Seminars Sorted by Series

Joint IAS/Princeton University Symplectic Geometry Seminar

Mar
08
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Lagrangian Caps in High-Dimensional Symplectic Manifolds
1:30pm|Fine Hall 322

I will present a recent result (joint with Yakov Eliashberg) demonstrating the existence of exact Lagrangian cobordisms with a loose Legendrian in the negative end, in all dimensions greater than 4. In particular, we show that there exists a...

Mar
15
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Resonance for Loop Homology on Spheres
1:30pm|S-101

Fix a metric (Riemannian or Finsler) on a compact manifold M. The critical points of the length function on the free loop space LM of M are the closed geodesics on M. Filtration by the length function gives a link between the geometry of closed...

Mar
29
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Dimers and Integrability
Richard Kenyon
1:30pm|S-101

This is joint work with A. B. Goncharov. To any convex integer polygon we associate a Poisson variety, which is essentially the moduli space of connections on line bundles on (certain) bipartite graphs on a torus. There is an underlying integrable...

Apr
05
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Manifolds with G_2 Holonomy and Contact Structures
Sema Salur
1:30pm|Fine Hall 322

A 7-dimensional Riemannian manifold (M,g) is called a G_2 manifold if the holonomy group of its Levi-Civita connection of g lies inside G_2. In this talk, I will first give brief introductions to G_2 manifolds, and then discuss relations between G_2...

Apr
12
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Construction of the Kuranishi Structure on the Moduli Space of Pseudo-Holomorphic Curves
1:30pm|S-101

To apply the technique of virtual fundamental cycle (chain) in the study of pseudo-holomorphic curve, we need to construct certain structure, which we call Kuranishi strucuture, on its moduli space. In this talk I want to review certain points of...

Apr
19
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Examples of Nearly Integrable Systems with Asymptotically Dense Projected Orbits
Jean-Pierre Marco
11:00am|Fine Hall 314

The talk is intended to give examples of Arnold diffusion for nearly integrable systems which are very likely to be generic. We will describe an explicit perturbation of the flat metric on the three dimensional torus which admits orbits whose...

Sep
26
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

GIT and \(\mu\)-GIT
Dietmar Salamon
1:00pm|S-101

In this lecture I will explain the moment-weight inequality, and its role in the proof of the Hilbert-Mumford numerical criterion for \(\mu\)-stability. The setting is Hamiltonian group actions on closed Kaehler manifolds. The major ingredients are...

Oct
04
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Positive loops and orderability in contact geometry
Peter Weigel
1:00pm|S-101

Orderability of contact manifolds is related in some non-obvious ways to the topology of a contact manifold \(\Sigma\). We know, for instance, that if \(\Sigma\) admits a 2-subcritical Stein filling, it must be non-orderable. By way of contrast, in...

Oct
11
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Finite Energy Foliations and Connect Sums
1:30pm|Fine 322, Princeton University

I will present some recent joint work with Richard Siefring on the behavior of finite energy foliations under the action of a 0-surgery (i.e. a connect sum) and a 2-surgery. We will then discuss applications to the restricted three body problem.

Oct
18
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

How not to define cylindrical contact homology
1:30pm|S-101

We consider the problem of defining cylindrical contact homology, in the absence of contractible Reeb orbits, using "classical" methods. The main technical difficulty is failure of transversality of multiply covered cylinders. One can fix this...

Oct
25
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Enumeration of real rational curves
Penka Georgieva
1:30pm|Fine 322, Princeton University

The classical problem of enumerating rational curves in projective spaces is solved using a recursion formula for Gromov-Witten invariants. In this talk, I will describe a similar relation for real Gromov-Witten invariants with conjugate pairs of...

Nov
01
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Volume in Seiberg-Witten theory and the existence of two Reeb orbits
Daniel Cristofaro-Gardiner
1:30pm|S-101

I will discuss recent joint work with Vinicius Gripp and Michael Hutchings relating the volume of any contact three-manifold to the length of certain finite sets of Reeb orbits. I will also explain why this result implies that any closed contact...

