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Workshop: Lie theory in differential geometry and integrable systems


 The Workshop takes place at the University of Jena from June 10 to June 12.

Confirmed participants

Milos Antic (Belgrade)

Neda Bokan (Belgrade)

Volodymir Kiosak (Jena)

Gianni Manno (Jena)

Vladimir Matveev (Jena)

Rada Mutavdic (Belgrade)

Stefan Rosemann (Jena)

Katja Sagerschnig (Canberra)

Konrad Schöbel (Jena)

Tijana Sukilovic (Belgrade)

Dennis The (Canberra)

Andreas Vollmer (Jena)

Srdjan Vukmirovic (Belgrade)

Schedule

All lectures take place in Carl-Zeiss-Straße 3 (which is the main building on the university campus Ernst-Abbe-Platz) but in different rooms.

Monday

10:15-11:15
SR 384

Neda Bokan (Belgrade):
"Induced representations of classical Lie groups and their applications"



Coffee Break

12:15-13:15
HS 6

Konrad Schöbel (Jena):
"Separation coordinates and moduli spaces of stable curves"



Lunch

14:30-15:30
HS 6

Gianni Manno (Jena):
"Contact geometry of Monge-Ampère equations"


Tuesday

09:00-10:00
HS 6

Srdjan Vukmirovic (Belgrade):
"Geometry of 4-dimensional Lie Groups with left invariant Lorentzian metric I"


At the begining we present some general facts regarding spaces left-invariant metrics on Lie groups. In dimension $4$ there are only two nonabelian nilpotent Lie algebras: $h_3 \oplus R$ (where $h_3$ is Heisenberg algebra) and $g_4$. The first is $2-$step nilpotent and the second is $3-$step nilpotent. We give classification of non-equivalent inner products on these Lie algebras. These metrics rise to non-equivalent left-invariant metrics on corresponding Lie groups. Geometry of these Lie groups is also discussed (curvature, isometry groups, projective equivalence...). As one can expect, the geometry in Lorentzian setting is far more interesting than the Riemannian one. This is joint work with N. Bokan.


Coffee Break

10:30-11:30
HS 6

Tijana Sukilovic (Belgrade):
"Geometry of 4-dimensional Lie Groups with left invariant Lorentzian metric II"



Lunch

16:00-17:00
HS 6

Stefan Rosemann (Jena):
"The conification construction for Kähler metrics and applications to c-projective geometry"


Wednesday

09:00-10:00
HS 6

Dennis The (Canberra):
"The gap phenomenon in parabolic geometries"


Many geometric structures (such as Riemannian, conformal, CR, projective, systems of ODE, and various types of generic distributions) admit an equivalent description as Cartan geometries. For Cartan geometries of a given type, the maximal amount of symmetry is realized by the flat model. However, if the geometry is not (locally) flat, how much symmetry can it have? Understanding this "gap" between maximal and submaximal symmetry in the case of parabolic geometries is the subject of this talk. I'll describe how a combination of Tanaka theory, Kostant's version of the Bott-Borel-Weil theorem, and a new Dynkin diagram recipe led to a complete classification of the submaximal symmetry dimensions in all parabolic geometries of type (G,P), where G is a complex or split-real simple Lie group and P is a parabolic subgroup. (Joint work with Boris Kruglikov.)


Coffee Break

10:30-11:00
SR 309

Milos Antic (Belgrade):
"TBA"


11:00-11:30
SR 309

Rada Mutavdic (Belgrade):
"TBA"


11:30-12:00
SR 309

Katja Sagerschnig (Canberra):
"TBA"



Lunch