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--- swissmapgeometrytopology [2015/01/11 23:54] – [FIRST SWISSMAP GEOMETRY&TOPOLOGY CONFERENCE] g.m
+++ swissmapgeometrytopology [2015/01/20 13:46] (Version actuelle) – [FIRST SWISSMAP GEOMETRY&TOPOLOGY CONFERENCE] g.m
@@ Ligne 39: / Ligne 39: @@
 Lothar Göttsche (Trieste, IT);
 Ilia Itenberg (Paris, FR);
-Felix Janda (ETHZ);
+Felix Janda (ETHZ) Jan 19-23;
 Andrés Jaramillo (Paris, FR);
 Johannes Josi (UNIGE);
@@ Ligne 50: / Ligne 50: @@
 Alina Pavlikova (St. Petersburg, RU);
 Maria Podkopaeva (SwissMAP);
-Michael Polyak (Haifa, IL);
 Arthur Renaudineau (Paris, FR);
 Christoph Schiessl (ETHZ);
@@ Ligne 62: / Ligne 61: @@
 |  ^  Monday  ^  Tuesday  ^  Wednesday  ^  Thursday  ^  Friday  |
-^09: 30 -- 10: 30|  Minicourse\\ Lenny NG  |  Minicourse\\ Lenny NG  |  Minicourse\\ Lenny NG  |  Minicourse\\ Lenny NG  |  Talk\\ Michael POLYAK  |
+^09: 30 -- 10: 30|  Minicourse\\ Lenny NG  |  Minicourse\\ Lenny NG  |  Minicourse\\ Lenny NG  |  Minicourse\\ Lenny NG  |  Talk\\ Andras SZENES  |
 ^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  |   |
+**Minicourses 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.
+\\
+**Lothar GÖTTSCHE**   //Refined curve counting and enumerative geometry// \\
+(1) We first introduce the Severi degrees, which count nodal curves in linear systems on surfaces.
+Then, using relative Hilbert schemes of points, we introduce refined invariants. These are are polynomials in a variable y, which specialize
+for sufficiently ample linear systems at y=1 to the Severi degrees and are given by nice generating functions.
+(2) We review Welschinger invariants, which count real curves. We review plane tropical curves and the tropical definition of Severi degrees and Welschinger invariants.
+Then using tropical geometry we introduce refined Severi degrees, polynomials in a variable y that interpolate between Severi degrees
+and Welschinger invariants, which are closely related to the refined invariants from before.
+(3) We introduce Floor diagrams, which under certain assumptions encode the relevant combinatorial information about plane tropical curves, and can be used
+to compute refined Severi degrees. We relate these to Feynman diagrams for an action of a Heisenberg algebra, and use this to show that
+the refined Severi degrees can be computed in terms of this Heisenberg algebra action.
+(4) Time permitting we will introduce refined Broccoli invariants and discuss some of their properties.
+The Welschinger invariants studied above were totally real, i.e. counting real curves  through a number of real points.
+The Broccoli invariants are one way to count real curves  through a number of real points and a number of pairs of complex conjugate points, using tropical geometry.
+We give a refined version of these invariants, again replacing numbers by polynomials, which specialize to the Broccoli invariants at y=-1.
+The description and properties are considerably nicer than for the nonrefined version.
+\\
+**Talks abstracts**
+**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// \\
+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.
+\\
+**Andras SZENES**   //K-theoretic Thom polynomials// \\
+Thom polynomials are obstructions to avoiding singularities of maps between manifolds.
+They are expressed as polynomials in the Chern classes of the relative tangent bundle.
+I will present joint work with R. Rimanyi, where we have calculated the K-theoretical versions of these invariants for certain simple contact singularity loci.
+\\
+**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.