Title: Almost global well-posedness for quadratic quasilinear 2D wave-Klein-Gordon systems with small and localized initial data. Abstract: In this talk we will discuss our recent result on the almost global existence of small solutions of strongly coupled wave-Klein-Gordon systems (WKG) in … Read more
Title: Emergent Clustering from Pairwise Interactions in Polymer Genome Models Abstract: The physical organization of chromosomes is known to be vital to cell function. Highly efficient compaction is achieved through various means, including histones, loop extrusion, and crosslinking. Prior work … Read more
Title: Modeling and simulation of symmetry breaking in cells Abstract: In order to initiate movement, cells need to form a well-defined "front" and "rear" through the process of cellular polarization. Polarization is a crucial process involved in embryonic development and cell motility … Read more
Title: The Quantum DELL System Abstract: We propose quantum Hamiltonians of the double elliptic many-body integrable system (DELL) and study its spectrum. These Hamiltonians are certain elliptic functions of coordinates and momenta. Our results provide quantization of the classical DELL system which … Read more
Title: Mathematical and Computational Modeling of the Heart Abstract: Cardiovascular diseases are a major health and economic concern both in the U.S. and worldwide. Although recent breakthroughs in medical treatments for heart disease have improved patient outcomes, a complete understanding of … Read more
Title: Macdonald polynomials and level two Demazure modules for affine sl_{n+1}. Abstract: An important result due to Sanderson and Ion says that characters of level one Demazure modules are specialized Macdonald polynomials.In this talk, I will introduce a new class … Read more
Title: Symplectic Toric Orbifolds Abstract: Toric varieties are a special class of algebraic T-varieties whose geometry is encoded in convex polytopes. In addition to being interesting in its own right, toric geometry often serves as a source simple examples where … Read more
Title: The dynamics of kink-antikink pairs for scalar fields on the line Abstract: We will discuss classical nonlinear scalar field models on the real line. If the potential is a symmetric double-well, such models admit static solutions called kinks and antikinks, which … Read more
Title: Dynamics of movement in complex environments Abstract: In this talk, we will highlight two different types of movement in viscosity dominated environments: sperm navigation and centrosome clustering in dividing cells. Sperm often interact with chemicals and other proteins in … Read more
Title: Symmetric Functions Abstract: The most basic type of symmetric functions appears when studying roots of a polynomial: the coefficients of a polynomial are the elementary symmetric functions of its roots. Much of mathematics was motivated by trying to write down formulas … Read more
Title: From quantization to holomorphic Lagrangian geometry Abstract: Sir George Biddel Airy discovered the rainbow integral and explained the classical analysis of rainbows. 150 years later, Kontsevich found that the same formula determined the multiplication table of cohomology classes … Read more
Title: Spectral analysis of Schrodinger operators and applications Abstract: I will report on recent results about quasimode, eigenfunction and spectral projection bounds for Schrodinger operators, $H_V=-\Delta_g+V(x)$, on compact Riemannian manifolds $(M,g)$ of dimension $n\ge2$ with critically singular potentials V. Using … Read more
