Wednesday, March 8, 2023
Time  Items 

All day 

1pm 
03/08/2023  1:00pm Boundary Value Problems (BVPs) are ubiquitous in engineering and scientific applications. One of the most robust and accurate methods for solving BVPs is the Boundary Integral Equation Method, which has the great advantage of dimensionality reduction: all of the unknowns reside on the boundary surface instead of in the volume. A key challenge when solving integral equations is that special quadrature methods are required to discretize the underlying singular and nearsingular integral operators. Accurate discretization of these operators is especially important in, for example, problems that involve close structurestructure or fluidstructure interactions. In this talk, we present some recent advancements on singular and nearsingular numerical integration based on one of the simplest quadrature methods  the Trapezoidal rule. Location:
AKW 200

4pm 
03/08/2023  4:15pm Ramsey theory is a branch of combinatorics which seeks to find patterns in disorganized situations. One of its main achievements, Szemeredi’s theorem on arithmetic progressions, got an ergodic theoretic proof in 1977 when Furstenberg created a Correspondence Principle to encode combinatorial information about sets of integers into a dynamical system. Since then ergodic methods have been very successfulÂ in obtaining new Ramsey theoretic results, some of which still have no purely combinatorial proof.
I will survey some of the history of how ergodic theory and Ramsey theory are interconnected, leading to a recent result involving infinite sumsets.
Location:
LOM 214