Nov
08
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Tori in four-dimensional Milnor fibres
1:30pm|Fine 322, Princeton University

The Milnor fibre of any isolated hypersurface singularity contains exact Lagrangian spheres: the vanishing cycles associated to a Morsification of the singularity. Moreover, for simple singularities, it is known that the only possible exact...

Nov
15
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Calabi-Yau mirror symmetry: from categories to curve-counts
Tim Perutz
1:30pm|S-101

I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds. We show (i) that Kontsevich's homological mirror symmetry (HMS) conjecture is a consequence of a fragment of the same...

Nov
22
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Gopakumar-Vafa conjecture for symplectic manifolds
Eleny Ionel
1:30pm|Fine 322, Princeton University

The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. In this talk, based on joint work with Tom Parker, I describe the proof...

Dec
06
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Feynman categories, universal operations and master equations
Ralph Kaufmann
1:30pm|S-101

Feynman categories are a new universal categorical framework for generalizing operads, modular operads and twisted modular operads. The latter two appear prominently in Gromov-Witten theory and in string field theory respectively. Feynman categories...

Dec
13
2013

Joint IAS/Princeton University Symplectic Geometry Seminar

Lagrangian submanifolds of complex projective space
Michael Usher
1:30pm|Fine 322, Princeton University

First, I will discuss a proof that a Lagrangian torus in \(\mathbb{CP}^2\) arising from a semitoric system described by Weiwei Wu coincides with the image in \(\mathbb{CP}^2\) of Chekanov's exotic Lagrangian torus in \(\mathbb R^4\). I will then...

Feb
03
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

A remark on the Euler equations of hydrodynamics
12:45pm|S-101

The time evolution of an ideal incompressible fluid is described by the Euler equations. In this mostly speculative talk I will discuss a connection between stationary solutions of these equations and symplectic topology, as well as possible...

Feb
07
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Cylindrical contact homology as a well-defined homology?
Joanna Nelson
1:30pm|S-101

In this talk I will explain how the heuristic arguments sketched in literature since 1999 fail to define a homology theory. These issues will be made clear with concrete examples and we will explore what stronger conditions are necessary to develop...

Feb
14
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

On Floer cohomology and non-archimedian geometry
1:30pm|S-101

Ideas of Kontsevich-Soibelman and Fukaya indicate that there is a natural rigid analytic space (the mirror) associated to a symplectic manifold equipped with a Lagrangian torus fibration. I will explain a construction which associates to a...

Feb
21
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

A criterion for generating Fukaya categories of fibrations
1:30pm|S-101

The Fukaya category of a fibration with singularities \(W: M \to C\), or Fukaya-Seidel category, enlarges the Fukaya category of \(M\) by including certain non-compact Lagrangians and asymmetric perturbations at infinity involving \(W\); objects...

Feb
28
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Implicit atlases and virtual fundamental cycles
1:30pm|Fine 322, Princeton University

An implicit atlas on a (moduli) space consists of certain auxiliary (moduli) spaces satisfying a precise set of axioms. We will summarize the construction of implicit atlases on moduli spaces of \(J\)-holomorphic curves, under the assumption of a...

Mar
05
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Contact invariants in sutured monopole and instanton homology
Steven Sivek
3:30pm|S-101

Kronheimer and Mrowka recently used monopole Floer homology to define an invariant of sutured manifolds, following work of Juhász in Heegaard Floer homology. In this talk, I will construct an invariant of a contact structure on a 3-manifold with...

Mar
06
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Non-displaceable Lagrangians via minimal model transitions
Chris Woodward
4:30pm|Fine 314, Princeton University

I will discuss some results, some older and some newer, on the general idea that in many birationally-Fano cases, generators of the Fukaya category seem to arise from transitions in the minimal model program. A specific result from a couple of years...

Mar
07
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

New combinatorial computations of embedded contact homology
Keon Choi
1:30pm|S-101

Embedded contact homology is an invariant of a contact three-manifold, which is recently shown to be isomorphic to Heegaard Floer homology and Seiberg-Witten Floer homology. However, ECH chain complex depends on the contact form on the manifold and...

