In this talk, we will discuss a ''new'' way to define an integral. Instead of using the standard definition of $\displaystyle \sum_{i=1}^{n} f(x_{i}) \hspace{3pt} \Delta x_{i}$, can we use an infinite product? How will this change the definition of an integral? Will this also change the definition of a derivative? This talk will examine the new mysteries of the so-called ''star-integral'' and ''star-derivative''.
We focus on the interaction of an incompressible fluid and an elastic structure. Two cases are considered: 1. the elastic structure covers part of the fluid boundary and undergoes small displacement and 2. the elastic structure is immersed in the fluid and features large displacement. For the first case, we propose an Arbitrary Lagrangian-Eulerian (ALE) method based on Lie’s operator splitting.
In this talk, we explore Zagier's famous formula for multiple zeta values involving 2's and 3's.
Zagier's formula is a remarkable example of both strength and the limits of the motivic formalism used by Brown in proving Hoffman's conjecture where the motivic argument does not give us a precise value for the special multiple zeta values $\zeta(2, 2, \ldots, 2, 3, 2, 2,\ldots, 2)$ as rational linear combinations of products $\zeta(m)\pi^{2n}$ with $m$ odd.
In this talk, the second of three, we introduce two fascinating objects in mathematics: the Riemann zeta and multiple zeta functions. We explore basic properties of these objects such as: their special values, analytic continuation and interesting connections to mathematical physics.
Abstract: In this talk, the first of three, we introduce two fascinating objects in mathematics: the Riemann zeta and multiple zeta functions. We explore basic properties of these objects such as: their special values, analytic continuation and interesting connections to mathematical physics.