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 […]
Speaker: Alexei Oblomkov (University of Massachusetts) Title: Knot homology and sheaves on the Hilbert scheme of points on the plane Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial […]
https://youtu.be/4wHwqYrCqVQ Speaker: Marijn Heule, Carnegie Mellon University Title: Computer-Aided Mathematics and Satisfiability Abstract: Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence […]
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: Peng Shan (Tsinghua University) Title: Categorification and applications Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.
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: Karim Adiprasito, Hebrew University and University of Copenhagen Title: Anisotropy, biased pairing theory and applications Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic […]
https://youtu.be/rRGh97sOtKE Speaker: Patrick Massot, Laboratoire de Mathématiques d’Orsay and CNRS Title: Why explain mathematics to computers? Abstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like, what kind of things it teaches us, and […]
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 […]
Speaker: Tamás Hausel (IST Austria) Title: Hitchin map as spectrum of equivariant cohomology Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.
https://youtu.be/h-LEf4YnWhQ Speakers: Curtis Bright, School of Computer Science, University of Windsor and Vijay Ganesh, Dept. of Electrical and Computer Engineering, University of Waterloo Title: When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics Abstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their […]
Member Seminar Speaker: Chuck Doran Title: The Greene-Plesser Construction Revisited Abstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach, uncover the hints it gives for some more general mirror constructions, and describe a brand-new variant […]