Date/Time
Date(s) - 09/01/2026
3:30 pm - 4:30 pm

Location: Hamilton Hall, Room 305

Speaker: Geunyoung Kim
Title: Heegaard diagrams for 5-manifolds  
Abstract: In three dimensions, Heegaard diagrams are a powerful combinatorial tool for studying 3-manifolds. In this talk, I will describe how this idea can be extended to 5-manifolds by introducing an analogue of Heegaard diagrams in higher dimensions. I will discuss the basic construction and present several examples to illustrate how these diagrams can be used to understand the topology of 5-manifolds.

Speaker: Reihaneh Vafadar
Title: Divergence-free drifts
Abstract: We consider the elliptic Kolmogorov operator with drifts in a large class of multiplicatively form-bounded vector fields, and with divergence belonging to a broad form-bounded class. We develop a De Giorgi–type approach and establish regularity theory for the elliptic Kolmogorov operator through a certain iteration procedure, which we call Caccioppoli’s iteration, in place of the classical compensated compactness method typically used to treat the class BMO^{?1}. This method allows us to handle highly irregular drift vector fields.

Speaker: Siyi Wang
Title: Hyperbolic Clustering Mapping
Abstract: The hyperbolic cluster mapping method  is intended to provide a fast, non-iterative visualization of the results of a clustering algorithm or of centroid estimation applied to a high-dimensional data set. The method takes a data set $S \subset \R^n$ together with centroid estimates or a clustering algorithm, and produces a visualization of the data set mapped into the 2-dimensional hyperbolic disk. We then extend this map by introducing multiple local sub-centers per cluster, so as to better capture intra-cluster geometry while preserving the global arrangement of clusters.

Coffee will be served in Hamilton Hall, Room 216 at 3:00pm. All are welcome.