Key research themes
1. How do degeneracy loci and determinantal conditions characterize special algebraic varieties?
This research theme focuses on varieties defined by rank conditions or degeneracy loci arising from symmetric or skew-symmetric bundle maps, or determinantal equations. It explores the geometric and cohomological properties of such varieties, including their classes expressed via Chern classes, conditions for generic finite determinacy, and geometric interpretations within algebraic geometry. These determinantal varieties bridge local and global properties and provide foundational examples for singularity theory and deformation problems.
2. What are the criteria and geometric conditions ensuring equisingularity and Whitney regularity in families of singular curves and varieties?
This theme investigates conditions under which families of algebraic curves and surfaces with singularities vary ‘equisingularly’ – that is, their singularities behave uniformly across the family. The focus is on characterizations of Whitney regularity, Zariski’s discriminant criterion, topological triviality, and their equivalence or nuances in non-reduced or generically reduced cases. It includes an analysis of equisingularity criteria's stability under modifications such as blow-ups and Nash modifications, and studies implications for normalization and smoothness of total spaces.
3. How do social and linguistic factors influence the acquisition and maintenance of nonstandard varieties and language use in education?
This theme addresses the sociolinguistic and educational dynamics of nonstandard language varieties, focusing especially on mixed languages or lingua francas (such as Sepitori) and their influence on standard language acquisition among home language learners. It examines the sociopolitical and cultural implications of mixed varieties in classrooms, how learners' home language backgrounds influence their written and spoken output, and educators' perspectives on the status and pedagogical treatment of nonstandard varieties within formal education.