During the Fall 2026 quarter, all of our meetings will be held in person in Skye Hall 268.
Talks will run from 11 am to 11:50 am PT, but you are welcome to arrive early to socialize with the speaker.
FALL 2026 SCHEDULE
September 25, 2026
Mario Rodriguez Sanchez de Toca, U. de Santiago de Compostela (and UCR)
Title: Harmonic manifolds: an overview.
Abstract: Given a Riemannian manifold, we say that it is locally harmonic if its volume density function is radial at any point. It was conjectured by Lichnerowicz that all such manifolds are symmetric spaces of rank one. While this is true for compact manifolds, in the non-compact case the Damek-Ricci spaces arise as a counterexample. In this talk we will discuss the basic aspects of locally harmonic manifolds and some of the open problems about them.
October 2, 2026
Shane Rankin and David Weed, Univ. of Calf., Riverside
Title: Curvature of Left-Invariant Magnetic Systems
Abstract: A magnetic system is a choice of Riemannian metric paired with a closed two-form, referred to as the magnetic form. Recently, Assenza introduced a notion of magnetic sectional curvature that generalizes the classical Riemannian notion to account for the influence of the induced Lorentz force on particle motion at various energy levels. In this talk, we will discuss recent joint work with Ivo Terek describing this curvature in the setting of left-invariant systems on Lie groups, extending in part classical work of Milnor on left-invariant metrics.
October 9, 2026
Tian Yang Texas A&M University
Title: Volume Conjecture and some recent progress
Abstract: In this talk, I will first give an overview of the Volume Conjecture, which connects two seeming different approaches to 3-dimensional topology – the hyperbolic geometry and the quantum invariants. Then I will talk about a recent joint
work with Tianyue Liu, Shuang Ming, Xin Sun and Baojun Wu, where we define a family of quantum invariants for hyperbolic 3-manifolds with cusp ends and with totally geodesic boundary from the representation theory of the a quantum group,
called the modular double of Uqsl(2; R), and prove that asymptotically these new invariants behave exactly in the way that the Volume Conjecture predicted.
October 16, 2026
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October 23, 2026
Tommy Murphy, CSU, Fullerton
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