Discipline: Mathematics

I work in mathematics related to algebra, arithmetic geometry, combinatorics, mathematical physics, and number theory. I specialize in theory of harmonic Maass forms, modular forms, and partitions.

My work concerns the geometry of the space of mappings from Riemann surfaces to algebraic varieties. The subject has roots in classical mathematics beginning with famous work of Riemann in the 19th century. However, rapid progress has been made in the past decade through the new perspective of topological string theory and the wave of … Continued

Currently working on boundary field equalities that generalize the idea of conservation laws, new methods for guiding stress in structures, bounds that provide limitations to cloaking, novel methods for obtaining bounds on the spectrum of operators, novel metamaterials, novel minimization variational principles for acoustic and electromagnetic scattering, characterizing the possible elasticity tensors of 3d printed … Continued

I study the complexity of mathematics. In mathematics there are constructions, proofs, and objects that are clearly more complicated than others. In computability theory we look for tools to measure this complexity and we measure it.

My work is in algebraic geometry. I have been studying invariants that measure the singularities of algebraic varieties, such as minimal log discrepancies, log canonical thresholds, multiplier ideals, Bernstein-Sato polynomials, and F-thresholds. Various points of view and techniques come in the picture when studying these invariants: resolutions of singularities, jet schemes, D-modules, and positive characteristic … Continued

I am a mathematician who works on analysis and geometry. My research investigates the extent to which abstract geometries with an intrinsic notion of distance (metric spaces) can be faithfully represented as points in better-understood geometries, such as Euclidean space. Such abstract geometries are ubiquitous in mathematics, computer science, and statistics. My work on understanding … Continued

Most of my work is concerned with questions related to the long-term dynamics of solutions of partial differential equations. These equations describe physical phenomena, such as water waves, plasma evolutions, and gravitation, and their relevance is often verified numerically. Ionescu studies the solutions of these equations rigorously, and recovers quantitative and qualitative information about their … Continued

I conduct laboratory experiments on fundamental problems in fluid mechanics.

A major focus of my work has been the development of “fast algorithms” for particle simulations, wave propagation, and heat flow. These algorithms (such as the Fast Mutipole Method) are now used in electromagnetic and acoustic design, quantum chemistry and a variety of other application areas. For the last few decades, I have been working … Continued

My research is concerned with representation theory, quantum field theory, integrable systems, and the interrelations between them.