In this talk, I will try to give a fun introduction to tropical geometry and Hassett spaces, and show how tropical geometry can be used to compute the Chow rings of Hassett spaces combinatorially. This is joint work with Siddarth Kannan and Shiyue Li.
Abstract: Mathematical modeling is an effective resource for biologists since it provides ways to simplify, study and understand the complex systems common in biology and biochemistry. Many mathematical tools can be applied to biological problems, some traditional and some more novel, all innovative. This presentation will review the mathematical tools that are used to model […]
Quandles are algebraic structures that play nicely with knots. The multiplicative structure of finite quandles gives us a way to "color" knot diagrams, and the number of such colorings for a given knot and quandle is called the quandle coloring invariant. We strengthen this invariant by examining the relationships between the colorings, which are given […]
Linear evolution equations, such as the heat equation, are commonly studied on finite spatial domains via initial-boundary value problems. In place of the boundary conditions, we consider “multipoint conditions”, where one specifies some linear combination of the solution and its derivative evaluated at internal points of the spatial domain, and “nonlocal” specification of the integral […]
A triple of natural numbers (a,b,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3, there exists s(n) such that for prime p […]
Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular, spectral methods based on conformal mappings are proposed to solve Steklov eigenvalues and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain […]
Suppose K is an oriented knot in a 3-manifold M with regular neighborhood N (K). For each element γ ∈ π 1 (∂N (K)) we define a quandle Q γ (K; M) which generalizes the concept of the fundamental quandle of a knot. In particular, when γ is the meridian of K, we obtain the […]
Data is exploding at a faster rate than computer architectures can handle. For that reason, mathematical techniques to analyze large-scale data need be developed. Stochastic iterative algorithms have gained interest due to their low memory footprint and adaptability for large-scale data. In this talk, we will study the Randomized Kaczmarz algorithm for solving extremely large […]
Augusta Ada Byron King Lovelace (1815-1852) is today celebrated as the first computer programmer in history. This might be confusing to some because in 1852 there were no machines that […]
Mathematics isnt done in a void: its done by groups of people. Those groups have different norms and values, which affect both who wants to engage in math and the […]
Knotting in proteins was once considered exceedingly rare. However, systematic analyses of solved protein structures over the last two decades have demonstrated the existence of many deeply knotted proteins, and […]
One of the main drivers of current research in geometry is the classification of Calabi-Yau threefolds. Towards this effort, a particular approach in algebraic geometry is via the study of […]