Mar
14
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Knot contact homology and topological strings
Tobias Ekholm
1:30pm|Fine 322, Princeton University

We describe the recently observed relation between knot contact homology and open topological strings. This in particular gives two ways of looking at the augmentation variety from knot contact homology, which describe the relevant string theory at...

Mar
14
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Moduli of marked disks, open KdV and Virasoro
2:30pm|Fine 322, Princeton University

Witten conjectured a relationship between intersection theory on the moduli space of marked stable curves and the KdV integrable hierarchy. Alternatively, the KdV hierarchy can be rephrased in terms of a representation of half the Virasoro algebra...

Mar
24
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

BCFG Drinfeld-Sokolov hierarchies and ADE LG-model with symmetry
Yongbin Ruan
1:30pm|Fine 224, Princeton University

More than twenty years ago, Witten proposed a remarkable conjecture connecting the geometry of moduli space of curve or Gromov-Witten theory of point to KdV integrable hierarchies (solved by Kontsevich). Since then, Witten's conjecture opened up a...

Mar
28
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Virtual neighbourhood technique and its applications
Bai-Ling Wang
1:30pm|Fine 322, Princeton University

In this talk, I will explain the recent joint work with Bohui Chen and Anmin Li on virtual neighborhood techniques for a Fredholm system \((B, E, S)\), where \(E\) is a Banach vector bundle over a Banach manifold \(B\) with a Fredholm section. Using...

Apr
04
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Towards Viterbo functoriality for nonexact Liouville embeddings
Janko Latschev
1:30pm|S-101

I will outline a way to extend the construction of Viterbo's transfer map in symplectic homology to nonexact embeddings of one Liouville domain into another. The approach is motivated by SFT, but at least parts of it can be implemented independently...

Apr
04
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Minimal Discrepancy of Isolated Singularities and Reeb Orbits
2:30pm|S-101

Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the...

Sep
25
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Symplectic fillings and star surgery
Laura Starkston
11:30am|S-101

Although the existence of a symplectic filling is well-understood for many contact 3-manifolds, complete classifications of all symplectic fillings of a particular contact manifold are more rare. Relying on a recognition theorem of McDuff for closed...

Oct
10
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Superconformal simple type and Witten's conjecture on the relation between Donaldson and Seiberg-Witten invariants
1:30pm|Fine 322, Princeton University

We shall discuss two new results concerning gauge-theoretic invariants of "standard" four-manifolds, namely closed, connected, four-dimensional, orientable, smooth manifolds with \(b^1 = 0\) and \(b^+ \geq 3\) and odd. We first describe how the SO(3...

Oct
17
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Equivariant structures in mirror symmetry
1:30pm|S-101

When a variety \(X\) is equipped with the action of an algebraic group \(G\), it is natural to study the \(G\)-equivariant vector bundles or coherent sheaves on \(X\). When \(X\) furthermore has a mirror partner \(Y\), one can ask for the...

Oct
31
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

On the Gromov width of polygon spaces
Alessia Mandini
1:30pm|S-101

After Gromov's foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold \((M, \omega)\) is a symplectic invariant that measures, roughly speaking, the size of the...

Nov
07
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

\(C^0\)-characterization of symplectic and contact embeddings
1:30pm|S-101

Symplectic and anti-symplectic embeddings can be characterized as those embeddings that preserve the symplectic capacity (of ellipsoids). This gives rise to a proof of \(C^0\)-rigidity of symplectic embeddings, and in particular, diffeomorphisms....

Nov
14
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Stability in Fukaya categories of surfaces
Fabian Haiden
10:45am|Math 407, Columbia University

I will report on recent joint work with L. Katzarkov and M. Kontsevich (arXiv:1409.8611) in which we construct Bridgeland stability conditions on partially wrapped Fukaya categories of surfaces. Stable objects in these stability conditions...

