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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) Jan 19-23;
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);
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.
Anna BELIAKOVA Trace of the categorified quantum groups
In this talk I will give a gentle introduction to the categorified quantum groups and show that the trace (or 0th Hochschild homology) of the Khovanov-Lauda 2-category is isomorphic to the current algebra. Then I'll discuss some applications of this fact to link homology theories.
(Coauthors: Zaur Guliyev, Kazuo Habiro, Aaron Lauda, and Ben Webster.)
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.
Tobias EKHOLM Cotangent bundles, knot contact homology, and physics
Knot contact homology is based on transporting phenomena in smooth topology (knots in a 3-manifold) to symplectic geometry (Lagrangian conromals in the cotangent bundle). This is a rather general scheme that can be applied also in other situations. We survey some recent results in that direction about cotangent bundles of high-dimensional homotopy spheres and about knot contact homology in other dimensions and codimensions. As will be clear, the 3-dimensional case has many special features. In particular we explain that it is related to topological string theory in a 3-dimensional Calabi-Yau manifold as well as to Chern-Simons gauge theory.
Vladimir FOCK Fay's trisecant formula and discrete integrable systems
Fay's trisecant identity is a quadratic relation satisfied by theta
functions on Jacobians of curves. We will present these relation in
different forms and show that they play a key role in solution of
discrete integrable system. An application to abelianization of local
systems on a Riemann surface will be also discussed.
Conan LEUNG Witten deformations and scattering in A-model
Abstract In this talk, I will describe the differential graded algebra structure on differential forms under Witten deformations. An application on scattering in Mirror Symmetry will be explained. This research is supported by research grant from HK Government.
Jean-Yves WELSCHINGER Betti numbers of random nodal sets of elliptic pseudo-differential operators
I will explain how to bound from above the expected Betti numbers of the vanishing loci of
random linear combinations of eigenvalues of any self adjoint positive elliptic pseudo-differential operator
on some smooth closed manifold. This is a joint work with Damien Gayet.