# Research

## Differential Equations

### Monday, November 26, 2018

Title: Some basic theories in atomic physics
Speaker: Xueping Cheng, Zhejiang Ocean University
China
Time: 2:00pm‐3:00pm
Place: NES 102

#### Abstract

In this seminar, I will introduce some basic theories in atomic physics, including the Maxwell's equation, the photoelectric effect, the atomic models, the dual nature of light, and so on.

### Monday, November 19, 2018

Title: MAPLE Day at USF
Speaker: Daniel Skoog, Product Manager for Maplesoft
Time: 2:00pm‐3:00pm
Place: NES 102

#### Abstract

In the past three decades, Maple has evolved from a symbolic computation engine to a fully featured mathematics software package that includes natural math notation for input and output, easy-to-use tools for creating interactive documents, and access to its vast library of commands for mathematical, scientific and engineering computation.

In this seminar, Maplesoft staff will provide an overview of Maple, with an emphasis on our newest tools for creating impressive documents and interactive applications that allow Faculty and Students to fully explore math concepts. Newcomers to Maple, as well as experienced users who are interested in trying out the latest we have to offer, are welcome.

### Monday, November 5, 2018

Title: Introduction to the standard model and beyond
Speaker: Bo Ren, Shaoxing University
China
Time: 2:00pm‐3:00pm
Place: NES 102

#### Abstract

The standard model is a theory of fundamental particles introduced in the 1970s. It incorporated all that was known about subatomic particles at the time and predicted the existence of additional particles as well. I will outline this model. In the meanwhile, some beyond the SM will also be briefly introduced.

### Monday, October 29, 2018

Title: Essential Physics for Applied Mathematicians (II) — General relativity
Speaker: Xiang Gu
Time: 2:00pm‐3:00pm
Place: NES102

#### Abstract

This is a seminar talk for applied mathematicians to know some essential physics. I will start from the principle of equivalence, which is the cornerstone of general relativity; then I shall make a brief review of the mathematical tools involved in the theory, i.e., basic Riemmanian geometry: from metric tensors, contra- and $$c$$-variant vectors/tensors, to geodesics, Christoffel symbols, curvatures and Ricci tensors. Based on this I will quickly show (i.e., not all details) how the Einstein field equations were established. Some additional topics will also be briefly covered if time permits.

### Monday, October 22, 2018

Title: Rigidity theorems of complete Kahler-Einstein manifolds and complex space forms
Speaker: Tian Chong, Shanghai Polytechnic University
Shanghai, China
Time: 2:00pm‐3:00pm
Place: NES102

#### Abstract

In this talk, we introduce some elliptic differential inequalities from the Weitzenbock for-mulas for the traceless Ricci tensor of a Kahler manifold with constant scalar curvature and the Bochner tensor of a Kahler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some $$L^p$$ and $$L^\infty$$ pinching results are established to characterize Kahler-Einstein manifolds among Kahler manifolds with constant scalar curvature, and others are given to characterize complex space forms among Kahler-Einstein manifolds. Finally, these pinching results may be combined to characterize complex space forms among Kahler manifolds with constant scalar curvature.

### Monday, October 15, 2018

Title: Essential Physics for Applied Mathematicians (I). — The principle of least action and the special relativity
Speaker: Xiang Gu
Time: 2:00pm‐3:00pm
Place: NES 102

#### Abstract

This is a seminar talk for applied mathematicians to know some essential physics. In this talk, I will start from one of the most fundamental principles of our Nature, the principle of least action (and certainly the mathematics behind — the celebrated calculus of variations); then I will briefly review the theory of special relativity.

### Monday, October 1, 2018

Title: The emergence of solitons of the Korteweg-de Vries Equation from sufficiently decaying initial conditions, Part II
Speaker: Fudong Wang
Time: 2:00pm‐3:00pm
Place: NES 102

### Monday, September 24, 2018

Title: The emergence of solitons of the Korteweg-de Vries Equation from sufficiently decaying initial conditions
Speaker: Fudong Wang
Time: 2:00pm‐3:00pm
Place: NES 102

#### Abstract

We will discuss the solution of the KdV equation with the initial conditions $$u(x,0)=u_0(x)$$, where $$u_0(x)$$ decays sufficiently rapidly as $$|x|$$ goes to $$\infty$$. The analysis is based on the method of the inverse scattering transformation. And, we will prove that the solution of the KdV equation can be uniformly approximated by $$N$$-soliton solution, where $$N$$ is the number of bound states of Schrödinger scattering problem with potential $$u_0(x)$$.

### Monday, September 10, 2018

Title: Lump solutions to PDEs via symbolic computations
Speaker: Wen-Xiu Ma
Time: 2:00pm‐3:00pm
Place: NES 102

#### Abstract

This talk introduces lump solutions to partial differential equations within the Hirota bilinear formulation. A characterization on the existence of lumps in general dimensions will be discussed, and via symbolic computations, a set of illustrative examples of linear and nonlinear equations that possess lumps will be presented in both $$(2+1)$$-dimensions and $$(3+1)$$-dimensions. A few open questions will be addressed at the end of the talk.