Lecturer

Title

Date

Time

Room

Francesco Matucci (IMECC-UNICAMP)

Introdução à Teoria Geométrica de Grupos (parte 2)

November 07, 2017

14:30-15:30

259-A

Abstract:

Um grupo é uma estrutura algébrica que descreve a simetria de algum objeto. Partindo de um grupo abstrato podemos sempre associar um objeto geométrico (o grafo de Cayley) que realize esta simetria. Daremos uma breve introdução as apresentações de grupos e como no estudo deles se pode usar técnicas de outras áreas da matemática (como geometria, combinatória, ciência da computação, análise e outras). Faremos esta caminhada falando de algumas classes de grupos interessantes e propriedades deles.

Lecturer

Title

Date

Time

Room

Francesco Matucci (IMECC-UNICAMP)

Introdução à Teoria Geométrica de Grupos

October 31, 2017

14:30-15:30

259-A

Abstract:

Um grupo é uma estrutura algébrica que descreve a simetria de algum objeto. Partindo de um grupo abstrato podemos sempre associar um objeto geométrico (o grafo de Cayley) que realize esta simetria. Daremos uma breve introdução as apresentações de grupos e como no estudo deles se pode usar técnicas de outras áreas da matemática (como geometria, combinatória, ciência da computação, análise e outras). Faremos esta caminhada falando de algumas classes de grupos interessantes e propriedades deles.

Lecturer

Title

Date

Time

Room

Jairo Z. Gonçalves (IME-USP)

Free subgroups in a normal subgroup of the multiplicative group of the field of fractions of k[x^±1, y^±1][X; σ]

September 26, 2017

14:30-15:30

259-A

Abstract:

Let σ be an automorphism of R=k[x^±1, y^±1] induced by an invertible matrix A ϵ GL₂(\mathbb{Z}), let D be the field of fractions of the skew polynomial

ring R[X; σ], and let N be a non central normal subgroup of D^{\bullet}, the multiplicative group of D. We show that N contains a free subgroup.

Lecturer

Title

Date

Time

Room

Misha Dokuchaev (IME-USP)

Globalization of partial cohomology of groups (part II)

September 19, 2017

14:30-15:30

259-A

Abstract:

We shall discuss the relations between partial and global group cohomology. One of our main results says that given a unital partial action of a group G on a ring A, such that A is a direct product of indecomposable rings, then any partial n-cocycle with values in A is globalizable. This is a joint work with Mykola Khrypchenko and Juan Jacobo Simon.

Lecturer

Title

Date

Time

Room

Misha Dokuchaev (IME-USP)

Globalization of partial cohomology of groups

September 12 , 2017

14:30-15:30

259-A

Abstract:

We shall discuss the relations between partial and global group cohomology. One of our main results says that given a unital partial action of a group G on a ring A, such that A is a direct product of indecomposable rings, then any partial n-cocycle with values in A is globalizable. This is a joint work with Mykola Khrypchenko and Juan Jacobo Simon.

Lecturer

Title

Date

Time

Room

Doryan Temmerman (Vrije Universiteit Brussel, Belgium)

Bovdi units and free products in integral group rings of finite groups

August 22, 2017

14:30-15:30

243-A

Abstract:

 In the study of the Isomorphism Problem and the Zassenhaus Conjecture, one often seeks specific subgroups of the unit group of an integral group ring.

In this talk we will discuss recent results of the construction of amalgamated products, in particular free products of finite groups, free semigroups, solvable
subgroups and other subgroups with nice properties. This is done via the study of a new type of generic, non-trivial torsion unit, introduced by V. Bovdi. These
so-called Bovdi units are deformations of trivial units using bicyclic units.

We will sketch how to construct free products of cyclic groups in matrix algebras and how to lift them back to the integral group ring. Interestingly, this method
also yields elements that, as a semigroup, generate a free semigroup but do not generate a free group.

We will also discuss some structure results on groups generated by such Bovdi units.

All this is based on joint works with A. Bächle, G. Janssens and E. Jespers.

Lecturer

Title

Date

Time

Room

Jairo Z. Gonçalves (IME-USP)

Free subgroups in the field of fractions of k[x,y][t;\sigma]

June 27, 2017

14:30-15:30

259-A

Abstract:

 Let k be a field, and let \sigma be a k-automorphism of the polynomial ring k[x,y] in the commuting indeterminates x and y over k. Let D be the field of fractions of the skew polynomial ring k[x,y][t;\sigma], and let D^{\bullet} be its multiplicative group. In support to Lichtman's Conjecture, we show that D^{\bullet} contains a free noncyclic subgroup.

Lecturer

Title

Date

Time

Room

Makar Plakhotnyk (IME-USP)

Max non-decomposable exponent matrices (part II)

June 6, 2017

14:30-15:30

243-A

Abstract:

We continue our study of non-negative exponent matrices, i.e. non-negative matrices A = (\alpha_{pq}) with zero diagonal and such that the inequalities \alpha_{ij} +\alpha_{jk} \geq \alpha_{ik} hold for all i, j, k. We describe all exponent matrices which can not be  expressed as an entry-wise maximum of two non-comparable non-zero exponent matrices. This result easily implies an alternative proof of the earlier obtained description of the generators of max-plus algebra of non-negative exponent matrices. This is a joint work with M. Dokuchaev, V. Kirichenko and G. Kudryavtseva.

