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FIRST SWISSMAP GEOMETRY&TOPOLOGY CONFERENCE
Sunday, 18 January, 2015 to Friday, 23 January, 2015, Engelberg, Switzerland
The program will consist of two minicourses, given by Lothar Göttsche (On refined enumerative invariants), and by Lenny Ng (Conormal bundles, knot invariants, and topological strings) as well as research talks by other participants.
Scientific Committee of the conference series: Anton Alekseev (Geneva); Anna Beliakova (Zürich); Paul Biran (ETH); Jérémy Blanc (Basel); Tobias Ekholm (Uppsala); Ilia Itenberg (Paris); Conan Leung (Hong Kong); Grigory Mikhalkin (Geneva); Oleg VIro (Stony Brook).
The conference will take place in Treff Hotel Sonnwendhof, Gerschniweg 1, 6390 Engelberg.
Organizers: Ilia Itenberg (Paris), Grigory Mikhalkin (Geneva), Oleg Viro (Stony Brook).
Participants:
Anton Alekseev (UNIGE) Jan 19-23;
Anna Beliakova (UNIZH);
Christan Blanchet (Paris, FR);
Tobias Ekholm (Uppsala, SE) Jan 18-22;
Vladimir Fock (Strasbourg, FR);
Sergey Galkin (Moscow, RU);
Lothar Göttsche (Trieste, IT);
Ilia Itenberg (Paris, FR);
Felix Janda (ETHZ);
Andrés Jaramillo (Paris, FR);
Johannes Josi (UNIGE);
Nikita Kalinin (UNIGE);
Natalia Kolokolnikova (UNIGE);
Sergei Lanzat (UNIGE);
Conan Leung (Hong Kong, HK);
Grigory Mikhalkin (UNIGE);
Lenny Ng (Durham, US);
Alina Pavlikova (St. Petersburg, RU);
Maria Podkopaeva (SwissMAP);
Michael Polyak (Haifa, IL);
Arthur Renaudineau (Paris, FR);
Christoph Schiessl (ETHZ);
Mikhail Shkolnikov (UNIGE);
Andras Szenes (UNIGE);
Oleg Viro (Stony Brook, US);
Jean-Yves Welschinger (Lyon, FR) Jan 18-21.
Schedule:
Monday | Tuesday | Wednesday | Thursday | Friday | |
---|---|---|---|---|---|
09: 30 – 10: 30 | Minicourse Lenny NG | Minicourse Lenny NG | Minicourse Lenny NG | Minicourse Lenny NG | Talk Michael POLYAK |
11: 00 – 12: 00 | Minicourse Lothar GÖTTSCHE | Minicourse Lothar GÖTTSCHE | Minicourse Lothar GÖTTSCHE | Minicourse Lothar GÖTTSCHE | Talk Vladimir FOCK |
16: 30 – 17: 30 | Talk Conan LEUNG | Talk Sergey GALKIN | Talk Christian BLANCHET | Departure |
|
17: 45 – 18: 45 | Talk Tobias EKHOLM | Talk Jean-Yves WELSCHINGER | Talk Anna BELIAKOVA | Talk Anton ALEKSEEV |
Abstracts
Lenny NG Conormal bundles, knot invariants, and topological strings
In this minicourse, we will explore a method for studying topological knots through the symplectic/contact geometry of their conormal bundles. This leads to a knot invariant called knot contact homology, which is quite strong as an invariant and can be combinatorially described. Knot contact homology is still fairly mysterious after more than a dozen years of study, but we will discuss two recently discovered relations, one to representations of the knot group, and another (conjectured) to colored HOMFLY knot polynomials. To see this last relation, we will describe a surprising connection (due to joint work with Mina Aganagic, Tobias Ekholm, and Cumrun Vafa) between knot contact homology and string theory, involving mirror symmetry and topological strings on the resolved conifold.
Anton ALEKSEEV On Geometry and Topology of Moment Maps
In this talk, we first review the classical moment map theory including symplectic reduction, convexity properties and Duistermaat-Heckman localization. We then pass to more exotic moment map theories with values in solvable and compact Lie groups.
Christian BLANCHET Non semi-simple TQFTs
In common work with François Costantino, Nathan Geer and
Bertrand Patureau, we have obtained new TQFTs based on an “unrolled”
variant of quantum sl(2).
We will present the relevant representation category, sketch the
construction of the TQFT vector spaces,
and describe the new Mapping Class Groups representations.