Member Seminar Speaker: Jue Liu Title: Instability of naked singularities in general relativity Abstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture, proposed by Penrose, which roughly states that for generic physical spacetime, the singularities (if existed) must be hidden behind the black holes. Unfortunately, the singularities visible to faraway observers, […]

Member Seminar Speaker: Michael Douglas Title: Knowledge Graph Embeddings and Inference Abstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data. A popular KG representation method is graph embedding, which facilitates […]

Member Seminar Speaker: Juven Wang Title: C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized […]

Speaker: Du Pei Title: Wall-crossing from Higgs bundles to vortices Abstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.

Speaker: Freid Tong Title: The complex Monge-Ampere equation in Kahler geometry Abstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk, I will introduce the complex Monge-Ampere equation […]