**Date/Time**

Date(s) - 19/01/2024*3:30 pm - 4:30 pm*

Friday January 19, 2024 @3:30pm; HH 305

**Speaker:** JE Paguyo

**Title:** Crossings, random graphs, and Stein’s method

**Abstract:** The number of crossings in a graph is an important graph statistic, with applications to topics such as integrated circuit design and graph visualization. In this talk, we give a brief history of graph crossings and survey some previous results. We then discuss some recent work on crossings in randomly embedded graphs and show how Stein’s method, a powerful probabilistic tool for distributional approximation, can be used to prove a central limit theorem for the number of crossings. As a concrete example, we apply this result to chord diagrams, a class of graphs which have connections to genetics, physics, and knot theory.

**Speaker: **Dominik Stantejsky

**Title: **Singularities in Nematic Liquid Crystals Droplets with Planar Boundary Anchoring

**Abstract:** Liquid crystals are a type of matter with properties intermediate between a liquid and a crystalline solid and are known to exhibit a rich structure of point and line defects. After a general introduction about the variational modelling, we will focus on the one-constant approximation of the Oseen-Frank energy and discuss recent results on the type and shape of singularities that can occur in nematic liquid crystal droplets, such as boundary “boojums” and interior vortices.

**Speaker: **Adele Padgett

**Title: **Some equations involving the Gamma function

**Abstract: **The Gamma function extends the factorial function to the complex numbers and thus appears in various mathematical contexts. In this talk, I will present recent work joint with S. Eterovi? in which we prove certain systems of equations involving addition, multiplication, and the Gamma function must have infinitely many solutions in the complex numbers. As an immediate corollary, the Gamma function has infinitely many periodic points of every period.

Coffee and cookies will be served in HH 216 at 3pm – All are welcome

Please see recording of these talks, here