Events

Kaiyi Huang: Guth’s polynomial method to prove the endpoint multilinear Kakeya problem

Abstract. This is a brief overview of Guth’s groundbreaking result of the endpoint multilinear Kakeya problem. The main tools are Borsuk-Ulam Theorem from algebraic topology and properties of the zero set (variety) of a low degree polynomial.

Allison Byars: Bootstrap Argument in Dispersive PDEs

Abstract.  The bootstrap argument is an abstract principle similar to an induction argument that can be applied to many areas of math. In this talk, we’ll look at the (very short) proof of the bootstrap principle, and see how it can be applied to prove dispersive estimates in PDEs. 

Rachel Heikkinen: Cospectral Pairs of Graphs

Abstract. In this talk, I will introduce some fundamental definitions that are used in spectral graph theory. We say two graphs are cospectral if they have the same eigenvalues with respect to some matrix. One may ask, is there always a cospectral pair of a tree and a nontree? I examine this question first through the adjacency matrix, the most commonly studied matrix in graph theory. However, the question extends further to the Laplacian, signless Laplacian, and normalized adjacency matrices.

Haley Kottler: An Introduction to Causal Inference

Abstract. In situations where randomized controlled trials would be unethical or impractical, there is often still observational data available for study.  Causal inference is a branch of applied probability that allows us to use observational data to answer causal questions.  I will introduce the basic assumptions and strategies of causal inference.

Boyana Martinova: Non-Standard Graded Polynomial Rings 

Abstract. In a first algebra course, we learn about polynomials and (crucially) the degree of a polynomial. In abstract algebra, we learn that the set of polynomials over some variables form a ring. But what would happen if we assign different “weights” to our variables? How does the underlying commutative algebra change if I begin to fiddle with the degrees of each variable? These are some questions we’ll explore during this (very short) overview of non-standard graded polynomial rings!

Amelia Stokolosa: Harmonic analysis on nilpotent Lie groups: inverses of singular integral operators

Abstract. What goes wrong when you study inverses of singular integral operators on nilpotent Lie group with a noncommutative group multiplication? Turns out a lot the ideas of harmonic analysis on Euclidean space (including the Fourier transform!) are no longer all that useful. Instead, one looks elsewhere for clues, for example, PDEs.

Applying for Grants slides

Slides by Grace Work on how to make a poster

Other Resources for making posters