Week of Events
Analysis seminar: Anna Skorobogatova (ETH)
Title: Non-uniqueness of locally-minimizing clustersAbstract: Optimal bubble cluster problems concern the study of partitions of $mathbb{R}^n$ into a finite collection of chambers, some with finite volume and some with infinite volume. One looks for local minimizers of interfacial area subject to volume constraints on the finite-volume chambers. The case of one infinite-volume chamber is the classical multiple […]
Topology Seminar: Rostislav Akhmechet (Columbia University)
Title: Annular web algebrasAbstract: We define equivariant SL(2) and SL(3) web algebras in the annulus using annular foam TQFTs introduced in earlier work with Khovanov. To a diagram of a tangle in the thickened annulus we assign a complex of bimodules over these algebras whose chain homotopy type is an invariant of the tangle. I […]
Algebraic Geometry Seminar: Tamás Darvas (UMD)
Title: A YTD correspondence for constant scalar curvature metricsAbstract: Given a compact Kähler manifold, to better understand Mabuchi's K energy we introduce a family of K^beta energies, whose favorable properties are similar to those of the Ding energy from the Fano case. The construction uses Berman's transcendental quantization, and we show that the slope of the K^beta […]
Yulong Lu
Title: In-Context Learning in Scientific ComputingAbstract: Transformer-based foundation models, pre-trained on large datasets spanning a wide range of tasks, have shown remarkable adaptability to diverse downstream applications—even in low-data regimes. A particularly striking capability is in-context learning (ICL): when given a prompt containing a few examples from a new task alongside a query, these models can […]
Math Physics Seminar: Michael Weinstein (Columbia University)
Title: EDGE STATES IN PERIODIC AND APERIODIC STRUCTURES Abstract: Edge states are solutions of energy conserving and dispersive wave equations which are bounded and oscillatory (plane-wave like) in the direction of a line defect, and localized transverse to it. We discuss edge states in systems with honeycomb symmetry, which arise in two dimensional quantum materials such as […]
Geometric analysis seminar: Filippo Gaia
Title: CMC surfaces with bounded genusAbstract: We will discuss the following problem: given a closed $3$-manifold $M$ and $Hgeq 0$, is there a surface with constant mean curvature $H$ in $M$ whose genus $g$ is controlled? We will show that for almost every $H$, one can construct a branched immersion with these properties, with $g$ […]