# AMUSE

## Fall 2023

Date: | September 13, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Andrea Bonito, Texas A&M University |

Title: | Curved Origami |

Abstract: | Origami is the Japanese art of folding paper. Since the famous Japanese crane described in the first known book on the topic (1797), the techniques and complexity of origami designs increased at an exponential rate. While originally for pure decorative purposes, the development of its mathematical language and theory paved the way for many applications in engineering science but also in natural science, computer visualization and architecture. The property exploited in most applications is their sheet-like behaviors when deployed while having the ability to fold to take a reduced amount of space when transported. In this talk, we explore the effects of non-necessarily straight creases forcing the folded paper to bend. These curved origami received recently significant attentions from the scientific community exploiting the fascinating variety of shapes they can exhibit, their ability to produce rigid configurations and flapping mechanisms, their capacity to undergo large deformations using a small amount of energy, and their applicability at small and large scales alike. We discuss in a simpler context how to mathematically model the folding processes, derive properties of the folded configurations, and present numerical simulations of more complex situations with applications in art, math biology, space exploration and other. |

Date: | September 27, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Suhan Zhong, Texas A&M University |

Title: | Distributionally Robust Optimization with Moment Ambiguity Sets |

Abstract: | In this talk, we introduce distributionally robust optimization when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with equivalent moment conic constraints. Under some general assumptions, we prove the DRO is equivalent to a linear optimization problem with moment and psd polynomial cones. A Moment-SOS relaxation method is proposed to solve it. Its asymptotic and finite convergence are shown under certain assumptions. |

Date: | October 4, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Patricia Alonso Ruiz, Texas A&M University |

Title: | How can one write the heat equation on a fractal? |

Abstract: | As the name refers to, the classical heat equation models the spread of heat inside of an object. The solution is a function whose input is a moment in time and a point of the object, and outputs the temperature at that specific time and point of the object. To write down the heat equation we need in particular to know how to take the second (partial) derivative of a function with respect to its space variable (the object). But what if the object where the heat spreads is fractal? How do we take that derivative? We will explore these questions in this talk by making a connection with electric network theory on a prototype fractal called the Sierpinski gasket. |

Date: | October 18, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Edriss Titi, Texas A&M University |

Title: | Mathematics of Turbulent Flows: A Million Dollar Problem! |

Abstract: | Turbulence is a classical physical phenomenon that has been a great challenge to mathematicians, physicists, engineers and computational scientists. In the end of the last century, chaos theory was developed to explore similar phenomena that occur in a wide range of applied sciences, but the eyes have always been on the big ball – Turbulence. Controlling and identifying the onset of turbulence have a great economic and industrial impact ranging from reducing the drag on cars and commercial airplanes to better design of fuel engines, and weather and climate predictions.
It is widely accepted by the scientific community that turbulent flows are governed by the Navier-Stokes equations, for large Reynolds numbers, i.e. when the nonlinear advective effects dominate the linear viscous effects (internal friction within the fluids) in the Navier-Stokes equations. As such, the Navier-Stokes equations form the main building block in any fluid model, in particular in global climate models. Whether the solutions to the three-dimensional Navier-Stokes equations remain smooth, indefinitely in time, is one of the most challenging mathematical problems. Therefore, by the turn of the millennium, it was identified by the Clay Institute of Mathematics as one of the seven most outstanding Millennium Problems in mathematics, and it has set one million US dollars prize for solving it. Notably, reliable computer simulations of turbulent flows is way out of reach even for the most powerful state-of-the art supercomputers. In this talk I will describe, using layman language, the main challenges that the different scientific communities are facing while attempting to attack this problem. In particular, I will emphasize the mathematical point of view of turbulence. |

Date: | October 25, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Chia-Yu Chang, Texas A&M University |

Title: | Complexity of Matrix Multiplication |

Abstract: | One motivation to study tensors is from Complexity theory. In this talk, we will first introduce the complexity of matrix multiplication. Then I will explain the relation between matrix multiplication and tensors. Finally, we will present some known results of the complexity of matrix multiplication that is proved by using tensors notions. This talk is based on Chapter 1 of Landsberg, J. M. (2012). Tensors: geometry and applications. |

Date: | October 25, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Madison Sheridan, Texas A&M University |

Title: | A Brief Introduction to Finite Element Methods |

Abstract: | Numerical methods play a fundamental role in solving complex mathematical problems that arise in various scientific and engineering disciplines. Finite Element Methods are one of the most versatile and robust tools in this computational toolbox. We will motivate the use of the Finite Element Method by presenting various examples in which they are applied. We will then describe how one goes about implementing finite element methods to solve real world problems. |

Date: | November 1, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Jonas Lührmann, Texas A&M University |

Title: | Dispersive Waves and Solitons |

Abstract: | From the dynamics of quantum particles to the propagation of electromagnetic radiation and gravitational waves, nonlinear waves are everywhere in nature. Mathematically, such wave propagation phenomena can be described in terms of nonlinear dispersive and hyperbolic partial differential equations. Their solutions can exhibit different behaviors: some waves spread out, other waves form coherent structures, often called solitons, and yet other waves collapse.
In this talk I will first explain how linear dispersive waves typically behave. Then I will talk about the historic origins of a remarkable nonlinear phenomenon, namely the existence of solitons. Finally, I will discuss the fundamental role that radiation (linear dispersive waves) and solitons play for the long-time dynamics of nonlinear dispersive equations. |

Date: | November 15, 2023 |

Time: | 6:00pm |

Location: | BLOC 302 |

Speaker: | Wencai Liu, Texas A&M University |

Title: | Algebraic geometry, complex analysis and combinatorics in inverse spectral problems of periodic graph operators |

Abstract: | In this talk, we will discuss the significant role that the algebraic and analytic properties of complex Bloch and Fermi varieties play in the study of periodic operators. I will begin with some basics of periodic graph operators. Then, I will discuss our recent work, demonstrating how techniques from algebraic geometry, complex analysis, and combinatorics can be applied to investigate inverse spectral problems. |

Date: | November 29, 2023 |

Time: | 4:30pm |

Location: | |

Speaker: | Directed Reading Program, Texas A&M |

Title: | Final Presentations from Math Directed Reading Program |

Date: | November 30, 2023 |

Time: | 5:00pm |

Location: | |

Speaker: | Directed Reading Program, Texas A&M |

Title: | Final Presentations from Math Directed Reading Program |