Gabriel H. Tucci Graduate Student in Mathematics Office: Milner 001 Phone: (979) 845-6720 e-mail: gtucci [at] math [dot] tamu [dot] edu Mailing address: Department of Mathematics Mailstop 3368 Texas A&M University College Station, TX 77843-3368 Education Ph.D. Texas A&M University, College Station, in progress. Electrical Engineer major in Telecommunications, Universidad de la Republica, Uruguay, 2003. Licenciatura in Mathematics, Universidad de la Republica, Uruguay, 2002.

---

Research Information

• My current interests are in Operator Theory, von Neumann algebras, C*-algebras and Free probability theory
• My thesis advisor is Ken Dykema
• Curriculum Vitae

Publications and preprints

7. The Bessis-Moussa-Villani conjecture for free random variables, in preparation.

6. The von Neumann algebra generated by Dykema's $L^\infty[0,1]$-circular operators, in preparation.

5. Limits laws for geometric means of free positive random variables, preprint arXiv:0802.4226, submitted to Probability Theory and Related Fields, 2008.

4. Some quasinilpotent generators of the hyperfinite II_1 factor, accepted in Journal of Functional Analysis, 2007.

3. The free entropy dimension of some $L^\infty[0,1]$-circular operators with Ken Dykema,  Internat. J. Math. 18, 613-631, 2007.

2. Appendix in Hyperinvariant subspaces for some B-circular operators, Ken Dykema, Math. Ann. 333, 485-523, 2005.

1. Analysis and Improvements To MATE Algorithm, Miguel Griot, Gabriel Tucci, Pablo Belzarena and Santiago Remersaro, IEEE International Performance, Computing, Communications Conference, 2004. This work is based on a research done during 2003 at Universidad de la Republica, Uruguay.

Others

• Electrical Engineering Thesis "Ingenieria de trafico en tiempo real sobre MPLS" (Traffic engineering over MPLS), 2003.


• Final work for the B.S. in Mathematics "Introduccion a la K-teoria y el teorema de periodicidad de Bott" (Introduction to K-theory and Bott's periodicity Theorem), 2002.

Teaching Information

• Grader Math 407, Spring 2007
• For the Summer 2007 semester, I will be grading for Math 601, Methods of Applied Mathematics
• Grader Math 407, Spring 2007
• Grader Math 617, Fall 2006
• Instructor Math 142, Summer 2006
• Teaching Assistant Math 152, Spring 2006
• Teaching Assistant Math 151, Fall 2005

Personal

• I am from Montevideo, Uruguay.
• I am married to Valentina Vega.

Fun Problems

• Find all real-valued functions on the reals such that (f(x)+f(y))((f(u)+f(v))=f(xu-yv)+f(xv+yu) for all x,y,u,v.
• Let P(x) be a polynomial of degree n > 1 with integer coefficients and let k be a positive integer. Consider the polynomial Q(x)= P(P(. . . P(P(x)) . . .)), where P occurs k times. Prove that there are at most n integers t such that Q(t) = t.
• In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2/5 of the contestants. Moreover, no contestant solved all the 6 problems. Show that there are at least 2 contestants who solved exactly 5 problems each.

Links

• Texas A&M University
• Texas A&M Math Department
• International Mathematical Olympiads