Mathematical Colloquim
Mathematical Colloquim
PROGRAM
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ODELJENJE ZA MATEMATIKU MATEMATIČKOG INSTITUTA SANU |
OPŠTI MATEMATIČKI SEMINAR NA MATEMATIČKOM FAKULTETU U BEOGRADU |
PROGRAM ZA SEPTEMBAR 2014.
NAPOMENA: Predavanja ce se odrzavati u Sali 301f na trecem spratu Matematickog instituta SANU, Knez-Mihailova 36 (zgrada preko puta SANU).
Petak, 26.09.2014. u 14:00h, sala 301f, MI SANU
Ulrich Koschorke (University of Siegen)
TOPOLOGICAL FIXED POINT AND COINCIDENCE THEORY
Abstract: In topological fixed point theory we are mainly interested in
the following question. Can a given selfmap $f$ of a manifold $M$ be
deformed continuously until it has no fixed points? And we try to
measure to what extent $f$ fails to be 'homotopically fixed point
free' in this sense. The classical Lefschetz number yields a
necessary condition. But a much better measure is the Nielsen number
of $f$. It vanishes precisely if $f$ is homotopic to a fixed point
free map EXCEPT when $M$ is a surface with strictly negative Euler
characteristic (in which case this statement can be dramatically
wrong).
In coincidence theory we do not just compare a selfmap $f$ with the
identity map but we study the coincidence set $C$ of an arbitrary
pair $f,g$ of maps from the domain $M$ to a possibly different
target manifold $N$ (i. e. $C$ is the set of points $x$ in $M$ where
$f(x)=g(x)$). Can the maps $f,g$ be deformed away from one another?
In other words: can $C$ be made empty by suitable homotopies?
Since the dimensions $m$ and $n$ of the domain and the target need
not agree, generically the coincidence set $C$ will be an
($m$-$n$)-dimensional manifold (and not just consist of isolated
points as in the fixed point setting). Thus the geometric methods of
differential topology come into play, and deep notions such as
bordism, Kervaire invariants, Hopf invariants etc. enter the
picture. In particular, Nielsen numbers get a new, deeper meaning
and answer some, but not all central questions (and may allow us to
measure what can go wrong).
REFERENCE: U. Koschorke, Minimum numbers and Wecken theorems in
topological coincidence theory. I ,J. Fixed Point Theory Appl. 10,1
(2011), 3-36.
Predavanja ce se odrzavati na Matematickom Institutu (sala 2), petkom sa pocetkom u 14 casova. Odeljenje za matematiku je opsti seminar sa najduzom tradicijom u Institutu.
Svakog meseca, jedno predavanje ce biti odrzano na Matematickom Fakultetu u terminu koji ce biti posebno odredjen.
Molimo sve zainteresovane ucesnike u radu naucnih sastanaka da posebno obrate paznju na vreme odrzavanja svakog sastanka. Na Matematickom fakultetu su moguce izmene termina.
Obavestenje o programu naucnih sastanaka ce biti objavljeno na oglasnim tablama MI (Beograd), MF (Beograd), PMF (Novi Sad), PMF (Nis) i PMF (Kragujevac).
Odeljenje za matematiku Matematickog instituta SANU
Stevan Pilipovic
Opsti matematicki seminar na Matematickom fakultetu u Beogradu,
Sinisa Vrecica
Ako zelite da se obavestenja o Vasim naucnim skupovima pojave u Newsletter of EMS (European Mathematical Society) i na Internetu na lokaciji EMS, onda se obratite na emsvesti@mi.sanu.ac.rs gde cete dobiti format obavestenja.