Faculty in the Department of Mathematics at Trinity conduct research in a number of areas.

The department also publishes Math Notes, a series of expository and research articles authored or coauthored by the faculty, students and visitors of the department.

A silly measure often cited in mathematical circles is the Erdos number of a mathematician, named after the prolific Hungarian mathematician, Paul Erdos. It is defined inductively: Erdos has an Erdos number of 0; anyone who wrote a paper with Erdos has an Erdos number of 1; anyone who wrote a paper with someone who wrote a paper with Erdos has an Erdos number of 2; and so on. A mathematician who cannot find a chain of co-authors stretching to Erdos has Erdos number Infinity. The following table contains the Erdos numbers of each member of the Department

Individual faculty interests

David Cruz-Uribe, SFO

Research interests:

Harmonic analysis on R^n, with particular interest in weighted norm inequalities for classical operators and Banach function spaces which appear in harmonic analysis. Also interested in the application of harmonic analysis to the study of PDE's.

Recent publications:

• D. Cruz-Uribe, SFO, and C. Perez, On the two-weight problem for singular integral operators. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. I (2002), 821-849.
• D. Cruz-Uribe, SFO, A. Fiorenza, C. Neugebauer, The maximal function on variable $L^p$ spaces. Ann. Acad. Sci. Fenn. Math. 28 (2003), 223-238, and 29 (2004), 247-249.
• D. Cruz-Uribe, SFO, J. M. Martell, and C. Perez, Extrapolation from $A_?nfty$ weights and applications. J. Funct. Anal. 213 (2004), 412-439.

John Georges and David Mauro

Research interests:

The Channel Assignment Problem in graph theory, especially L(2,1) and L(j,k) labelings and radio labelings.

Representative publications:

• J. Georges and D. Mauro, Edge Labelings with a Condition at Distance Two. Ars Combinatoria. To appear.
• J. Georges and D. Mauro, Labeling Trees with a Condition at Distance Two. Discrete Mathematics. To appear.
• J. Georges and D. Mauro, On Generalized Petersen Graphs Labeled with a Condition at Distance Two. Discrete Mathematics. To appear.
• J. Georges, D. Mauro, and M. Stein, Labeling Products of Complete Graphs with a Condition at Distance Two. SIAM Journal on Discrete Mathematics (2001) 14, 28--35.
• J. Georges and D. Mauro, Some Results on the $?ambda^j_k$-Numbers of Products of Complete Graphs. Congressus Numerantium (1999) 140, 141--160.
• J. Georges and D. Mauro, On the Size of Graphs Labeled with a Condition at Distance Two Journal of Graph Theory (1996) 22, 47--57.
• J. Georges, D. Mauro and M. Whittlesey, On the $?ambda$-Number of $Q_n$ and Related Graphs. SIAM Journal on Discrete Mathematics (1995) 8, 499--506.
• J. Georges and D. Mauro, Generalized Vertex Labelings with a Condition at Distance Two. Congressus Numerantium (1995) 109, 141--160.
• J. Georges and D. Mauro, On the Criticality of Graphs Labeled with a Condition at Distance Two Congressus Numerantium (1994) 10, 33--49.
• J. Georges, D. Mauro, and M. Whittlesey, Relating Path Coverings to Vertex Labelings with a Condition at Distance Two Discrete Mathematics (1994) 135, 103--111.

David Robbins

Research interests:

Functional analysis (bundles of Banach spaces; geometry of Banach spaces; Banach algebras; category-theoretic aspects of functional analysis).

Recent publications:

• Some extremal properties of section spaces of Banach bundles and their duals, II (with T. H›im), Quaestiones Math., 26 (2003), 57-66.
• Sectional representation of Banach modules and their multipliers (with T. H›im), International J. Math. and Math. Sci., 33 (2003), 817-825.
• A note on the space of weakly continuous sections of a Banach bundle (with A. V. Koptev), Siberian Adv. Math., 12 (2002), 51-62.
• Some extremal properties of section spaces of Banach bundles and their duals, International J. Math. and Math. Sci., 29 (2002), 563-572.
• Modules over commutative C*-algebras and the BSE condition, Houston J. Math. 28 (2002), 159-168.