Andrea Orazio CARUSO

Assistant Professor of Mathematical analysis [MAT/05]
Office: MIII-51 - Blocco Tre del Dipartimento di Matematica e Informatica
Email: aocaruso@dmi.unict.it aocaruso@gmail.com
Phone: 095 7383022
Mobile: +393478336816
Office Hours: Monday from 16:00 to 18:00 Eventuali variazioni vengono comunicate agli studenti mediante i canali dedicati su Studium e Telegram. | Thursday from 11:00 to 13:00 Eventuali variazioni vengono comunicate agli studenti mediante i canali dedicati su Studium e Telegram.



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 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).

Main papers:

- “Two conditions for a function to be convexpublished on “Journal of Convex Analysis , Vol. 20, N.4, pp. 1189-1201, 2013, with. A.Villani (Catania);

- “Regularity properties of H-Convex setspublished on “The Journal of Geometric Analysis , Vol. 22, N.2, pp. 583-602, 2012, with. G.Arena (Trento) and R.Monti (Padova);

- “Taylor formula on step two Carnot groups, with G.Arena (Trento) and A.Causa (Catania), published on “Revista Matematica Iberoamericana”, Vol. 26, N.1, pp. 239-259, 2010 (announced at the the workshop “Equazioni a derivate parziali: aspetti metodologici, modellistica, applicazioni” held on July 2005 in Ragusa Ibla – Ragusa - and at the “Meeting on Geometric Measure Theory and Calculus of Variations” held on February 2006 in Levico Terme, Trento);

- “Continuity results for some classes of variational inequalities and applications to time dependent equilibrium problems , with A.A.Khan (Wisconsin) and F.Raciti (Catania), published on Numerical Functional Analysis and Optimization, Vol. 30, N.(11–12), pp. 1272–1288, 2009;

- “BMO in Spaces of Homogeneous Type: a density result on C-C spaces (2003, extracted from P.h.D. Thesis), with M.S.Fanciullo (Catania), published on “Annales Academiæ Scientiarum Fennicæ Mathematica”, Vol. 32, pp. 1-14, 2007, (announced at the Department of Mathematics of Bologna on July 2003, at the XVII Congress of U.M.I. held on September 2003 in Milano, and at the workshop “Aspetti teorici ed applicativi di equazioni alle derivate parziali” held in Maiori, Amalfi, Salerno).

Teachings held in other departments

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.

President of the Catania Section of the "Accademia Italiana per la Promozione della Matematica". The Catania Section of the academy, has been founded by professors of the University of Catania, as well as by teachers at all levels of school education. The academy supports promoting activities in the field of Methamatics (courses, seminars, etc.) and, mainly, organizes a mathematical competition for players between 7 and 17 years og age, that involves the participation of hundreds of thousands of Italian, as well as students who are receiving education abroad.