During the Fall 2025 quarter, all of our meetings will be held in-person in Skye Hall 268.
Talks will run from 11a-12p PT, but feel free to show up early for socializing with the speaker.
Current organizers: Brian Collier, Filippo Mazzoli
Fall 2025 schedule
October 3, 2025
Shane Rankin (UCR)
Title: Shadows of Symplectic Geometry in some Poisson Manifolds
Abstract: In this talk, we’ll discuss a broad class of Poisson manifolds that are "almost" symplectic in some sense. We’ll first discuss how one can recover a remnant of "symplectic symmetry" inside the tangent algebra via a natural subalgebra that carries a rich algebraic structure. We'll then discuss a long exact sequence linking Poisson cohomology with Lie algebroid cohomology, which computes Poisson Cohomology and clarifies some discrepancies such as those appearing in E-Poisson cohomology. If time permits, we will also describe ongoing work toward assigning harmonic representatives to certain Poisson cohomology classes.
October 10, 2025
Ivo Terek (UCR)
Title: Compact plane waves with parallel Weyl curvature
Abstract: We present some background and discuss recent developments in the study of essentially conformally symmetric (ECS) manifolds - that is, those with parallel Weyl curvature which are not locally symmetric or conformally flat - including the topological structure in the rank-one case and the existence of compact examples.
Joint work with Andrzej Derdzinski. If you are interested in learning more about this topic, you can read about it in this recently published book of proceedings: https://link.springer.com/book/10.1007/978-3-031-99212-4
October 17, 2025
Leslie Mavrakis (University of Utah)
Title: Combinatorial Characterizations and Branched Manifolds
Abstract: A family F of compact n-manifolds is locally combinatorially defined (LCD) if there is a finite number of triangulated n-balls such that every manifold in F has a triangulation that locally looks like one of these n-balls. In joint work with Daryl Cooper and Priyam Patel, we show that LCD is equivalent to the existence of a compact branched n-manifold W, such that F is precisely those manifolds that immerse into W. In this way, W can be thought of as a universal branched manifold for F. In current and future work, we use this equivalence to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD. In this talk, I will present the main ideas of the proof of the equivalence and then construct branched 3-manifolds for a few of the geometries.
October 24, 2025
Filippo Mazzoli (UCR)
Title: Geometric transitions between the deformation spaces of quasi-Fuchsian representations in hyperbolic and anti-de Sitter space
Abstract: Let S be a closed oriented surface of genus g larger than or equal to 2. By the work of Donaldson, the deformation space of almost-Fuchsian hyperbolic metrics on the 3-manifold SxR admits a mapping class group-invariant hyperKahler structure. More recently, Seppi, Tamburelli and I showed that a similar phenomenon occurs for the deformation space of quasi-Fuchsian anti-de Sitter structures on SxR, which turns out to carry a natural para-hyperKahler structure. Hyperbolic and anti-de Sitter geometries are both subgeometries of the 3-dimensional projective space. Since the work of Danciger, geometric transitions between hyperbolic and anti-de Sitter structures via half-pipe geometry have been studied. In a joint work in progress with El Emam, Seppi, and Tamburelli, we show that a similar phenomenon of geometric transition occurs at the level of the defomation spaces between the aforementioned hyperKahler and para-hyperKahler structures, passing through so-called quasi-Fuchsian half-pipe 3-manifolds and their deformation spaces.
October 31, 2025
Kai-Wei Zhao (UC Irvine)
Title: Classification of Finite-Entropy Shortening Curves
Abstract: Curve shortening flow is a one-dimensional variant of mean curvature flow. In the compact case, it can be considered as the gradient flow of the arc-length functional. The classification of ancient solutions of CSF under some geometric conditions is a parabolic version of Liouville-type theorem. The previous results by Daskalopoulos–Hamilton–Sesum, X.-J. Wang, and Bourni–Langford–Tinaglia technically rely on the assumption of convexity of the curves. In the joint work with Kyeongsu Choi, Donghwi Seo, and Weibo Su, we replace the convexity condition by finite entropy, a mild measure of geometric complexity. In this talk, we will show that an ancient, embedded, smooth solution of CSF with finite entropy must be a static line, a shrinking circle, a paper clip, a translating grim reaper, or one in the large class of trombones constructed by Angenent–You.
November 7, 2025
TBA
Title: TBA
Abstract: TBA
November 28, 2025
NO SEMINAR (Thanksgiving break)