Faculty
Anne Yust
Welcome to the Department!
I received my PhD in mathematics from Carnegie Mellon University in 2010, advised by Shlomo Ta’asan. Since then, I’ve held teaching-centered positions at Birmingham-Southern College in Birmingham, AL and Eugene Lang College of Liberal Arts at The New School in New York City. I enjoy thinking about mathematical applications to biology; though, I’ve recently delved into mathematics and its role in promoting fair political representation, such as detecting gerrymandering. Frequently, I approach these topics using agent-based models to simulate the phenomena, which I’ve found to be a fun way to incorporate undergraduates in mathematical research. Even in this virtual environment, I am really enjoying teaching at Pitt, especially within the actuarial mathematics program. I am very excited to have joined the Pitt Mathematics Department!
Featured Research
Here, we briefly describe the research topics of three recently funded National Science Foundation grant awards to Department of Mathematics faculty:
1) Roman Fedorov – Principle Bundles and Higgs Bundles in Algebraic Geometry
This project is directed at the study of principal bundles, which was begun in the early 20th century by physicists as a formalism to describe electromagnetism. Later, this was extended to encompass strong and weak interactions, so that principal bundles became a basis for the so-called standard model -- a physical theory describing three out of four fundamental interactions. In mathematics, principal bundles penetrate many areas: geometry, number theory, mathematical physics, and others. In 1950's Fields Medalist Jean-Pierre Serre recognized the importance of principal bundles in algebraic geometry. In his 1958 seminal paper he gave the first modern definition of a principal bundle and formulated a certain deep conjecture. This conjecture, as well as some remaining questions, are among the oldest unsolved foundational questions in mathematics. The first part of the project is aimed at proving some of these conjectures. The remaining parts of the projects are related to the so-called Higgs principal bundles, which can be thought of as mathematical incarnations of the Higgs boson -- a recently found elementary particle. These parts of the project belong to the famous Langlands program unifying number theory, algebraic geometry, harmonic analysis, and mathematical physics.
2) Marta Lewicka – Dimension Reduction and Singular Limits of Prestrained Structures
This project is directed at the study of properties and behavior of "prestrained elastica". Elastica (elastic materials) are the solid materials which return to their original shape and size after forces applied to them are removed. If an elastic body is appropriately processed mechanically (e.g. rolled), thermally (cooled non-uniformly during heat treatment), chemically ("nitrided" through surface absorption of nitrogen) or exposed to inhomogeneous growth, stresses and strains may develop in the body at equilibrium, leading to the material that has been prestrained (strained in advance). A characteristic which singles out the quality of prestraining in a body is that even in the absence of exterior forces the body assumes a shape that is radically different from the same body without strains.
3) Jonathan Rubin – Emergence and Coordination of Rhythmic Activity in Respiratory Neurons and Networks
This award will support the study of mathematical issues involved in how the brain produces the rhythmic outputs needed for breathing. For example, much neural activity occurs on millisecond timescales, but respiratory rhythms have periods closer to a full second, and this project will investigate how fast processes lead to slow rhythms. It will also explore ways that ideas from graph theory and dynamical systems can be used to understand organized neural dynamics. The work will lead to predictions that will be tested by experimental collaborators.