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                              NOTIZIARIO

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                      DIPARTIMENTO DI MATEMATICA

                   UNIVERSITA' DI ROMA LA SAPIENZA

               Settimana dal 27 giugno al 2 luglio 2005

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Lunedi' 27 Giugno 2005

Ore 9:30, Aula di Consiglio
Minisimposio di Combinatoria Algebrica
Jennifer Morse (Universita' di Miami)
k-Schur functions, Macdonald polynomials, and quantum cohomology

The k-Schur functions arose in our study of an open problem on Macdonald polynomials, 
and were conjectured to satisfy properties that refine classical ideas in symmetric 
function theory such as Pieri rules, Kostka numbers, the Young lattice and 
Young tableaux. We have recently proven these conjectures, illustrating that 
the k-Schur functions refine the Schur functions in a combinatorial sense. 
More generally, we have discovered that the k-Schur functions also play a geometric 
role that mimics the Schur function role in the cohomology of the Grassmannian. 
It turns out that the k-Schur functions are connected to quantum cohomology, 
and their Littlewood-Richardson coefficients are 3-point Gromov-Witten invariants. 
This leads to a new approach to the open problem of finding a combinatorial 
interpretation for these constants. This is joint work with Luc Lapointe. 


Lunedi' 27 Giugno 2005

Ore 10:30, Aula di Consiglio
Minisimposio di Combinatoria Algebrica
Mike Zabrocky (Universita' di York, Canada)
Symmetric functions in non-commutative variables

I will introduce two algebras which are non-commutative analogues of symmetric 
functions. I will try to give a motivation for why one might want to study 
these algebras by drawing connections between the algebras and the combinatorics 
and representation theory that they correspond to. 


Lunedi' 27 Giugno 2005

Ore 11:30, Aula di Consiglio
Minisimposio di Combinatoria Algebrica
Rikard Bogdav (Universita' di Stoccolma)
Polynomial solutions to differential equations and algebraic functions

I will describe certain ordinary differential equations depending on a complex 
parameter, that have polynomial solutions of arbitrary high degree for an infinite 
discrete set of values of the parameter. Using these one can construct approximations 
to some algebraic functions and also get asymptotic results on the zero-sets 
of these polynomial families - for example families of hyper-geometric polynomials. 



Lunedi' 27 Giugno 2005

Ore 14:30, Aula di Consiglio
Seminario di Equazioni Differenziali
Marco Squassina (Politecnico di Milano)
Sulla localizzazione dei punti di concentrazione nei problemi ellittici singolarmente 
perturbati 

Si discutono alcune condizioni necessarie per la concentrazione di soluzioni, 
attorno ad un dato punto, di alcune classi di equazioni e sistemi ellittici 
singolarmente perturbati. Le condizioni coinvolgono i sottodifferenziali di 
opportune funzioni di minima energia.