## Saturday, March 11, 2006

## Friday, March 10, 2006

### Abstracts of talks February 2006

15th February 2006

Matias Menni (Universidad Nacional de La Plata, Argentina), Some developments on top of a problem posed by Carboni about the exact completion of the classifier of subterminals.

During CT99 in Coimbra, Carboni proposed to test a recently proved characterization categories whose exact completions are toposes by solving a very concrete problem. Namely, to answer the question: Is the the exact completion of the topos of sheaves on Sierpinski space a topos?

This was obviously pointing to the more general problem of characterising the toposes whose exact completions are toposes.

In this talk we will answer this question for two well known classes of toposes: the locally connected and the toposes with enough points.

The sketch of the proofs will show that the main idea is to reduce these problems to that posed by Carboni in 1999.

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22 February 2006

Matias Menni (Universidad Nacional de La Plata, Argentina), Categories of combinatorial structures in general and differential equations in particular.

In this talk we present a combinatorial proof a result by Stanley (J. AMS 1). Stanley's result is about the enumertation of walks in certain class of posets (discovered independently by him and by Fomin) which share a number of key properties with Young's poset (partitions ordered by inclusion of Young diagrams). One of the main challenges is that Stanley's proof involves the solution to differential equations in some curious spaces.

Our combinatorial proof relies on variations of Joyal's theory of species and on a theory of combinatorial differential equations developped on top of it.

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Matias Menni (Universidad Nacional de La Plata, Argentina), Some developments on top of a problem posed by Carboni about the exact completion of the classifier of subterminals.

During CT99 in Coimbra, Carboni proposed to test a recently proved characterization categories whose exact completions are toposes by solving a very concrete problem. Namely, to answer the question: Is the the exact completion of the topos of sheaves on Sierpinski space a topos?

This was obviously pointing to the more general problem of characterising the toposes whose exact completions are toposes.

In this talk we will answer this question for two well known classes of toposes: the locally connected and the toposes with enough points.

The sketch of the proofs will show that the main idea is to reduce these problems to that posed by Carboni in 1999.

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22 February 2006

Matias Menni (Universidad Nacional de La Plata, Argentina), Categories of combinatorial structures in general and differential equations in particular.

In this talk we present a combinatorial proof a result by Stanley (J. AMS 1). Stanley's result is about the enumertation of walks in certain class of posets (discovered independently by him and by Fomin) which share a number of key properties with Young's poset (partitions ordered by inclusion of Young diagrams). One of the main challenges is that Stanley's proof involves the solution to differential equations in some curious spaces.

Our combinatorial proof relies on variations of Joyal's theory of species and on a theory of combinatorial differential equations developped on top of it.

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