Tuesday, 4:00–5:00pm, Pearce Hall, Room 227.

Date | Speaker | Affiliation | Title |
---|---|---|---|

September 24 |
Mohye Sweidan | Central Michigan University | An introduction to finite difference scheme for two-point boundary problems |

October 1 |
Sidney Graham | Central Michigan University | The Duffin-Schaeffer Conjecture |

October 8 |
Nung Kwan (Aaron) Yip | Purdue University | Absolutely an Introduction to Algebraic Statistics |

October 15 |
Kapil Paranjape (Colloquium) | Washington University in St. Louis, and IISER Mohali, India | Beyond Abel and Jacobi |

October 22 |
Xiaoming Zheng | Central Michigan University | A Darcy's law model of tumor growth |

October 29 |
Talon Ward | Central Michigan University | The Collatz Conjecture: An Introduction |

November 5 |
Yeonhyang Kim | Central Michigan University | Water Diffusion by means of MRI |

November 12 |
Suzanne Craig | CIRES/University of Colorado Boulder | Reformulating the Target Visitation Problem for Fujitsu's Digital Annealer |

November 19 |
Philip Renne | Central Michigan University | Fejer's Theorem: An introduction |

November 26 |
Lisa DeMeyer | Central Michigan University | The Zero-Divisor Graph Problem |

December 3 |
Paul Cappaert | Central Michigan University | Complemented Zero Divisor Graphs of Commutative Semigroups |

**Speaker: ** Mohye Sweidan

**Title: ** An introduction to finite difference scheme for two-point boundary problems

**Abstract: ** This talk will present the central difference scheme for two-point boundary
problems and its error analysis. This is a standard material in numerical analysis.
It uses the discrete maximum principle and stability analysis. Finally,
the error estimate of the whole scheme is obtained from the local truncation error.

**Speaker: ** Nung Kwan (Aaron) Yip

**Title: ** Absolutely an Introduction to Algebraic Statistics

**Abstract: ** Though not intended to be an absolute introduction, this talk is absolutely an introduction
to algebraic statistics which has become an emerging field. While I am a complete novice in this area, the talk
is purely inspired by my curiosity in both algebra and statistics. I will go over some examples from statistics
such as experimental design, maximum likelihood estimation and Markov models and demonstrate how
they can be related to some ''familiar" algebraic concepts such as Grobner basis and Toric varieties.

**Speaker: ** Xiaoming Zheng

**Title: ** A Darcy's law model of tumor growth

**Abstract: ** This talk introduces a popular mathematical model to simulate tumor growth. It is based on the Darcy's law
in porous media. It assumes the tumor cells migrate in a porous tissue with holes and the pressure produced by cell
proliferation and death creates the flow which pushes cell to move.
The tumor cells rely on the nutrient from surrounding region to proliferate and thus the tumor volume increases.
We will focus on a one dimensional model to derive some of its interesting mathematical properties.

**Speaker: **Talon Ward

**Title: **The Collatz Conjecture: An Introduction

**Abstract:** We provide a brief introduction to the Collatz Conjecture and then present a minor new result on a distribution of divergent trajectories.

**Speaker: ** Yeonhyang Kim

**Title:** Water diffusion by means of MRI

**Abstract:** In this talk, we review the theory of q-ball imaging and describe a simple linear matrix formulation for the q-ball reconstruction based on spherical harmonic basis function interpolation.

**Speaker: **Suzanne Craig

**Title:** Reformulating the Target Visitation Problem for Fujitsu's Digital Annealer

**Abstract:** The Target Visitation Problem (TVP) is a complication on the classic combinatorial optimization problem, the Traveling Salesman. Fujitsu's Digital Annealer is a simulated quantum computer than can solve combinatorial optimization in seconds for extremely large numbers of possible combinations, but requires that problems be formulated as Quadratic Unconstrained Binary Optimization (QUBO) equations. This talk will primarily focus on the TVP and this reformulation process, but will also include information on IPAM's g-RIPS Sendai program and some more general observations on switching from academia to industry as a fresh graduate.

**Speaker: **Philip Renne

**Title:**Fejer's Theorem: An introduction

**Abstract:** Fourier series arose out of the study of trigonometric solutions to certain differential equations. A natural question that arose in the study of these series was how to reconstruct the original function from a Fourier series representation. Fejer's theorem provides an answer when the original function is continuous: the Cesaro means of the partial sums of the Fourier series converge uniformly to the original function. The proof of Fejer's theorem uses some important and critical ideas heavily useful in analysis which will be expounded upon in this talk.

**Speaker: **Lisa DeMeyer

**Title:**The Zero-Divisor Graph Problem

**Abstract:** Let $S$ be a commutative semigroup with $0$ element. A nonzero element $a\in S$ is called a zero-divisor if there exists a nonzero element $b\in S$ so that $ab=0$. The zero-divisor graph, $\Gamma (S)$ is the simple graph whose vertices are given by the nonzero zero-divisors of $S$ where two distinct vertices, $a$ and $b$, are adjacent in case $ab=0$ in $S$. We will begin with a discussion of the history of this construction and foundational results, including examples. We conclude with some very recent results, other zero divisor graph constructions, and some open questions.

**Speaker: **Paul Cappaert

**Title:**Complemented Zero Divisor Graphs of Commutative Semigroups

**Abstract:** This talk establishes broad classifications about complemented zero divisor graphs of commutative semigroups and their properties. In particular, the graph theoretic properties that can produce a complemented zero-divisor graph are explored. Limits are established as to what properties are necessary for a complemented graph to be a zero divisor graph.