ANNO ACCADEMICO 2009-2010
In questa pagina si trovano titoli, sunti e altro materiale relativo alle
conferenze tenute nel corso dell'anno accademico 2009/10.
Mercoledì 18 novembre 2009, ore 14, Aula di Consiglio
- George Glauberman (University of Chicago)
Analogies between finite p-groups and algebraic groups
In this talk, I plan to discuss how analogies and differences between
finite p-groups and algebraic groups have suggested new results and open
problems.
Giovedì 19 novembre 2009, ore 14, Aula di Consiglio
- Ecaterina Sava (TU Graz)
Entropy sensitivity of languages associated with infinite graphs
A language L over a finite alphabet S is growth-sensitive if forbidding
any set of subwords F yields a sub-language L(F) whose exponential growth
rate is smaller than that of L. Let X be an oriented labelled graph, with
label alphabet S. We associate with X a class of languages and we prove
that these languages are growth-sensitive, by using Markov chains with
forbidden transitions.
Giovedì 19 novembre 2009, ore 15, Aula di Consiglio
- Wilfried Huss (TU Graz)
Internal aggregation models
Internal diffusion limited aggregation is a stochastic growth model on an
infinite Markov chain. We give an overview of shape theorems for this
model, and about its relation with deterministic variants, like rotor
router aggregation and the divisible sandpile model.
Giovedì 14 gennaio 2010, ore 14:30, Aula di Consiglio
- Emanuele Delucchi (State University of New York-Binghamton)
Complex Matroids
Matroid theory can be viewed as an abstraction of some combinatorial
properties of linear dependencies among elements of vector spaces.
The theory of oriented matroids specifically
deals with the combinatorics of linear dependencies over the real numbers.
A substantial part of the richness of those theories lies in the fact that
they each can be axiomatized in a
number of equivalent ways. Some work has been devoted to the search for a
similar structure for linear dependencies over the complex numbers. After
a quick review of matroids and
oriented matroids, we will present our attempt at a theory of
"complex matroids" that shares much of the structural richness of
oriented matroid theory. The talk is based on joint work with Laura
Anderson.
Giovedì 4 febbraio 2010, ore 14:30, Aula di Consiglio
- Alessandro Figà Talamanca (Sapienza)
Lezioni introduttive ai gruppi di automorfismi degli alberi infiniti. I.
Giovedì 11 febbraio 2010, ore 14:30, Aula C
- Alessandro Figà Talamanca (Sapienza)
Lezioni introduttive ai gruppi di automorfismi degli alberi infiniti. II.
Giovedì 18 febbraio 2010, ore 14:30, Aula di Consiglio
- Alessandro Figà Talamanca (Sapienza)
Lezioni introduttive ai gruppi di automorfismi degli alberi infiniti. III.
Giovedì 25 febbraio 2010, ore 14:30, Aula C
- Alessandro Figà Talamanca (Sapienza)
Lezioni introduttive ai gruppi di automorfismi degli alberi infiniti. IV.
Giovedì 4 marzo 2010, ore 14:30, Aula di Consiglio
- Alessandro Figà Talamanca (Sapienza)
Lezioni introduttive ai gruppi di automorfismi degli alberi infiniti. V.
Sulla scorta di alcuni appunti di Claudio Nebbia, si cercherà di
pervenire a una ragionevole classificazione dei sottogruppi del gruppo
degli automorfismi di un albero infinito e di indicare alcuni problemi
aperti.
Gli interessati ad una versione preliminare di questi appunti possono
richiederli all'autore Claudio Nebbia (nebbia@mat.uniroma1.it).
Giovedì 25 marzo 2010, ore 14:00, Aula di Consiglio
- James W.P. Hirschfeld (University of Sussex)
Maximum sets in a finite projective spaces.
There is an equivalence between three concepts over
the finite field Fq of order q:
I) a linear code of length n, dimension k, and minimum
distance n - k + 1;
II) a set V of n vectors in the k-dimensional vector
space over the field, with every k vectors in V forming a
basis;
III) an n-arc K in the projective space PG(k -1,
q), that is, a set of n points with no k in a
hyperplane.
Let M(k, q) denote the maximum value of n for
given k and q. The Main Conjecture for MDS codes is that,
for q greater or equal than k,
M(k, q) = q + 2 for k = 3 and k
= q - 1 both with q even,
M(k, q) = q + 1 in all other cases.
This number is also denoted by m(r, q) for the space
PG(r, q).
Old and new results for m(r, q) are discussed. Also,
the values and upper bounds for m'(2, q), the size of
the second largest arc in PG(2, q), are
considered.
Giovedì 8 aprile 2010, ore 14.30, Aula di Consiglio
- Daniele D'Angeli (Technion di Haifa)
Grafi di Schreier infiniti di gruppi self-similar
I gruppi self-similar costituiscono un'interessante classe di gruppi di
automorfismi di alberi con radice. Nel caso finitamente generato, si
può associare a ciascuno di questi gruppi una sequenza di grafi che
descrivono l'azione su ogni livello dell'albero: i grafi di Schreier
dell'azione. Quando si passa a considerare l'azione sul bordo dell'albero
si hanno infiniti grafi orbitali. Un interessante problema è dato
dalla classificazione a meno d'isomorfismo di tali grafi. Nel talk
descriverò esplicitamente il caso del gruppo Basilica ed
esporrò generalizzazioni e congetture riguardanti questo
problema.
(Ricerca in collaborazione con I. Bondarenko, A. Donno, M. Matter e T.
Nagnibeda.)
