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:

• Orsola Capovilla-Searle, Oregon State University

• Simone Cecchini, Texas A & M University

• Alena Erchenko, University of Oregon

• Nicki Magill, University of California, Berkeley

• Jan Nienhaus, University of California, Los Angeles

• Charles Ouyang, Washington University

• Tracy Payne, Idaho State 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: Jan Nienhaus, University of California Los Angeles.
  
  Einstein metrics on spheres of even dimension

The first non-round Einstein metrics on spheres were described in 1973 by Jensen in dimensions 4n+3 (n > 0). For the next 25 years it remained an open problem whether the same could be done in even dimensions. This question was settled in 1998 when C. Böhm constructed infinite families of Einstein metrics on all Spheres of dimension between 5 and 9, in particular on S^6 and S^8. Over the last 25 years, all spheres of odd dimension (at least 5) have been shown to admit non-round Einstein metrics, but there have been no new developments in even dimensions above 8, leaving open to speculation the question of whether non-uniqueness of the round metric is a low-dimensional phenomenon or to be expected in all dimensions. I will give an overview of the methods used to construct non-round Einstein metrics, which we recently used to construct three new Einstein metrics on S^10. This is joint work with Matthias Wink.

• 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.
  
  

• 7:00 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: Tracy Payne, Idaho State University.
  
  Homogeneous Spaces with Negative Curvature
  
  We discuss negatively curved homogeneous spaces. Even in dimension four, negatively curved homogeneous spaces are not classified.  We identify negatively curved homogeneous spaces within a large class in dimension four.   Within this class, we also consider homogeneous spaces with curvature bounded above by a specific constant, bounded below by a specific constant, and with specified pinching constant. We find extremal planes. We also present some general results about curvature pinching. This is joint work with Romina Arroyo, Karen Butt, Karla Garcia, Ruth Gornet and Meera Mainkar.

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.