Lecturer

Title

Date

Time

Room

Makar Plakhotnyk (IME-USP)

Max non-decomposable exponent matrices

May 30, 2017

14:30-15:30

243-A

Abstract:

We continue our study of non-negative exponent matrices, i.e. non-negative matrices A = (\alpha_{pq}) with zero diagonal and such that the inequalities \alpha_{ij} +\alpha_{jk} \geq \alpha_{ik} hold for all i, j, k. We describe all exponent matrices which can not be  expressed as an entry-wise maximum of two non-comparable non-zero exponent matrices. This result easily implies an alternative proof of the earlier obtained description of the generators of max-plus algebra of non-negative exponent matrices. This is a joint work with M. Dokuchaev, V. Kirichenko and G. Kudryavtseva.

Lecturer

Title

Date

Time

Room

Misha Dokuchaev (IME-USP)

The ideal structure of skew group rings coming from
topological partial actions (part III)

May 16, 2017

14:30-15:30

243-A

Abstract:

Given a Hausdorff, locally compact, totally disconnected topological space X and a field K, denote by L_c(X)  the algebra of all locally constant, compactly supported functions on X, taking values in K. For a topological partial action of a discrete group G on X with clopen domains, we consider the corresponding partial action of G on the algebra L_c(X) and study the ideal structure of the partial skew group ring L_c(X) \rtimes G. We develop a theory of induced ideals
and show that every ideal in L_c(X) \rtimes G may be obtained as the intersection of ideals induced from isotropy groups. This a joint work with R. Exel.

Lecturer

Title

Date

Time

Room

Misha Dokuchaev (IME-USP)

The ideal structure of skew group rings coming from
topological partial actions (part II)

May 09, 2017

14:30-15:30

243-A

Abstract:

Given a Hausdorff, locally compact, totally disconnected topological space X and a field K, denote by L_c(X)  the algebra of all locally constant, compactly supported functions on X, taking values in K. For a topological partial action of a discrete group G on X with clopen domains, we consider the corresponding partial action of G on the algebra L_c(X) and study the ideal structure of the partial skew group ring L_c(X) \rtimes G. We develop a theory of induced ideals
and show that every ideal in L_c(X) \rtimes G may be obtained as the intersection of ideals induced from isotropy groups. This a joint work with R. Exel.

Lecturer

Title

Date

Time

Room

Misha Dokuchaev (IME-USP)

The ideal structure of skew group rings coming from
topological partial actions

May 02, 2017

14:30-15:30

243-A

Abstract:

Given a Hausdorff, locally compact, totally disconnected topological space X and a field K, denote by L_c(X)  the algebra of all locally constant, compactly supported functions on X, taking values in K. For a topological partial action of a discrete group G on X with clopen domains, we consider the corresponding partial action of G on the algebra L_c(X) and study the ideal structure of the partial skew group ring L_c(X) \rtimes G. We develop a theory of induced ideals
and show that every ideal in L_c(X) \rtimes G may be obtained as the intersection of ideals induced from isotropy groups. This a joint work with R. Exel.

Lecturer

Title

Date

Time

Room

Antonio Giambruno (Universita di Palermo, Italy)

 Central polynomials versus polynomial identities

April 07, 2017

14:30-15:30

241-A

Abstract:

A central polynomial for an algebra A is a polynomial in noncommuting variables taking central values under all evaluations in A. Polynomial identities are central polynomials taking only the zero value. A central polynomial is proper if it takes at least one nonzero value. The existence of proper central polynomials for n x n matrices was conjectured by Kaplansky in the 50's and proved in the early 70's independently by Formanek and Razmyslov. Here we want to compare the growth of the space of central polynomials to the growth of the space of polynomial identities for any finite dimensional algebra in characteristic zero.

Lecturer

Title

Date

Ti

Jairo Z. Gonçalves (IME-USP)

Free symmetric and unitary pairs in the field of
fractions of free nilpotent group algebras (part II)

March 28, 2017

14:30-15:30

243-A

Abstract:

Let G be a free nilpotent group, let kG be the group algebra of G over the field k of characteristic different from 2, let D be its field of fractions, and let D^{\bullet} be the multiplicative group of D. If * is an involution of G extended linearly to kG, and to D, then D^{\bullet} contains free pairs of *-symmetric and *-unitary elements. If N is a normal subgroup of D^{\bullet} which contains G, and such that N*=N, then N contains free symmetric pairs. Some partial results are presented  when char k=2.

Lecturer

Title

Date

Time

Room

Jairo Gonçalves (IME-USP)

Free symmetric and unitary pairs in the field of
fractions of free nilpotent group algebras

March 21, 2017

14:30-15:30

243-A

Abstract:

Let G be a free nilpotent group, let kG be the group algebra of G over the field k of characteristic different from 2, let D be its field of fractions, and let D^{\bullet} be the multiplicative group of D. If * is an involution of G extended linearly to kG, and to D, then D^{\bullet} contains free pairs of *-symmetric and *-unitary elements. If N is a normal subgroup of D^{\bullet} which contains G, and such that N*=N, then N contains free symmetric pairs. Some partial results are presented  when char k=2.