de Cergy-Pontoise, France. 2008 Universidade de São Paulo, August 26 September 5, 2008 - Invited Professor at the Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil. 2008 Technische Universität Graz, September 17 September 25, 2008 - Invited Professor, at the Institut für Matematik, Technische Universität Graz, Austria. 2011 Universidade de São Paulo, November 27 December 6, 2011 - Invited Professor at the Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil. 2011 Universidade de São Paulo, November 4 November 13, 2014 - Invited Professor at the Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil. Visiting 1998 Università di Vienna, November 1998 - Department of Mathematics, University of Wien, Wien, Austria. 1999 Università di Vienna, January 1999 - Department of Mathematics, University of Wien, Wien, Austria. 2001 Technische Universität Graz, January 2001 - Institut für Matematik, Technische Universität Graz, Austria. 2008 University of Louisville, November 2008 - Department of Mathematics, University of Louisville, Louisville, KY (USA). 2009 Technische Universität Graz, October 2009 - Institut für Matematik, Technische Universität Graz, Austria. 2012 Technische Universität Graz, July 2012 - Institut für Matematik, Technische Universität Graz, Austria.
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.
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. 2000 V Convegno Nazionale di Fisica Statistica, Parma, Italia, 6/21/00 6/23/00, Poster: Equidistribution of random walks on spheres. 2001 Random Walks and Statistical Physics, Vienna, Austria, 2/19/01 3/2/01, Talk: Equidistribution of random walks on spheres. 2001 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. 2001 Processi Stocastici, Calcolo Stocastico ed Applicazioni, Pisa, Italia, 9/13/01 9/14/01, Talk: Equidistribution of random walks on spheres. 2005 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. 2007 Workshop on Interacting Particle System, Milano, Italia, 19/22/07 19/23/07, Talk: Ecological equilibrium for restrained random walks. 2008 4th 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. 2008 1st Workshop Stochastic Modeling, Ribeirão Preto, Brazil, 8/27/08 8/29/08, (invited plenary speaker) - Talk: Survival for branching random walks. 2010 6th Cornell Summer School In Probability, Ithaca, NY, USA, 7/19/10 7/30/10, Talk: Approximating critical parameters of branching random walks. 2012 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?. 2012 16th Brazilian School Of Probability, Recife, Brazil, 8/6/12 8/11/12, Talk: Can frogs survive locally?. 2013 36th 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. 2014 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.
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. 1997 Milano, Department of Mathematics, 4/16/1997 & 4/23/1997, Introduction to Combinatorics. 1997 Milano, Department of Mathematics, 17/12/2001, Generic differentiability for convex functions on Banach spaces. 2001 Cergy-Pontoise, Département de Mathématique, 12/17/2001, Strong and weak mean value properties on trees. 2002 Milano, Politecnico di Milano, Department of Mathematics, 7/11/2002, Equidistribution of random walks on spheres. 2003 Cergy-Pontoise, Département de Mathématique, 3/3/2003, Discrete integral maximal principle and applications. 2003 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. 2004 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. 2005 Bologna, Università degli Studi, Department of Mathematics, 4/14/2005, The Discrete integral maximal principle and its applications. 2008 São Paulo, Brazil, University of São Paulo, Instituto de Matemática e Estatística, 9/1/2008, Survival for branching random walks. 2008 Graz, Austria, Technische Universität Graz, Institut für Matematik, 9/17/2008, Survival for branching random walks. 2008 Louisville, KY (USA), University of Louisville, Department of Mathematics, 11/14/2008, Survival for branching random walks. 2009 Verona, Università degli Studi, Department of Mathematics, 1/26/2009, Survival for branching random walks. 2009 Graz, Austria, Technische Universität Graz, Institut für Matematik, 10/8/2009, Patchy restrained processes and other models.
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. 2011 São Paulo, Brazil, University of São Paulo, Instituto de Matemática e Estatística, 12/1/2011, Local survival for a frog model. 2014 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 6/1/96. 1997 Random Walks and Discrete Potential Theory, Cortona, Italia, 7/22/97 7/28/97. 2000 Research Workshop on Graph Theory and Statistical Mechanics, ICTP Trieste, Italy, 5/22/00 5/25/00. 2000 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. 2001 Random Walks and Geometry, Vienna, Austria, 6/18/2001 7/13/2001. 2002 Analysis on Graphs and Metric Spaces, Paris, France, 6/26/2002 6/28/2002. 2003 International Conference on Group Theory: combinatorial, geometric, and dynamical aspects of infinite groups, Gaeta, Italy, 6/1/2003 6/6/2003. 2003 Discrete Random Walks: Theory and Applications in Combinatorics, Computational Biology, Computer Science, Probabilities, and Statistical Physics, Paris, France, 9/1/2003 9/5/2003. 2004 Stochastic Models in the Continuum, Florence, Italy, 6/14/2004 6/18/2004. 2006 Second Cornell Summer School In Probability, Ithaca, NY, USA, 6/26/2006 7/7/2006. 2007 Third Cornell Summer School In Probability, Ithaca, NY, USA, 6/18/2007 6/29/2007. 2011 7th Cornell Summer School In Probability, Ithaca, NY, USA, 7/11/2011 7/22/2011.
