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Beran’s tests of uniformity for discrete data (Michael Orrison, HMC)

On Zoom

Suppose you are given a data set that can be viewed as a nonnegative integer-valued function defined on a finite set. A natural question to ask is whether the data can be viewed as a sample from the uniform distribution on the set, in which case you might want to apply some sort of test […]

Monodromy groups of Belyi Lattes maps (Edray Goins, Pomona College)

Estella 1021, Pomona College Claremont, CA

An elliptic curve $ E: y^2 + a_1 \, x \, y + a_3 \, y = x^3 + a_2 \, x^2 + a_1 \, x + a_6 $ is a cubic equation which has two curious properties: (1) the curve is nonsingular, so that we can draw tangent lines to every point $ P […]

Kriz’s theorem via dynamics of linear operators (Yunied Puig de Dios, CMC)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

The existence of a set $A\subset \N_0$ of positive upper Banach density such that $A-A:=\{m-n:m, n\in A, m>n\}$ does not contain a set of the form $S-S$ with $S$ a piecewise syndetic is in essence the content of a popular result due to K\v r\'{i}\v z in 1987. Since then at least four different proofs […]

Arithmetical structures (Luis Garcia Puente, Colorado College)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

An arithmetical structure on a finite, connected graph G without loops is given by an assignment of positive integers to the vertices such that, at each vertex, the integer there is a divisor of the sum of the integers at adjacent vertices, counted with multiplicity if the graph is not simple. Alternatively,  an arithmetical structure […]

Spinning switches on a wreath product (Peter Kagey, HMC)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

This talk discusses a puzzle called “Spinning Switches,” based on a problem popularized by Martin Gardner in his February 1979 column of “Mathematical Games". This puzzle can be generalized to a two-player game on a finite wreath products. This talk will provide a classification of several families of these generalized puzzles, including a full classification […]

On the geometry of lattice extensions (Max Forst, CGU)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

Given a lattice L, an extension of L is a lattice M of strictly greater rank so that L is equal to the intersection of the subspace spanned by L with M. In this talk, we will discus constructions of such lattice extensions with particular geometric invariants of M, such as the determinant, covering radius […]

Properties of redistricting Markov chains (Sarah Cannon, CMC)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

Markov chains have become widely-used to generate random political districting plans. These random districting plans can be used to form a baseline for comparison, and any proposed districting plans that differ significantly from this baseline can be flagged as potentially gerrymandered. However, very little is rigorously known about these Markov chains - Are they irreducible? […]

A tale of two worlds: parking functions & reduction algebras (Dwight Anderson Williams II, Pomona)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

"A Tale of Two Cities" is a novel told in three books/parts. Here we describe three projects related both to published work and ongoing pieces: PROJECT 1: In the world of combinatorics, parking functions are combinatorial objects arising from the situation of parking cars under a parking strategy. In this part of the talk, we […]

Factoring translates of polynomials (Arvind Suresh, University of Arizona – Tucson)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

Given a degree d polynomial f(x) in Q, consider the subset S_f  of Q consisting of rational numbers t for which the translated polynomial f(x) - t factors completely in Q. For example, if f is linear or quadratic then S_f is always infinite, but if degree of f is at least 3, then interesting […]

Minimal Mahler measure in number fields (Kate Petersen, University of Minnesota Duluth)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA

The Mahler measure of a polynomial is the modulus of its leading term multiplied by the moduli of all roots outside the unit circle.  The Mahler measure of an algebraic number b, M(b) is the Mahler measure of its minimal polynomial. By a result of Kronecker, an algebraic number b satisfies M(b)=1 if and only […]

Partial orders on standard Young tableaux( Gizem Karaali, Pomona)

On Zoom

Young diagrams are all possible arrangements of n boxes into rows and columns, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n, a standard Young tableau S of shape λ is built from the Young diagram of shape λ by filling it with the numbers 1 to […]