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 […]
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 […]
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 […]
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 > s(n), x^p + y^p = z^p (mod p) has a nontrivial solution. A (p,q)-graph G is said to be vertex Ho-Lee-Schur graph if there exists a bijection […]
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 […]
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 […]
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 […]
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 looked like what we call computers today. In this talk I attempt to explain what Ada really did, and delineate the mathematics involved. Bernoulli numbers […]
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 stability conditions. In this talk, I will explain what constitutes a notion of stability in algebraic geometry, and what the challenges are in studying them.
