The next PNGS

University of Washington, Seattle, WA.  May 2--3, 2026.

Registration is now open!  Please visit this google form to register.

Invited speakers:

• Eric Bahuaud, Seattle University

• Orsola Capovilla-Searle, Oregon State University

• Simone Cecchini, Texas A & M University

• Alena Erchenko, University of Oregon

• Nicki Magill, University of California, Berkeley

• Jacob Ogden, University of Washington

• Charles Ouyang, Washington University

Location:

UW Seattle Campus.  All talks in Johnson Hall 175.  Here is a map.  Look just to the upper-left of Drumheller Fountain in blue.

Schedule:

Saturday May 2, 9 am -  5 pm

• 9:00--9:30: Coffee.

• 9:30--10:30: Orsola Capovilla-Searle, Oregon State University.
  
  Which polynomials can be ruling polynomials of Legendrian links?
  
  An important problem in symplectic and contact topology is to classify exact Lagrangian surfaces in the symplectic 4-ball that intersect the boundary contact 3-sphere as Legendrian links up to exact Lagrangian isotopy fixing the boundary. Such surfaces are called fillings of the Legendrian link. In the last decade, our understanding of the moduli space of fillings for various families of Legendrians has greatly improved thanks to tools from sheaf theory, Floer theory and cluster algebras. The ruling polynomial is a Legendrian invariant in a many to one correspondence with immersed fillings. In joint work with Yu Pan we show that any even degree polynomial can be realized as the ruling polynomial of a Legendrian. The Legendrian links we construct have augmentation varieties with trivial cluster algebras and fillings that are not smoothly isotopic. Our family of Legendrians exhibits distinct behavior to that of the better studied Legendrian (-1) closures of positive braids containing a full twist.
  
  

• 10:30--10:45: Break
  
  

• 10:45--11:45: Nicki Magill, University of California Berkeley.
  
  Generalized convex toric domains and symplectic embedding problems
  
  A convex toric domain XΩ is a 4-dimensional subset of R4, defined as the preimage of a bounded convex region Ω in the positive quadrant of R2 under the moment map. We consider how geometric features of Ω such as the curviness of its boundary and its affine perimeter impact symplectic packing problems. Some of our results come from considering the asymptotics of the ECH capacities. These capacities are known to obey a Weyl law and detect the volume of XΩ. We show that their subleading asymptotics detect the affine perimeter of Ω. We’ll discuss how these asymptotic results lead to new applications in symplectic embedding problems. This is based on joint work with Dan Cristofaro-Gardiner and Dusa McDuff.
  
  

• 11:45--1:30: Lunch! 
  
  

• 1:30--2:30: Jacob Ogden, University of Washington.
  
  Rigidity results in calibrated geometry

The theory of calibrated geometry, introduced by Harvey and Lawson, provides rich families of high-codimension volume-minimizing submanifolds. There is substantial interest in understanding Bernstein-type results for calibrated submanifolds, i.e. finding conditions which force a calibrated submanifold to be a plane. In this talk, we present two such results. We first discuss a simple argument demonstrating that a submanifold of Euclidean space whose normal bundle is flat and which is calibrated by a constant-coefficient form must be a plane. We then focus on special Lagrangian submanifolds, discussing a constant rank theorem for solutions of the special Lagrangian equation. This result asserts that solutions of the PDE with a certain lower bound on the Hessian have a strong minimum principle for the smallest Hessian eigenvalue. As a consequence, we derive a new rigidity result for special Lagrangian cones and a Liouville theorem for entire solutions of the special Lagrangian equation. This is based on joint work with Yu Yuan.

• 2:30--2:45: Break
  
  

• 2:45--3:45: Simone Cecchini, Texas A & M University.
  
  Spin^c Structures, Scalar Curvature, and Comass Bounds

In this talk I will describe how Spin^c Dirac operators can be used to convert degree-two cohomology classes into quantitative lower bounds for scalar curvature. Under a natural Spin^c index-type hypothesis, this yields an estimate in terms of the comass norm, the norm dual to the stable norm on homology. The key ingredients are the Spin^c Lichnerowicz formula and a sharp pointwise estimate for the curvature term. I will then discuss rigidity in the equality case: in even dimensions equality forces the metric to be Kähler-Einstein, while in odd dimensions the universal cover splits off a line and the transverse factor is Kähler-Einstein. Finally, I will explain applications to stable 2-systolic inequalities, including the sharp case of  ℂℙn and its rigidity. This is joint work with Sven Hirsch and Rudi Zeidler.

• 3:45--4:00: Break
  
  

• 4:00--5:00: Charles Ouyang, Washington University.
  
  New Minimal Lagrangians in ℂℙ2
  
  Minimal Lagrangian tori in ℂℙ2 are the expected local model for particular point singularities of Calabi-Yau 3-folds, and numerous examples have been constructed. In stark contrast, very little is known about higher genus examples, with the only ones to date due to Haskins-Kapouleas and only in odd genus. Using loop group methods, we construct new examples of minimal Lagrangian surfaces of genus (k-1)(k-2)/2 for large k, hence providing the first examples in even genus. Time permitting, we show our surfaces lift to embedded special Legendrian surfaces in the 5-sphere. These are the first embedded examples. This is joint work with Sebastian Heller and Franz Pedit.
  
  

• 6:30 Conference dinner: Cedar's Seattle. (https://cedarsseattle.com/). More details to follow.

Sunday May 3, 9 am - 12 pm

• 9:00--9:30: Coffee.

• 9:30--10:30: Alena Erchenko, University of Oregon.
  
  Marked Poincaré spectrum rigidity
  
  For a closed, negatively curved manifold, in analogy to the marked length spectrum, we consider marked dynamical data, called the marked Poincaré determinant, which measures the unstable volume expansion of the geodesic flow around periodic orbits. We show that the marked Poincaré determinant determines the metric up to homothety among metrics in a neighborhood of the hyperbolic metric of a closed 3-manifold. This is a joint work with Butt, Humbert, Lefeuvre, and Wilkinson.
  
  

• 10:30--10:45: Break
  
  

• 10:45--11:45: Eric Bahuaud, Seattle University.
  
  Basics of the Bach flow
  
  For a compact Riemannian 4-manifold, the Bach tensor is a multiple of the gradient of the Weyl energy functional. This symmetric 2-tensor is conformally covariant and fourth-order in the metric, and vanishes for any metric conformal to an Einstein metric. Thus finding a Bach flat metric can be thought of as a generalization of the Einstein equation.  In my talk I'll review the basics of a geometric flow by the Bach tensor and then report on ongoing work concerning stability of the  flow in various settings.

Transportation (From SEA to UW)

PUBLIC TRANSPORT (via Link Light Rail, approx. 50 minutes): From airport gate exit, navigate toward ground transportation and walk across the skybridge to the Link Light Rail station.  Purchase ticket ($3) before entering platform and keep ticket during voyage in case of fare check.  Take Link Light Rail (#1 line) from SeaTac airport in the direction of downtown Seattle ( the train direction is Lynnwood City Center ).  Get off the train at either the UW station (on south campus near Husky Stadium) or U district Station ( close to hotel recommended below ).

UBER/TAXI/SHUTTLES: Also available at the SeaTac airport.  

Hotels near UW

Graduate Hotel by Hilton. This hotel is in the University District and a block away from light rail.

Dining near UW

There are many low cost options in the University District near the hotel and conference venue.  The street University Way, also called "The Ave" by locals is popular amongst students for cafes and restaurants.

Things to see and do; more dining recommendations

Jack Lee has compiled this extensive list of things to see and do in Seattle and the surrounding area.  There are also dining suggestions further from campus.