Andrea Orazio CARUSO

Studies and positions:
- Assistant professor of Mathematical Analysis (MAT05) in the Engineering Faculty of the University of Catania, from January 2, 2004;
- Research Assistant of Mathematical Analysis (MAT05) in the Engineering Faculty of the University of Catania, 2003;
- Ph.D. in Mathematics on April 1, 2003, title of thesis: "Stime di tipo W_{X,loc}^{1,p} per operatori ipoellittici variazionali a coefficienti localmente VMO_{X}$}", University of Catania;
- Graduate Degree "cum laude" in Mathematics on March 26, 1998, University of Catania.

Research:
- My research field is mainly devoted to calculus on metric measure spaces (e.g. Carnot-Caratheodory (sub-Riemannian) spaces, Carnot Lie groups), with particular emphasis to geometric aspects: relations between calculus, measures and regularity properties of real functions are investigated;

Talks:
- Meeting on "Equazioni a derivate parziali: aspetti metodologici, modellistica, applicazioni", talk's title "Formula di Taylor nei gruppi di Carnot ed applicazioni", Ragusa Ibla, July 2005;
- Meeting "Aspetti teorici e applicativi di equazioni alle derivate parziali", talk's title "Stime interne di tipo S_X^{1,p} per operatori ipoellittici variazionali a coefficienti discontinui", Maiori, April 2004;
- "XVII National Meeting of U.M.I.", talk's title, "Stime interne di tipo S_X^{1,p} per operatori ipoellittici variazionali a coefficienti localmente in VMO_{X}", Milano, September 2003;
- Department of Mathematics of Bologna "Stime interne di tipo S_{X}^{1,p} per operatori ipoellittici variazionali a coefficienti VMO_{X}: una applicazione di un risultato di densità in spazi C-C", Bologna, July 2003.

Meetings:
- "Convegno Internazionale su "Renato Caccioppoli and Modern Analysis", Roma, June 2002;
- International meeting on "L'Opera di Gabriele Darbo", Acquasparta, June 2000;
- "International Workshop on Variational Methods and Optimization", Genova, June 2000.

Workshops:
- "Sesta Scuola di Analisi in Spazi Metrici, Trento, June 2009;
- "Quinta Scuola di Analisi in Spazi Metrici, Trento, June 2007;
- Trimester on Calculus of Variations and Partial Differential Equations: 01 Sept.06-15 Dec.06", C.R.M. Ennio De Giorgi, S.N.S., Pisa, September 2006;
- "Quarta Scuola di Analisi in Spazi Metrici, Trento, May 2005;
- "Scuola Estiva su Equazioni Ipoellittiche", Milano, July 2004;
- "Problemi Geometrici del Calcolo delle Variazioni", Trento, September 2004;
- "Corso introduttivo alla Teoria Geometrica della Misura", Trento, May-July 2003;
- "Terza Scuola di Analisi in Spazi Metrici", Trento, May 2003;
- "Scuola di Calcolo delle Variazioni e Teoria Geometrica della Misura", S.N.S., Pisa, May 2002;
- "Scuola di Analisi Non Lineare", Trento, February 2002;
- "Scuola di Calcolo delle Variazioni: Metodi Diretti, Problemi di Ottimizzazione di Forma", Cortona, S.N.S., August 2001;
- "Seconda Scuola di Analisi in Spazi Metrici", Trento, June 2001;
- "Scuola di Analisi in Spazi di Carnot-Caratheodory: Introduzione alle metriche CC ed applicazioni alle Equazioni Ellittiche Degeneri", Trento, February 2001;
- "Scuola di Logica", Cesena, September 1998;
- "Workshop di Teoria della Misura ed Analisi Reale", Grado, September 1997.

Visiting:
- Department of Mathematics of the University of Trento, from 2004 up to June 2009, supported by the local group of calculus of variations and geometric measure theory.

Teaching:

- One course of "Calculus 1", Acad.Year 2022/23;

- One course of "Calculus 1", Acad.Year 2021/22;

- One course of "Calculus 2", Acad.Year 2020/21;

- One course of "Calculus 1", Acad.Year 2019/20;

- One course of "Calculus 2", Acad.Year 2018/19;

- One course of "Calculus 2", Acad.Year 2017/18;

- One course of "Calculus 2", Acad.Year 2016/17;

- One course of "Calculus 2", Acad.Year 2015/16;

- One course of "Calculus 2", Acad.Year 2014/15;

- One course of "Calculus 2", Acad.Year 2013/14;

- One course of "Calculus 2", Acad.Year 2012/13;

- One course of "Calculus 1", Acad.Year 2011/12;

- Tutor for several courses of "Calculus 1", Acad.Year 2010/11;

- One courses of "Calculus 2", Acad.Year 2009/10;

- One course of "Calculus 1", Acad.Year 2009/10;

- Two courses of "Calculus 2", Acad.Year 2008/09;

- Two courses of "Calculus 1", Acad.Year 2007/08;

- Two courses of "Calculus 1", Acad.Year 2006/07;

- Two courses of "Calculus 2", Acad.Year 2005/06;

- Two courses of "Calculus 1", Acad.Year 2004/05;

- One course of "Calculus 2", Acad.Year 2003/04;

- One course of "Calculus 2", Acad.Year 2002/03;

- Tutor for several courses of "Calculus 1,2,3" and "Mathematics for Biology", in the Acad.Years 2000/01 and 2001/02.

Further teaching activities:
- Several university-preparatory courses (Engineering and Medical C.O.F. Courses) 
- Two course at S.S.C. of University of Catania, A.Y. 2011/12 : "Partial differential equations" and "Special functions";
- Several thirty hours crash course of advanced mathematics for last-year high school students in view of graduate studies, 2006, 2007, 2009, 2010;
- Short course on "Calculus on Carnot groups" for last years graduate and Ph.D. Students, March-May 2006;
- Advisor and co-advisor for the degree thesis in mathematics.

Basic computer knowledges: windows, mac, linux, and applications: 
office/openoffice, HTML, TeX, LaTeX.

Spoken languages:
- English (spoken, written), French (read).