Algebra, Combinatorics and Number Theory

On some open problems and applications of coalgebra theory

Speaker: 

Miodrag Cristian Iovanov (University of Southern California and University of Bucharest)

Date: 

Tuesday, 29 June, 2010 - 10:00

Venue: 

Mathematics Department Bldg, Room 0.07

I shall talk about some new developments in the theory of coalgebra. In particular I will talk about quasi-co-Frobenius coalgebras and the splitting problem for certain chain and serial coalgebras as well as for semiartinian profinite algebras. I will also discuss some questions of Nastasescu,...

Subgroup depth

Speaker: 

Lars Kadison (University of Porto)

Date: 

Thursday, 6 May, 2010 - 10:00

Venue: 

FC1 M0.07

Depth two is a nice little theory for subrings (reminiscent to and generalizing H-separable ring extensions) that combines properties of being normal in the sense of Hopf subalgebras and normal in the sense of Galois field extensions. We will discuss why depth two when applied to Hopf...

The Gelfand-Kirillov dimension and some results in noncommutative ring theory.

Speaker: 

Agata Smoktunowicz (University of Edinburgh)

Date: 

Friday, 30 April, 2010 - 09:00

Venue: 

Mathematics Department Bldg, Room 0.07

It the first part of talk we will mention the definition and general informations on the Gelfand-Kirillov dimension, and its connections with noncommutative ring theory, noncommutative projective algebraic geometry and Lie Algebras. We will mention open questions and results on the Gelfand...

A homological hammer to pound an infinite problem into a finite calculation.

Speaker: 

Thomas Cassidy

Date: 

Monday, 8 March, 2010 - 14:30

Venue: 

Room 0.07 (Mathematics Department Building)

A list of generators and relations offers a succinct presentation for an algebra over a field, but what can we deduce when looking at this presentation? If two algebras have similar presentations, they may also share other characteristics. I will illustrate several ways in which deformations of...

Combinatorial aspects of Escher Tilings

Speaker: 

Srecko Brlek (Université du Québec à Montréal )

Date: 

Tuesday, 17 November, 2009 - 16:00

Venue: 

room 0.03

When Maurits Cornelis Escher started to produce astonishing tesselations of the plane in the late 30's, very few properties were known about theses. The ``simplest" tesselations make use of just one polygon or tile for tiling the entire plane, and the polygons that tile the plane by translation...

Chain Conditions in Modular Lattices

Speaker: 

Patrick F. Smith (University of Glasgow)

Date: 

Thursday, 17 September, 2009 - 10:30

Venue: 

DMP 0.42

Results concerning chain conditions in rings or, more generally, modules give information about the lattice of ideals of the ring or submodules of the module. By considering modular lattices we can not only generalize theorems from Ring Theory but also prove results which can be applied to...

Hahn's generalized problem

Speaker: 

Ana Filipa Loureiro (CMUP & ISEC)

Date: 

Wednesday, 13 May, 2009 - 10:00

Venue: 

DMP 0.35

In this talk, some aspects of the theory of orthogonal polynomials will be in discussion. The elements of a classical polynomial sequence (Hermite, Laguerre, Bessel and Jacobi) are eigenfunctions of a second order linear differential operator with polynomial coefficients L, known as the Bochner...

On ideal extensions of rings

Speaker: 

Edmund Puczylowski (University of Warsaw)

Date: 

Monday, 15 December, 2008 - 14:00

Venue: 

DMP 1.04

A fundamental problem in ring theory is to determine and describe ideal extensions of a given ring A by another ring B, i.e. all rings R with A an ideal of R and R/A isomorphic to B. One meets such problems (more general or more specific) in many studies, especially when looking for some...

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