Nov
14
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

The Lefschetz Hyperplane Theorem is mostly wrong (symplectically speaking)
1:30pm|Math 407, Columbia University

We show that for any symplectic manifold of dimension \(2n > 4\), there exists a symplectic hypersurface Poincare dual to some positive multiple of the symplectic form whose \((n - 2)\)th Betti number is as large as we like. The idea here is to find...

Nov
21
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Cyclic homology and \(S^1\)-equivariant symplectic cohomology
1:30pm|S-101

In this talk, we study two natural circle actions in Floer theory, one on symplectic cohomology and one on the Hochschild homology of the Fukaya category. We show that the geometric open-closed string map between these two complexes is \(S^1\)...

Dec
05
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

Gauged linear $\sigma$-model and gauged Witten equation
Guangbo Xu
1:30pm|Fine 322, Princeton University

This is a joint work with Gang Tian. I will talk about the analytical properties of the classical equation of motion in gauged linear $\sigma$-model, which we call the gauged Witten equation. This is a generalization of the Witten equation in Landau...

Dec
12
2014

Joint IAS/Princeton University Symplectic Geometry Seminar

On normal crossings symplectic divisors
1:30pm|Fine 322, Princeton University

I will describe purely symplectic notions of normal crossings divisor and configuration. They are compatible with the existence of the desired auxiliary almost Kahler structures, provided ``existence" is suitably interpreted. These notions lead to a...

Jan
30
2015

Joint IAS/Princeton University Symplectic Geometry Seminar

Symplectic forms in algebraic geometry
1:30pm|S-101

Imposing the existence of a holomorphic symplectic form on a projective algebraic variety is a very strong condition. After describing various instances of this phenomenon (among which is the fact that so few examples are known!), I will focus on...

Feb
06
2015

Joint IAS/Princeton University Symplectic Geometry Seminar

Path products in projective space
1:30pm|S-101

We compute the mod 2 homology of the space of paths in $\mathbb CP^n$ with endpoints in $\mathbb RP^n$, and its algebra structure with respect to the Pontryagin-Chas-Sullivan product. Our method combines Morse theory with geometry. Joint work with...

Feb
13
2015

Joint IAS/Princeton University Symplectic Geometry Seminar

Symplectic homology via Gromov-Witten theory
Luis Diogo
1:30pm|S-101

Symplectic homology is a very useful tool in symplectic topology, but it can be hard to compute explicitly. We will describe a procedure for computing symplectic homology using counts of pseudo-holomorphic spheres. These counts can sometimes be...

Feb
19
2015

Joint IAS/Princeton University Symplectic Geometry Seminar

Existence of Lefschetz fibrations on Stein/Weinstein domains
2:30pm|Fine 110, Princeton University

I will describe joint work with E. Giroux in which we show that every Weinstein domain admits a Lefschetz fibration over the disk (that is, a singular fibration with Weinstein fibers and Morse singularities). We also prove an analogous result for...

Feb
20
2015

Joint IAS/Princeton University Symplectic Geometry Seminar

The symplectic displacement energy
Peter Spaeth
1:30pm|S-101

To begin we will recall Banyaga's Hofer-like metric on the group of symplectic diffeomorphisms, and explain its conjugation invariance up to a factor. From there we will prove the positivity of the symplectic displacement energy of open subsets in...

Feb
27
2015

Joint IAS/Princeton University Symplectic Geometry Seminar

Disc filling and connected sum
Kai Zehmisch
1:30pm|S-101

In my talk I will report on recent work with Hansjörg Geiges about a strong connection between the topology of a contact manifold and the existence of contractible periodic Reeb orbits. Namely, if the contact manifold appears as non-trivial contact...

Mar
02
2015

Joint IAS/Princeton University Symplectic Geometry Seminar

From knots to clusters: the path via sheaves
Eric Zaslow
4:30pm|Fine 110, Princeton University

Given a Legendrian knot, I will construct a category of constructible sheaves, invariant under Legendrian isotopy up to equivalence. The constructble sheaves live on the front plane and are stratified by the front diagram of the Legendrian knot. I...