# Past Events

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## February 2020

### Quandle module quivers (Sam Nelson, CMC)

Quandle coloring quivers categorify the quandle counting invariant. In this talk we enhance the quandle coloring quiver invariant with quandle modules, generalizing both the quiver invariant and the quandle module polynomial invariant. This is joint work with Karma Istanbouli (Scripps College).

Find out more »### On badly approximable numbers (Nikolai Moshchevitin, Moscow State University)

It is well known that a real number is badly approximable if and only if the partial quotients in its continued fraction expansion are bounded. Motivated by a recent wonderful paper by Ngoc Ai Van Nguyen, Anthony Poels and Damien Roy (where the authors give a simple alternative solution of Schmidt-Summerer's problem) we found an unusual generalization of this criterion for badly approximable d-dimensional vectors.

Find out more »### Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota)

The talk will concentrate on open questions related to the optimal bounds for the discrepancy of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of points in axis-parallel rectangles, and thus measures the equidistribution of the set. This notion has been explored by H. Weyl, K. Roth, and many others, however many questions still remain open, especially in higher dimensions. We shall discuss the two main conjectures on the order of star-discrepancy and present evidence in…

Find out more »## March 2020

### Graph coloring reconfiguration systems (Prateek Bhakta, University of Richmond)

For k >= 2, the k-coloring graph C(G) of a base graph G has a vertex set consisting of the proper k-colorings of G with edges connecting two vertices corresponding to two different colorings of G if those two colorings differ in the color assigned to a single vertex of G. A base graph whose k-coloring graph is connected is called k-mixing; here it is possible to reconfigure a particular k-coloring of G to any other k-coloring of G by…

Find out more »### Finding bases of new infinite dimensional representations of $\mathfrak{osp}(1|2n)$ ( Dwight Williams, UT Arlington)

The orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2n)$ is rich in representation theory: while the finite dimensional $\mathfrak{osp}(1|2n)$-module category is semisimple, the study of infinite dimensional representations of $\mathfrak{osp}(1|2n)$ is wide open. In this talk, we will define the orthosymplectic Lie superalgebras, realize $\mathfrak{osp}(1|2n)$ as differential operators on complex polynomials, and describe the space of polynomials in commuting and anti-commuting variables as a representation space for $\mathfrak{osp}(1|2n)$. Moreover, we will present operators---and perhaps generalized versions of these operators---which help give explicit bases for…

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