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SUMMARY:ICTP-EAUMP School on Modern Functional Analysis | (smr 3133)
DTSTART;VALUE=DATE-TIME:20170619T060000Z
DTEND;VALUE=DATE-TIME:20170707T200000Z
DTSTAMP;VALUE=DATE-TIME:20170625T102208Z
UID:indico-event-7977@ictp.it
DESCRIPTION:\n The summer school is intended to provide a thorough introdu
ction to various topics in functional analysis\, from introductory to more
advanced\, and with a particular focus on functional analytic methods use
d in current research.\n The two introductory courses in the first week co
ver some of the fundamentals of functional analysis and of operator theory
\, before two more advanced courses in the second week will introduce idea
s which establish a link between the methods of classical functional analy
sis and the modern theory of partial differential equations.\n Finally\, t
he two courses in week three will expose participants to some more advance
d topics which tie together the areas of functional analysis\, differentia
l equations and geometry. Each of the courses will consist of a series of
lectures and accompanying classes\, which are intended to give participant
s an opportunity to deepen their understanding of the material introduced
in the lectures.\n All of the lecture courses will be delivered by interna
tionally recognised researchers in analysis.\n In the final week of the su
mmer school\, participants will have a chance to work independently on a s
mall topic of their choice.COURSESWeek 1\, 19-23 June - Introductory cours
esCourse 1: An introduction to function spacesLecturer: Dr Lassi Paunonen
(Tampere\, Finland)Description: An overview of the basic theory of Banach
and Hilbert spaces\, with a focus on function spaces which play a part in
modern applications of functional analysisSyllabus: Overview of basic prop
erties of Banach and Hilbert spaces (completeness\, separability\, reflexi
vity\, etc)\, some fundamental theorems in functional analysis (e.g. the R
iesz Representation theorem and the Hahn-Banach theorem)\, examples with r
elevance to modern applications of functional analysis (Sobolev spaces\, B
ergman spaces\, Hardy spaces etc)Course 2: An introduction to operator the
oryLecturer: Prof. Charles Batty (Oxford\, UK)Description: An overview of
some of the central theorems on linear operators between normed vector spa
ces\, touching on the theory of unbounded linear operatorsSyllabus: Overvi
ew of the basic theory of bounded linear operators between Banach spaces\,
spectral theory\, some fundamental results in classical operator theory (
uniform boundedness theorem\, closed graph theorem\, open mapping theorem\
, inverse mapping theorem)\, introductory material on the theory of closed
unbounded operators (as time permits)Week 2\, 26-30 June - Advanced cours
esCourse 3: Advanced operator theoryLecturer: Dr David Seifert (Oxford\, U
K)Description: An overview of some more advanced topics in operator theory
\, making the connection with modern PDE theorySyllabus: Compactness in no
rmed vector spaces\, compact operators (characterisation\, properties\, sp
ectral theory\, examples)\, operators with closed range\, the closed range
theorem\, Fredholm theory (Fredholm index\, Fredholm alternative\, pertur
bation results)\, existence and uniqueness for simple elliptic PDEs via th
e Fredholm alternativeCourse 4: The theory of operator semigroups and thei
r applicationsLecturer: Dr Sachi Srivastava (University of Delhi)Descripti
on: An introduction to the theory of strongly continuous operator semigrou
ps and their applicationsSyllabus: C0-semigroups\, infinitesimal generator
s\, spectral theory of generators\, Lumer-Phillips theorem\, Hille-Yosida
theorem\, examples\, abstract Cauchy problems\, mild solutions\, applicati
ons to simple PDEs (heat equation\, wave equation) and quantum systemsWeek
3\, 3-7 July - Modern applications of functional analysisCourse 5: The La
placian on a Riemannian manifoldLecturers: Prof Claudio Arezzo and Dr Luca
Di Cerbo (ICTP)Syllabus: Basic theory of differential and Riemannian mani
folds. Differential forms and integration. L2 functions and forms. Gradien
t\, divergence and Laplacian on a Riemannian manifold. Towards Hodge Theor
em\, as much as time permits.Course 6: Distribution solutions to ordinary
differential equationsLecturer: Dr Ismail Mirumbe (Makerere\, Uganda)Local
organizing committee\n • James Katende (University of Nairobi)\n • Da
mian Maingi (University of Nairobi)\n • Bernard Nzimbi (University of Na
irobi)\n • Jared Ongaro (University of Nairobi\, Chair)\n • Patrick We
ke (University of Nairobi)Scientific advisory committee\n • Leif Abraham
son (University of Uppsala\, Sweden)\n • Rikard Bogvad (Stockholm Univer
sity\, Sweden)\n • Damiani Maingi (University of Nairobi\, Kenya)\n •
Fernando Rodrigues Villegas (ICTP)\n • David Ssevviiri (Makerere Univers
ity\, Uganda)\n • Balazs Szendroi (University of Oxford\, UK\, main Inte
rnational Organizer)\n • Patrick Weke (University of Nairobi\, Kenya)EAU
MP Country Coordinators\n • Juma Kasozi (Makerere University\, Uganda)\n
• Sylvester E. Rugeihyamu (Dar es Salaam University\, Tanzania)\n • J
ared Ongaro (University of Nairobi\, Kenya)\n • Michael Gahirima (Univer
sity of Rwanda)\n • Mubanga Lombe (University of Zambia)\n\nhttp://indic
o.ictp.it/event/7977/
LOCATION:Nairobi - Kenya
URL:http://indico.ictp.it/event/7977/
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