Dario Trevisan. (Since 2015) Assistant professor at Università degli Studi di Pisa, Italy

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1 Dario Trevisan Università degli Studi di Pisa Dipartimento di Matematica Largo Bruno Pontecorvo, 5 Pisa, 56127, Italy Mobile: dario.trevisan@unipi.it Homepage: Areas of specialization Mathematical probability and analysis: ordinary, stochastic and partial differential equations; Markov processes and semigroups; Gaussian analysis (Malliavin calculus); functional inequalities. Current position (Since 2015) Assistant professor at Università degli Studi di Pisa, Italy Education Perfezionamento (Ph.D.) in Mathematics, Scuola Normale Superiore Diploma corso ordinario, Scuola Normale Superiore Laurea magistrale (M.Sc.) in Mathematics, Università degli Studi di Pisa Laurea triennale (B.Sc.) in Mathematics, Università degli Studi di Pisa Publications Since 2012, I have been (co-)author of 18 articles published in international scientific journals and 1 contribution in peer-reviewed volumes (n. 14) V. Magnani, E. Stepanov, D. Trevisan, A rough calculus approach to level sets in the Heisenberg group, 2. L. Ambrosio, F. Stra, D. Trevisan, A PDE approach to a 2-dimensional matching problem, Probability Theory and Related Fields, (online first) DOI: /s x 3. G. de Palma, D. Trevisan, The Conditional Entropy Power Inequality for Bosonic Quantum Systems Communications in Mathematical Physics, Communications in Mathematical Physics (online first) DOI: /s G. de Palma, D. Trevisan, V. Giovannetti, Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels, Physical Review Letters, vol. 118, n. 16, DOI: /physrevlett

2 Dario Trevisan 2 5. L. Ambrosio, D. Trevisan, Lecture notes on the DiPerna-Lions theory in abstract measure spaces, Ann. Fac. Sci. Toulouse, vol. XXVI, p , DOI: /afst V. Magnani, D. Trevisan, On Lipschitz vector fields and the Cauchy problem in homogeneous groups, Communications in Contemporary Mathematics, (online first), DOI: /S E. Musta, M. Pratelli, D. Trevisan, Functional Cramér Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes, Journal of Multivariate Analysis, vol. 154, pp , DOI: /j.jmva E. Stepanov, D. Trevisan, Three superposition principles: currents, continuity equations and curves of measures, Journal of Functional Analysis, vol. 272, n.3, DOI: /j.jfa G. De Palma, D. Trevisan, V. Giovannetti, Gaussian states minimize the output entropy of the one-mode quantum attenuator, IEEE Transactions on Information Theory, vol. 63, n. 1, pp , DOI: /TIT L. Ambrosio, F. Stra, D. Trevisan, Weak and strong convergence of derivations and stability of flows with respect to MGH convergence, Journal of Functional Analysis, vol. 272, n. 3, DOI: /j.jfa G. De Palma, D. Trevisan, V. Giovannetti, Passive states optimize the output of bosonic Gaussian quantum channels, IEEE Transactions on Information Theory, vol. 62, n. 5, pp , DOI: /TIT D. Trevisan, Well-posedness of multidimensional diffusion processes with weakly differentiable coefficients, Electronic Journal of Probability, vol. 21, DOI: /16-EJP D. Trevisan, Lagrangian flows driven by BV fields in Wiener spaces, in Probability Theory and Related Fields, vol. 163, n. 1 (2015), DOI: /s D. Trevisan, A short proof of Stein s universal multiplier theorem, in Séminaire de Probabilités XLVI 15. L. Ambrosio and D. Trevisan, Well posedness of Lagrangian flows and continuity equations in metric measure spaces, in Analysis & PDE, vol. 7, n. 5, DOI: /apde G.M. Dall Ara and D. Trevisan, Uncertainty Inequalities on Groups and Homogeneous Spaces via Isoperimetric Inequalities, in The Journal of Geometric Analysis, DOI: /s

3 Dario Trevisan D. Trevisan, BV -regularity for the Malliavin derivative of the maximum of the Wiener process in Electronic Communications in Probability, vol. 18, DOI: /ECP.v D. Trevisan, Zero noise limits using local times, in Electronic Communications in Probability, vol. 18, DOI: /ECP.v M. Pratelli and D. Trevisan, Functions of bounded variation on the classical Wiener space and an extended Ocone-Karatzas formula, in Stochastic Processes and their Applications, vol. 122, DOI: /j.spa Academic Talks and Posters A PDE approach to random matching problems. Invited talk at Workshop Metrics and Measures, Sendai, 10/01/ On the parametrization of level sets in the Heisenberg group. Invited talk at workshop Rough paths in Toulouse, Toulouse, 20/10/ On level sets in the Heisenberg group. Invited talk at Workshop on Geometric Measure Theory, Warwick, 11/07/ A PDE approach to the 2-dimensional random matching problem. Contributed talk at First Italian meeting in Probability and Mathematical Statistics, Torino, 21/06/ A rough(-young) calculus approach to level sets in the Heisenberg group. Contributed talk at Seventh Berlin-Oxford meeting, Berlin, 19/05/ A rough calculus approach to level sets in the Heisenberg group. Contributed talk at XXVII Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 08/02/ A PDE approach to the 2-dimensional random matching problem. Invited talk at TU Wien, 26/01/ A particle systems approach to cell-cell interaction. Poster session at CIRM Scientific Event Present Challenges of Mathematics in Oncology and Biology of Cancer, Marseille, 9/12/ Well-posedness of Multidimensional Diffusion Processes with Weakly Differentiable Coefficients. Invited talk at Oberseminars Stochastics, Bonn, 29/10/2015

