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Mathematics & Statistics

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**Title**

**Speaker**

**Time**

**Place**

On some 2D orthogonal \(q\)-polynomials

Ruiming Zhang

Northwest A&F University

PR China

2:00pm-3:00pm

NES 104

**Abstract**

This talk is based on a joint work with Professor Mourad E. H. Ismail recently published on AMS Transactions, in which we have generalized several families of 2D orthogonal polynomials used in probability theory and physics (a.k.a. Zernike polynomials). In this talk, I introduce two \(q\)-analogues of the 2D-Hermite polynomials that are polynomials in two complex variables. For both families, I present explicit formulas, raising and lowering operator relations, generating functions, and Rodrigues formulas. These \(q\)-orthogonal polynomials also have unexpected connections to the theory of integer partitions.

**Title**

**Speaker**

**Time**

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A matrix spectral problem based on \(\mathrm{so}(3,R)\) and its associated soliton hierarchy

Sumayah Batwa

2:00pm-3:00pm

NES 104

**Abstract**

In this talk, I will discuss a spectral problem associated with the real Lie algebra \(\mathrm{so}(3,R)\) and generate a hierarchy of soliton equations from zero curvature equations linked with the spectral problem. Moreover, I will give an illustrative example of soliton equations with a bi-Hamiltonian structure.

**Title**

**Speaker**

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Contour deformation in oscillatory Riemann-Hilbert problems associated with the mKdV equation III

Fudong Wang

2:00pm-3:00pm

NES 104

**Title**

**Speaker**

**Time**

**Place**

Nonlocal symmetries with pseudopotentials

Xiazhi Hao

East China Normal University

2:00pm-3:00pm

NES 104

**Abstract**

In this talk, I will discuss nonlocal symmetries by including pseudopotentials, which are equivalent to Lie point symmetries of a prolonged system. Moreover, I will show that through the transformations resulted from nonlocal symmetries, exact solutions to the original system can be generated.

**Title**

**Speaker**

**Time**

**Place**

Contour deformation in oscillatory Riemann-Hilbert problems associated with the mKdV equation II

Fudong Wang

2:00pm-3:00pm

NES 104

**Title**

**Speaker**

**Time**

**Place**

Contour deformation in oscillatory Riemann-Hilbert problems associated with the mKdV equation

Fudong Wang

2:00pm-3:00pm

NES 104

**Abstract**

I will discuss about how to extend oscillatory Riemann-Hilbert problems to an augmented contour. The focus will be on how to apply the steepest descent method introduced by Percy Deift and Xin Zhou to analyze long time asymptotics for the mKdV equation.