“Positive Grassmannians and the Geometry of Wilson Loop diagrams”
Susama Agarwala, United States Naval Academy
Susama Agarwala, United States Naval Academy
David Duncan, McMaster University
A variant of the Atiyah-Floer conjecture states that the SO(3)-Donaldson invariants are iso- morphic to certain invariants coming out of symplectic geometry. I will discuss this conjecture in a few special cases that suggest an outline for proving the more general statement.
MC 5413
Charlotte Kirchoff-Lukat, University of Cambridge
Ben Sibley, Simons Center, Stony Brook University
Manousos Maridakis, Rutgers University
Lojasiewicz-Simon gradient inequalities have become increasingly useful in convergence properties of gradient flows and uniqueness of singularity models. Recently they played important role in the proof of discreteness of critical energies for energy functionals. We discuss an abstract version of a Lojasiewicz-Simon gradient inequality established under very weak assumptions and its applications for coupled Yang-Mills energy functionals and Harmonic map energy functionals on closed manifolds.
MC 5413
Teng Fei, Columbia University
The Strominger system is a system of PDEs describing the compactification of heterotic strings with torsion. Mathematically it can be thought of as a generalization of Ricci-flat metrics on non-Kähler Calabi-Yau 3-folds. In this talk we present newly obtained smooth solutions to the Strominger system on infinitely many compact non-Kähler Calabi-Yau 3-folds with distinct topological types and sets of Hodge numbers. This is a joint work with Zhijie Huang and Sebastien Picard.
MC 5413
Dhruv Ranganathan, MIT
Ajneet Dhillon, University of Western Ontario
Let X be a smooth projective curve over a finite field and $G$ a semisimple algebraic group over its function field. Let $\mathcal{G}$ be a smooth group scheme over X with generic fiber $G$. The Tamagawa number of $G$ is an arithmetic invariant obtained from a Haar measure on the adelic points of $G$. A conjecture of Harder relates this number to the number of components of the moduli stack of $\mathcal{G}$-bundles.
Esther Cabezas-Rivas, Universität Frankfurt
We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time.
Mykola Matviichuk, University of Toronto