Networks in Physics and Geometry: Spectral, Exponential, and Beyond

Contribution List

1. Exponential networks and the life of partitions

Prof. Johannes Walcher (Heidelberg University)

7/8/25, 10:00 AM

Following a quick summary of exponential networks, I will describe in some detail the explicit correspondence, obtained in collaboration with Banerjee, Romo and Senghaas, between torus fixed points of the Hilbert scheme of points in the plane and anomaly-free finite webs attached to the quadratically framed pair of pants.

2. Some aspects of exponential networks (Online)

Prof. Mauricio Romo (SIMIS/Fudan University)

7/8/25, 11:30 AM

I will describe exponential networks and its uses in defining (some version of) Donaldson-Thomas invariants and BPS quivers. If time allows I will present some other interpretation of these invariants as Euler characteristic of certain families of special Lagrangians.

3. (Partial) abelianization and higher Teichmüller spaces

Dr Clarence Kineider (MPI Leipzig)

7/8/25, 2:00 PM

Higher Teichmüller spaces are connected components in the space of representations from a surface group into a higher rank Lie group. The first examples of these are Hitchin components for split real Lie groups. I will give an overview of the known examples of higher Teichmüller spaces, via the notion of Theta-positivity introduced by Guichard-Wienhard to generalize Fock-Goncharov and Lusztig...

4. Spectral networks as screening contours (Online)

Prof. Andrew Neitzke (Yale University)

7/8/25, 3:30 PM

I will describe a role of spectral networks in 2-dimensional conformal field theory: they can be used as "screening contours" in a new construction of Virasoro conformal blocks from branched double covers. The key new point is that, when three exponentiated screening contours end on a branch point of the cover, they cancel an unwanted singularity of the conformal block there. The talk is...

5. Spectral networks and Betti Lagrangians (Online)

Dr Nick Nho

7/9/25, 10:00 AM

In this talk I will discuss the interface of spectral network theory and real contact symplectic topology. I begin with an introduction to weave theory, which allows one to construct exact Lagrangians from totally degenerate spectral networks (otherwise known as N-graphs). I then broaden the classical notion of a meromorphic spectral curve to the wider setting of Betti Lagrangians and...

6. Thimbles and resummation to networks

Dr Cambell Wheeler (IHES)

7/9/25, 11:30 AM

I will discuss how parametric resurgence recovers many
of the basic properties of networks and some examples that arise
from q-hypergeometric functions, which play an important role in
Chern-Simons theory and open topological strings. I will explain
how to construct these networks from some basic building blocks
coming from the Faddeev quantum dilogarithm and the geometry
of thimbles in...

7. Alternating diagrams and non-commutative cluster Lagrangians

Prof. Alexander Goncharov (Yale University)

7/9/25, 2:00 PM

Given a bipartite graph G on a possibly punctured surface S, there is a (non-commutative) cluster Poisson variety X(G,S). It depends only on the equivalence class of G under certain elementary transformations. A threefold M which bounds the surface S with filled punctures gives rise to a Lagrangian in the generic symplectic fibers of X(G,S). I will explain that it carries a natural...

8. Discussion session

7/9/25, 3:30 PM