Teaching Courses 1997-1998 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). 1998-1999 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). 1999-2000 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). 1999-2000 Tutor for the annual course in Mathematical Analysis II, for graduate students in Computer Science at the Università degli Studi di Milano (Italy). 2000-2001 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). 2002-2003 Teaching assistant for the courses in Statistics (2 classes), 2003-2004 Teaching assistant for the courses in Statistics (2 classes), Teaching assistant for the course in Probability, 2004-2005 Teaching courses in Statistics (2 classes), 2005-2006 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, 2006-2007 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,
2007-2008 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, 2008-2009 Teaching course in Mathematical Analysis II, Teaching assistant for the course in Mathematical Analysis II, 2009-2010 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, 2010-2011 Teaching course in Applied Statistics, Teaching assistant for the course in Applied Statistics, 2011-2012 Teaching course in Statistics, Teaching assistant for the course in Statistics, 2012-2013 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.
Graduate students 2006-2007 Studio della passeggiata aleatoria semplice sul pettine bidimensionale (Random walks on the 2-dimensional comb), Advisor, Student: Emanuele Fumagalli, ING MAT. 2010-2011 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. 2011-2012 Reading Course: Introduzione alle catene di Markov (Introduction to Markov chains), Advisor, Student: Gabriele Mazza, ING MAT. 2012-2013 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.
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), 400-421. [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), 256-278. [7] F. Zucca, Persistent and susceptible bacteria with individual deaths, J. Theor. Biol. 343 (2014), 69-78. [8] D. Bertacchi, F. Zucca, Rumor processes in random environment on N and on Galton-Watson trees, J. Stat. Phys. 153 n.3 (2013), 486-511. [9] D. Bertacchi, F. Zucca, Recent results on branching random walks, Statistical Mechanics and Random Walks: Principles, Processes and Applications, Nova Science Publishers, 2012, 289 340. [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), 1215-1252. [11] F. Zucca, Survival, extinction and approximation of discrete-time branching random walks, J. Stat. Phys. 142 n. 4 (2011), 726-753. [12] L. Belhadji, D. Bertacchi, F. Zucca, A self-regulating and patch subdivided population, Adv. Appl. Probab. 42 n.3 (2010), 899-912. [13] D. Bertacchi, F. Zucca, Approximating critical parameters of branching random walks, J. Appl. Probab. 46 (2009), 463-478. [14] D. Bertacchi, F. Zucca, Characterization of the critical values of branching random walks on weighted graphs through
infinite-type branching processes, J. Stat. Phys. 134 n. 1 (2009), 53-65. [15] D. Bertacchi, F. Zucca, Critical behaviors and critical values of branching random walks on multigraphs, J. Appl. Prob. 45 n. 2 (2008), 481-497. [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), 1117-1137 [18] T. Coulhon, A. Grigor yan, F. Zucca, The discrete integral maximum principle and its application, Tohoku Math. J. 57 n. 4 (2005), 559-587. [19] F. Zucca, The Monty Hall problem and Napier s number, Crux Mathematicorum with Mathematical Mayhem 30 n. 3 (2004), 168-171. [20] D. Bertacchi, F. Zucca, Classification on the average of random walks, J. Stat. Phys. 114 n. 3-4 (2004), 947-975. [21] D. Bertacchi, F. Zucca, Uniform asymptotic estimates of transition probabilities on combs, J. Aust. Math. Soc. 75 (2003), 325-353. [22] F. Zucca, Strong and weak mean value property on trees, Int. J. Pure Appl. Math. 6 n. 1 (2003), 33-49. [23] F. Zucca, On some properties of transition operators, Extr. Math. 17 n. 2 (2002), 201-209. [24] F. Zucca, The mean value property for harmonic functions on graphs and trees, Ann. Mat. Pura Appl. IV. Ser. 181 (2002) 1, 105-130. [25] D. Bertacchi, F. Zucca, Equidistribution of random walks on spheres, J. Stat. Phys. 94 (1999), 91-111. [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), 69-86. [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), 356-376. The paper was submitted April 23, 1997 and the book was released in 1998. The official date of the book is 1996. Published papers (italian journals) [28] F. Zucca, Vinca il migliore!, Periodico di Matematiche (Mathesis) Serie VII, Vol. 7, 2-3 (2000).
[29] F. Zucca, Una colonia di microbi eterna, Periodico di Matematiche (Mathesis) Serie VII, Vol. 6, 4 (1999), 15-22. [30] F. Zucca, Uomini e Cappelli, Archimede 2 (1994), 97-103. [31] F. Zucca, Il Solitario dei 4 Re, Archimede 3 (1992), 134-137. 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).