[Turkmath:8029] Doğuş University Mathematics Seminars: Richard Gonzales, Nov 25th 16:00 H-BLOCK 606

[Turker Ozsari]

*Mathematics Seminars *
Richard Gonzales, will give a talk on group embeddings, to be held on
Friday, Nov 25th by the Doğuş University Mathematics Department.  His talk
titled "Standard group embeddings and GKM theory" will commence at 16:00.
The seminar, set from 16:00 to 17:00 taking place at H-Block 606, will also
include refreshments afterward.

*Title*
Standard group embeddings and GKM theory.

*Speaker*
Richard Gonzales
The speaker is supported under TUBITAK ISBAP Grant  107T897 -
Matematik İşbirliği Ağı: Cebir ve Uygulamaları.

*Location and Time*
Doğuş University, H-Blok 606, 25 Nov, 16:00
**
*Abstract *
GKM theory is a topological tool that owes its name to the work of Goresky,
Kottwitz and MacPherson.
It allows to describe the cohomology ring of certain algebraic varieties
endowed with a torus action in terms
of finite combinatorial data coming from the set of fixed points and
one-dimensional closed orbits.  On the
other hand, a group embedding is, broadly speaking, an appropriate
compactification of a reductive group.
Standard embeddings form a distinctive and natural class among all possible
compactifications. A key feature
of standard embeddings is their close relationship to algebraic monoids. In
this talk, we aim at providing a
link between GKM theory and Embedding theory. Our major result explains how
GKM theory can be effectively
applied to describe the equivariant cohomology of rationally smooth
standard embeddings.

References:

Brion, M. ''The behaviour at infinity of the Bruhat decomposition''.
Comment. Math. Helv. 73, pp. 137-174 (1998).

Gonzales, R. ''GKM theory of rationally smooth group embeddings''. PhD
thesis (2011). http://ir.lib.uwo.ca/etd/216/

Goresky, M., Kottwitz, R., MacPherson, R. ''Equivariant Cohomology, Koszul
duality, and the localization theorem''. Invent. math. 131, pp. 25-83
(1998).

Renner, L. '' The H-polynomial of an Irreducible Representation''. Journal
of Algebra 332, pp. 159-186 (2011).


Asst. Prof. Türker Özsarı
Deparment of Mathematics
Doğuş University
Kadıköy, İstanbul
Phone: +902165445555/1688
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