Update collaboration.html

Author: saramaloni

RTG_geomtop/collaboration.html

@@ -14,7 +14,24 @@ <h1 class="mb-5">Collaborative Research Projects</h1>
 research in geometry and topology. Projects will be led by senior researchers; the first round of projects were held in summer 2022 and 2023.
 Another round of projects will be held in summer 2025 and 2026.
 
-#### COLLABORATIVE PROJECTS IN ALGEBRAIC TOPOLOGY
+#### COLLABORATIVE PROJECTS IN GEOMETRIC TOPOLOGY (Summer 2026)
+**Organizers: Harry Bray, Anton Lukyanenko, Sara Maloni and Allison Moore**
+
+The upcoming round of research projects will focus on three problems in geometric topology. Research teams will begin meeting virtually
+during the end of spring 2026 before participating in an in-person collaborative workshop **August 10-14, 2026**, in the Blue Ridge Mountains. The planned
+projects are described briefly below.
+<a href="TBA">Please click here to apply</a>. Application deadline: April 13, 2026.
+
+* **Unknotting numbers of trivalent spatial graphs**
+  - Team Leaders: Allison Moore (VCU) and Danielle O’Donnol (Marymount).
+  - Description: This project is focused on unknotting numbers of spatial graphs. Generalizing a knot, a spatial graph is an embedding of a graph in the three-sphere. Planar spatial graphs are unknotted when they are isotopic to planar embeddings. As with the classic setting of knots and links, a wide variety of invariants (geometric, polynomial, homological) may be used to obstruct unknotting pathways and bound or calculate unknotting numbers. Although unknotting numbers of spatial graphs are less understood than knots and links, yet natural applications arise in both low-dimensional topology and molecular biology. We will focus on calculating and bounding unknotting numbers of trivalent spatial graphs via existing methods and by developing new ones. Familiarity with geometric topology and knot theory is helpful, but not required.
+
+* **Distinguishing links using surface intersection patterns**
+  - Team Leaders: Nir Gadish (UPenn) and Ryan Stees (UVA).
+  - Description: Starting with the classical linking number of Gauss and the triple linking number which detects the linking of the Borromean rings, Milnor's mu-invariants are among the most fundamental tools for distinguishing links in the 3-sphere. A recent series of works centers the Bar construction of cochain algebras as a generalization of these invariants, leading simultaneously to a geometric interpretation involving intersections of surfaces in the link exterior as well as to subtle new invariants. This project seeks to systematize and rigidify the choices of surfaces, thus resolving the problem of self-intersection. This should ultimately facilitate explicit geometric formulas for Milnor's invariants, and possibly computer implementation that takes link diagrams as input.
+
+#### COLLABORATIVE PROJECTS IN ALGEBRAIC TOPOLOGY (Summer 2025)
+**Organizers: Rebecca Field and J. D. Quigley**
 
 The upcoming round of research projects will focus on three problems in algebraic topology. Research teams will begin meeting virtually
 during spring 2025 before participating in an in-person collaborative workshop June 16–20, 2025, in the Blue Ridge Mountains. The planned