4 Dario Trevisan Uncertainty Principle via Isoperimetric Inequalities. Contributed talk at XXXIV Convegno Nazionale di Analisi Armonica, Pisa, 11/06/ Lagrangian Flows and Continuity Equations on Metric Measure Spaces. Invited talk at Analysis Seminar at Mathematisches Institut, Universität Basel, 26/03/ Towards a Di Perna-Lions Theory on RCD Spaces. Contributed talk at XXIV Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 30/01/ A Di Perna-Lions Theory on Wiener Spaces. Invited talk at Seminari di calcolo delle variazioni e analisi geometrica, Università di Pisa, 04/12/ Diseguaglianza isoperimetrica con tecniche di semigruppi (Isoperimetric Inequalities via Semigroups). Invited talk at Seminari del Dottorato di Ricerca, Università di Firenze, 18/03/ BV Functions on the Classical Wiener Space: an Extended Clark- Ocone-Karatzas Formula. Contributed talk at PRIN 2008 final conference, Pescara 10/08/ Malliavin Regularity for sup 0 t T W t. Poster session at Workshop on Stochastic Analysis and Applications, EPFL Lausanne, 06/06/ BV Functions on the Classical Wiener Space and an Extension of the Clark-Ocone-Karatzas Formula. Contributed talk at 5th ICSAA, Bonn, 05/09/2011 Scientific Projects and Memberships Coordinator (P.I.) of GNAMPA research project Campi vettoriali, superfici e perimetri in geometrie singolari, 03/ / Participant in Project PRA , Singular Phenomena and Singular Geometries, Università degli studi di Pisa (P.I. prof. M. Romito), Personal research project on Well-posedness of deterministic and stochastic evolution equation, Scuola Normale Superiore (supervisor: prof. L. Ambrosio), 11-12/ Participant in local group (Pisa, supervisor: prof. L. Ambrosio) PRIN Calcolo delle Variazioni, P.I. Prof. L. Dal Maso, 01/ Member of the GNAMPA group Analisi Reale, Teoria della Misura e Probabilità, 2012-ongoing

5 Dario Trevisan Participant in local group (Pisa, supervisor: prof. M. Pratelli) PRIN 2008 Teoria generale dei Processi Stocastici e Finanza Matematica, P.I. Prof. M. Frittelli, 11/ Organization of scientific events Organizing committee of mini-workshop Vector Fields, Surfaces and Perimeters in Singular Geometries, Università degli studi di Ferrara, Ferrara 27-28/02/ Organizing committee of probability summer school Mathematical Modeling in Life Sciences, Centro di Ricerca Matematica Ennio de Giorgi, Pisa 13-16/09/ Organizing committee of workshop Singular Phenomena and Singular Geometries Università degli studi di Pisa, Pisa 20-23/06/2016 Teaching Activities 2018 Equazioni differenziali stocastiche e applicazioni, at Università degli studi di Pisa (Mathematics), main lecturer, hours: 42 (ongoing) 2017 Calcolo delle Probabilità e statistica, at Università degli studi di Pisa (Informatics), main lecturer, hours: 48 Probabilità superiore, at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Romito, hours: 20 Elementi di Probabilità e statistica at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Pratelli, hours: Calcolo delle Probabilità e statistica, at Università degli studi di Pisa (Informatics), main lecturer, hours: 46 Stochastic Processes and Stochastic Calculus with application to Economics and Finance, Summer School of Mathematics for Economic and Social Sciences, Scuola Superiore Sant Anna, Pisa, (Finance and Economy) 12-16/09/2016, main lecturer prof. M. Pratelli, hours: 8 Istituzioni di Matematica I, at Università degli studi di Pisa (Chemistry), main lecturer prof. E. Fortuna, hours: 50

6 Dario Trevisan 6 Ricerca operativa II e statistica II, at Università degli studi di Pisa (Engineering), main lecturer prof. F. Flandoli, short introduction to R, hours: 2 Istituzioni di Probabilità, at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Romito, hours: Calcolo delle Probabilità e statistica, at Università degli studi di Pisa (Informatics), main lecturer prof R. Giuliano, hours: 18 Statistica Matematica, at Università degli studi di Pisa (Mathematics), main lecturer prof. R. Giuliano, brief introduction to R, hours: 2 Istituzioni di Probabilità, at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Romito, hours: 20 Elementi di Probabilità e statistica at Università degli studi di Pisa (Mathematics), main lecturer prof. F. Flandoli, hours: TA (tutoring) Complementi di Matematica at Scuola Normale Superiore. Lectures by prof. L. Ambrosio 2013 TA (tutoring) Complementi di Matematica at Scuola Normale Superiore. Lectures by prof. F. Ricci 2012 TA (tutoring) Istituzioni di Probabilità at Università di Pisa. Lectures by F. Flandoli TA (tutoring) Complementi di Matematica at Scuola Normale Superiore. Lectures by by F. Ricci Teaching assistant (tutoring): Introduzione alla Teoria della Misura e l Analisi Funzionale at Scuola Normale Superiore. Lectures by L. Ambrosio. Pre-undergraduate Talks 2013 Il problema di Didone, at Corso di orientamento universitario della Scuola Normale Superiore (pre-undergraduate courses), in Rome 2012 L equilibrio di Nash nella teoria dei giochi at Corso di orientamento universitario della Scuola Normale Superiore (pre-undergraduate courses), in San Miniato (Pisa) 2011 Betti, Dini, Bianchi e l insegnamento della matematica guided tours to Scuola Normale Superiore historical math collection (main organizer: A. Andrei)

7 Dario Trevisan Two lectures on elementary number theory at Settimana Matematica 2010 (pre-undergraduate courses), in Pisa Last updated: March 13, 2018