[Turkmath:727] GSU-matematik bölümü seminer duyurusu (Jose Luis Cisneros-Molina, Manfred Hartl)

[Serap Gürer]

Degerli liste üyeleri,

Galatasaray Üniversitesi Matematik Bölümü Seminerleri kapsaminda 4 Kasım
çarsamba günü  aşağıda belirtilen saatlerde  FEF 9 nolu sinifta Jose Luis
Cisneros-Molina (UNAM-Unidad Cuernavaca) ve Manfred Hartl (Université de
Valenciennes et du Hainaut-Cambrésis) konusma yapacaktir.
Konusmalar ile ilgili bazi detaylar söyledir:

4 Kasım, 15:00, Fef 9
Jose Luis Cisneros-Molina (UNAM-Unidad Cuernavaca)
Başlık: On the topology of real analytic maps
Özet:

In this talk we describe a fibration theorem for real analytic maps
$f:\mathbb{R}^n\to\mathbb{R}^p$
with arbitrary singularities. Now suppose that $f$ satisfies Thom's
property with respect to a Whitney stratification and let
$g:\mathbb{R}^n\to\mathbb{R}^k$ be another real analytic map with isolated
singularity at the origin in the stratified sense. We give a Le-Greuel type
formula which
relates the Euler-Poincaré characteristic of the fibres of $f$ and $(f,g)$.
When $f$ and $(f,g)$ are isolated complete intersections we construct an
integer valued invariant called the curvature integra which gives the Euler
characteristic of the fibres.



4 Kasım 16:15, Fef 9
Konuşmacı: Manfred Hartl (Université de Valenciennes et du Hainaut-Cambrésis
)Başlık:  Linearisation of algebraic structures via functor calculusÖzet:

As the result of a long optimization process in categorical algebra, the
notion of semi-abelian category allows for developing highly non-trivial
algebraic theory in a very general framework which encompasses almost all
algebraic structures usually studied, and even certain types of objects
having additional topological or analytic structures, such as compact
topological groups and C$^*$-algebras. In particular, a new approach to
commutator theory, internal object actions including the important special
case of representations (Beck modules), crossed modules and cohomology is
currently being developed in this framework. This even leads to the
foundation of categorical Lie theory generalizing both classical Lie theory
(for groups) and recent non-associative Lie theory (for various varieties
of loops) to a broad variety of other non-linear algebraic structures. The
key new tool consists of a functor calculus in the framework of
semi-abelian categories, which (in an abelian or homotopical framework)
originated from algebraic topology.


In this talk I will focus on basic functor calculus, categorical commutator
and Lie theory which so far culminates in associating a linear operad (i.e.
type of algebras) to any suitable type $\mathbb{T}$ of non-linear algebraic
structure (actually, algebraic theory in the sense of Lawvere); the
algebras over this operad are supposed to play the same role for objects
with structure $\mathbb{T}$ as Lie algebras play for groups, Mal'cev
algebras play for Moufang loops and Sabinin algebras for arbitrary loops.
This is proven for certain aspects and is conjectural for others, being the
subject of currently initiated investigations with Pérez-Izquierdo and
Mostovoy who developed the corresponding theory in the case of loops.

Saygılarımla
Serap Gürer

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