IMBM GEOMETRY & TOPOLOGY
MEETINGS
12
December 2015
IMBM
|
10:00 - 11:00 |
Danny
Gillam |
The Hausdorff topology and Hausdorff
quotients |
|
11:00 - 11:30 |
Break |
|
|
11:30 - 12:30 |
Barış
Coşkunüzer |
Minimal Surfaces with arbitrary topology in
H2xR |
|
12:30 - 2:30 |
Lunch |
|
|
2:30 - 3:30 |
Mohan
Bhupal |
Nonexistence of rational homology disk weak
fillings |
|
3:30 - 4:00 |
Break |
|
|
4:00 - 5:00 |
Takahiro
Oba |
Compact Stein surfaces as branched covers with same branch sets |
The talks will be at main lecture hall of Istanbul Center for Mathematical Sciences (IMBM)
ABSTRACTS
|
The Hausdorff topology and Hausdorff
quotients Danny
Gillam - Boğaziçi University In
1914 Felix Hausdorff defined a metric on the set of closed subspaces of a
metric space X. We will give a new
interpretation of the resulting topology on the set H(X) of *compact* subsets
of X as a "moduli space" for certain "families" of such
subsets. In particular it will follow
that the topology on H(X) depends only on the topology of X and not the
choice of metric inducing it, so the "Hausdorff space" H(X) is
attached naturally to any metrizable space X.
I will explain how H(X) can be used to form a kind of quotient
analogous to the Hilbert quotient in algebraic geometry, then I will give
some examples and results about this quotient that allow us to identify it in
some interesting situations. This is
based on joint work with A. Karan. |
|
Minimal Surfaces with arbitrary topology in
H2xR Barış Coşkunüzer - Koç
University In this talk, we show that any open
orientable surface can be embedded in H^2xR as a complete area minimizing
surface. Furthermore, we will discuss the asymptotic Plateau problem in
H^2xR, and give a fairly complete solution. |
|
Nonexistence
of rational homology disk weak fillings of certain singularity links Mohan
Bhupal - METU In this talk, I will show that the Milnor
fillable contact structure on the link of a singularity with a specific
family of resolution graphs with arbitrary large number of nodes does not
admit a weak symplectic filling having the rational homology of the 4-disk.
This result provides further evidence to the conjecture that no such weak
symplectic filling exists once the mininal resolution tree has at least two
nodes. This is a joint work with
Andras Stipsciz. |
|
Compact Stein surfaces as branched covers with same branch sets Takahiro Oba - Tokyo Institute of Technology Loi and Piergallini showed that a smooth
compact, connected 4-manifold X with boundary admits a Stein structure if and
only if X is a simple cover of a 4-disk D^4 branched along a positive braided
surface S in a bidisk D_1^2 \times D_2^2 \approx D^4. For each integer N
greater than one, we construct a braided surface S_N in D^4 and simple covers
X_{N,1}, X_{N,2}, ... , X_{N,N} of D^4 branched along S_N such that the
covers are mutually diffeomorphic, but the Stein structures determined by the
covers are mutually not homotopic. Furthermore, by reinterpreting this result
in terms of contact topology, we also construct transverse links in the
standard contact 3-sphere and contact 3-manifolds, similar to the above. arXiv:1508.01020 |
For accommodation, Etiler Uygulama Oteli is reasonably
priced, and nearby.
Please click Uygulama tab in
the top of the page.