Giovedì 15 aprile 2010, ore 14, Aula di Consiglio
- Jeremie Guilhot (University of East Anglia)
Kazhdan-Lusztig Cells in Affine Weyl Groups
In this talk, i will present the notion of affine Weyl groups and
Kazhdan-Lusztig cells (in the unequal parameter case). Then, using a
geometric presentation of an affine Weyl group, I will establish that the
Kazhdan-Lusztig polynomials are invariant under (long enough)
translations. Using these results I will then show how one can determine
the partition of an affine Weyl group of rank 2 into cells for all
parameters from the knowledge of cells in all proper (hence finite)
parabolic subgroups.
Giovedì 22 Aprile 2010, ore 14, Aula di Consiglio
- Eiichi Bannai (Kyushu University)
Spherical designs and toy models for D. H. Lehmer's
conjecture in number theory.
(This talk is based on joint work with Tsuyoshi Miezaki.)
In 1947, Lehmer conjectured that the Ramanujan tau-function tau(m)
never vanishes for all positive integers m, where the tau(m) are
the Fourier coefficients of the cusp form Delta_{24} of weight 12.
Lehmer verified the conjecture in 1947 for m<214928639999. In 1973,
Serre verified the conjecture up to m<10^{15}, and in 1999,
Jordan and Kelly for m < 22689242781695999, and so on.
The theory of spherical t-designs, and in particular those which are
the shells of Euclidean lattices, is closely related to the theory of
modular forms, as first shown by Venkov in 1984. In particular,
Ramanujan's tau-function gives the coefficients of a weighted theta
series of the E_{8}-lattice. It is shown, by Venkov, de la Harpe, and
Pache, that tau (m)=0 is equivalent to the fact that the shell of
norm 2m of the E_{8}-lattice is an 8-design. So, Lehmer's conjecture
is reformulated in terms of spherical t-design.
Lehmer's conjecture is difficult to prove, and still remains open. In
this talk, we consider toy models of Lehmer's conjecture. Namely, we
show that the m-th Fourier coefficient of the weighted theta series of
the Z^2-lattice and the A_{2}-lattice does not vanish, when
the shell of norm m of those lattices is not the empty set. In other
words, the spherical 4 (resp. 6)-design does not exist among the shells
in the Z^2-lattice (resp. A_2-lattice).
Further toy models for certain two dimensional lattices will also be
mentioned.
Giovedì 22 Aprile 2010, ore 15, Aula di Consiglio
- Etsuko Bannai (Kyushu University)
On Euclidean t-designs
The concept of Euclidean t-design was first defined by Neumaier-Seidel
(1988), as a two-step generalization of
the concept of spherical t-design. Neumaier-Seidel and Delsarte-Seidel
gave natural lower bounds of the cardinalities of Euclidean t-designs for
even integer t. However the natural lower bounds of the cardinalities of
Euclidean t-designs are already given by Moller (1976) in more general
context, i.e., in terms of cubature formula. In this talk we give the
definition of the Euclidean t-designs. Then introduce some basic facts
on Euclidean t-designs. Give the definition of the tightness of Euclidean
t-designs.Usually tight Euclidean designs have some good combinatorial
structures. One of the main purpose of our study is to classify tight
Euclidean designs. We introduce the recent progress of our works on
Euclidean designs.
Giovedì 6 maggio 2010, ore 14.00, Aula di Consiglio
- Alessandro Figà Talamanca (Università di Roma "La
Sapienza")
Lezioni introduttive ai gruppi di automorfismi degli alberi infiniti.
VI.
Sulla scorta di alcuni appunti di Claudio Nebbia, si cercherà di
pervenire a una ragionevole classificazione dei sottogruppi del gruppo
degli automorfismi di un albero infinito e di indicare alcuni problemi
aperti.
Giovedì 20 maggio 2010, ore 14.00, Aula di Consiglio
- Michel Coornaert (IRMA, Strasbourg)
A Garden of Eden theorem for linear subshifts
Let G be an amenable group and let V be a finite-dimensional vector
space over an arbitrary field K. We show that if X is a strongly
irreducible linear subshift of finite type in V^G and T: X --> X is a
linear cellular automaton, then T is surjective if and only if it is
pre-injective (joint work with Tullio Ceccherini-Silberstein).
Giovedì 8 luglio 2010, ore 14.00, Aula di Consiglio
- Hao Shen (Shanghai Jiao Tong University)
Existence of resolvable group divisible designs with subdesigns
For given positive integers v, k and m, a group divisible design, denoted
GD(k,m;v), is a triple (X,G,A) where X is a v-set, G is a set of m-subsets
of X (called groups), G forms a partition of X, and A is a set of
k-subsets (called blocks) such that each block intersects each group in at
most one point, and each pair of distinct points from distinct groups is
contained in a unique block. A GD(k,m;v) is called resolvable and denoted
RGD(k,m;v) if the blocks can be partitioned into parallel classes. Let
(X,G,A) be an RGD(k,m;v) and (Y,H,B) be an RGD(k,m;u), if X is a subset of
Y, A is a subset of B, and each parallel class of A is a part of some
parallel class of B, then (X,G,A) is called a subdesign of (Y,H,B), or
(X,G,A) is said to be embedded in (Y,H,B). In this talk, we will survey
the progresses on the existence of resolvable group divisible designs. We
will also survey the progresses in the study of the embedding problem for
resolvable group divisible designs. We will determine necessary and
sufficient conditions for the embeddings of resolvable group divisible
designs with block size three and any group size. Embeddings for related
structures are also discussed.
Sunday, 20-Jun-2010 11:59:15 CEST