Our colloquia feature researchers from around the world sharing their accomplishments and insights.

## 2019 Colloquia

#### Relative entropy of compressible model for fluid mixtures

**Speaker:** Xiaokai Huo, KAUST**Date:** Jan. 10**Time:** 3:45pm-4:45pm**Room:** DM 409A

The relative entropy method was first developed in the context of

#### Global Well-Posedness and Sobolev Bounds for Non-Focusing Schrodinger Equations on Mixed Domains

**Speaker:** Nathan Totz, University of Miami**Date:** Jan. 31**Time:** 3:45pm-4:45pm**Room:** DM 409A

We consider the

#### How stochastic shocks influence a determistic life

**Speaker:** Annie Millet, University Paris 1**Date:** Feb. 7**Time:** 3:45pm-4:45pm**Room:** DM 409A

I will present some results on parabolic or dispersive nonlinear PDEs subject to a random perturbation. This « noise » models the sum of many infinitesimal shocks in the environment. Besides

#### On Markov statistical solutions of differential equations

**Speaker:** Lev Kapitanski, University of Miami**Date:** Feb. 21**Time:** 3:45pm-4:45pm**Room:** DM 409A

In this

#### Calculus Yesterday, Today, and Tomorrow

**Speaker:** Deb Hughes Hallett, University of Arizona Harvard Kennedy School**Date:** March 4**Time:** 2pm-3pm**Room:** DM 409A

Has the teaching of calculus changed over the past decades? If so, how and why? What are the challenges in teaching calculus today? Can we anticipate future challenges? This talk will suggest answers to these questions and discuss how mathematics departments can best prepare our current and future students.

#### Dynamics of complex singularities and integrability of surface motion

March 7, 3:45-4:45pm, DM 409A

**Speaker:** Pavel Lushnikov, University of New Mexico**Date:** March 7**Time:** 3:45pm-4:45pm**Room:** DM 409A

A motion of fluid's free surface is considered in two dimensional (2D) geometry. A time-dependent conformal transformation maps a fluid domain into the lower complex half-plane of a new spatial variable. The fluid dynamics is fully characterized by the complex singularities in the upper complex half-plane of the conformal map and the complex velocity. Both a single ideal fluid dynamics (corresponds e.g. to oceanic waves dynamics) and a dynamics of superfluid Helium 4 with two fluid components are considered. A superfluid Helium case is shown to be completely integrable for the zero gravity and surface tension limit with the exact reduction to the Laplace growth equation which is completely integrable through the connection to the dispersionless limit of the integrable Toda hierarchy and existence of the infinite set of complex pole solutions. A single fluid case with nonzero gravity and surface tension turns more complicated with the infinite set of new moving poles solutions found which are however unavoidably coupled with the emerging moving branch points in the upper half-plane. Residues of poles are the constants of motion. These constants commute with each other in the sense of underlying non-canonical Hamiltonian dynamics. It suggests that the existence of these extra constants of motion provides an argument in support of the conjecture of complete Hamiltonian integrability of 2D free surface hydrodynamics.

#### Exploring New Version of DIMTEST for Polytomous Data

**Speaker:** Tan Li, Department of Biostatistics, FIU**Date:** March 21**Time:** 3:45pm-4:45pm**Room:** DM 409A

Item Response Theory (IRT), a latent trait theory, is the major paradigm describing how to model the relationship between examinee ability and the examinee responses to the items on a test. It can be applied to statewide standardized tests, such as SAT and GRE, for purposes including scoring, equating, and scaling. Unidimensionality is

#### On some extremal problems for polynomials

**Speaker:** Alex Stokolos, Georgia Southern University**Date:** April 11**Time:** 3:45pm-4:45pm**Room:** DM 409A

In this

#### On orthogonal polynomials, Hermite-Padé approximants and Riemann-Hilbert problems

**Speaker:** Sergio Medina**Date:** April 18**Time: **3:45pm-4:45pm**Room:** DM 409A

In this talk, we will introduce a general formulation of the Hermite-Padé approximation problem which will allow us to show a direct connection among orthogonal polynomials, Hermite-Padé approximants, and Riemann-Hilbert problems. We will state this connection as general as possible, therefore all the most interesting cases (orthogonal polynomials, matrix orthogonal polynomials, multiple orthogonal polynomials, biorthogonal polynomials, among others) can be included in this general formulation.

#### Problems and Methods in Environmental Finance

**Speaker: **Pablo Olivares, Ryerson University**Date:** May 2**Time:** 11am-12pm**Room:** DM 409A

We review some models and methods that have been