Department of Mathematics

Yuri Berest, Cornell University In 1982, I. G. Macdonald published a series of beautiful  combinatorial conjectures related to classical root systems (or equivalently, compact Lie groups). These conjectures were in the focus of research in representation theory and geometry for over 30 years. In the early 1990s,…

Mulase Motohico, UC Davis Quantum curves are conceived in physics literature. They are linear differential or difference equations in one variable, and sometimes a mixture of them. These are Weyl quantization of spectral curves appearing in different contexts of mathematics, such as integrable systems, random matrix theory, and…

Bjorn Birnir, Department of MathematicsUniversity of California, Santa Barbara Angiogenesis is a multiscale process by which a primary blood vessel issues secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be a natural process of organ growth and development or a pathological one induced by a…

Bjorn Birnir, UCSBAngiogenesis is a multiscale process by which a primaryblood vessel issues secondary vessel sprouts that reach regions lackingoxygen. Angiogenesis can be a natural process of organ growth anddevelopment or a pathological one induced by a cancerous tumor.A mean-field approximation for a stochastic model of…

Milen Yakimov, Northeastern University The talk will provide a gentle introduction to Cluster Algebras based on an example with the first Weyl algebra and not using elaborate combinatorics. We will explore the interplay between the three worlds of cluster algebras: classical, quantum and root of unity, building a bridge between…

Susan Sierra, University of Edinburgh (Universal) enveloping algebras of finite-dimensional Lie algebras are some of the most well-understood examples in noncommutative ring theory. On the other hand, enveloping algebras of infinite-dimensional Lie algebras are much more mysterious. This talk will survey what's known about these…

Bo Li, UC San Diego: Ligand-receptor binding and unbinding are fundamental molecular processes, whereas water fluctuations impact strongly their thermodynamics and kinetics. We develop a variational implicit-solvent model (VISM) and a fast binary level-set method to calculate the potential of mean force and the molecule-water…

Chi-Wang Shu, Division of Applied Mathematics, Brown University In scientific and engineering computing, we encounter time-dependent partial differential equations (PDEs) frequently. When designing high order schemes for solving these time-dependent PDEs, we often first develop semi-discrete schemes paying attention only to…