Keller VandeBogert -- How it's Made: Schemes

In this episode of How it's Made, we talk about schemes. We construct them from the ground up, talk about how they are in some sense the algebraic analogue of manifolds, and take special care to sweep technical details under the rug.

Duncan Wright -- Dynamical Entropy of Quantum Random Walks

We will introduce quantum dynamical entropy and non-commutative generalizations of random walks. These topics will be motivated from the classical versions and connections will be drawn to their classical counterparts. We will finish by discussing applications in quantum information theory.

Trevor Olsen -- The Sperner property for posets, a probabilistic approach

Motivated by the problem of estimating the age of a population that evolves according to the Galton-Watson process, we consider graded partially ordered sets on which a probability measure is defined. By looking at the antichain of maximal probability, one derives a new proof of Sperner’s lemma on the subsets of a set. More importantly, the proof technique can be generalized to infinite posets and provides sufficient conditions on the probability measure and the order relation so that the poset has the Sperner property.

Alex Duncan -- Undecidable Problems in Mathematics

Mathematicians are very happy when we have a general method that solves all problems of a given type. Maybe the method is too complicated to carry out by hand. Maybe it has yet to be implemented as a computer program. Maybe it's too slow to use in all but toy examples. But at the end of the day the problem is solved - even if only in theory.

However, there are some families of problems that we'll never know how to solve - they are undecidable. In fact, we can prove that we cannot solve them! Far from being esoteric pathologies, natural questions in every branch of mathematics turn out to be undecidable. I'll discuss several examples from all over mathematics.

Matt Boylan -- Q & A with the Graduate Director

Come get answers for all the pressing questions you have as a graduate student!

Changhui Tan -- Fluid Dynamics: From stirring a cup of coffee to tracking a hurricane

There are many interesting complex dynamical systems in physics, biology and other sciences. These systems have large sizes, and are therefore very hard to solve.

One way to reduce the size of the system is to introduce continuum models and study the corresponding partial differential equations.

In this talk, I will introduce several interesting fluid dynamics models which are derived from large dynamical systems. We will explore four applications: (1) stirring a cup of coffee; (2) traffic flows on highway; (3) tracking a hurricane; (4) modeling animal swarms.

Inne Singgih -- Subtractive Magic and Antimagic Total Labeling

Graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. What seems to be a simple topic has grown over the years and now there are at least 50 different types of graph labeling. A Dynamic Survey of Graph Labeling by Gallian summarizes the results and open problems in graph labeling. It is currently 432 pages long and had been cited over 3,333 times. Magic labelings were introduced by Sedlacek in 1963, and became a popular topic among graph labeling enthusiasts. In 2004, Barone introduced new variants of magic labeling as part of his master's thesis. These variants were proposed at the 2016 GRWC, and were left as open problems. We'll discuss some very basic results for these new labelings.

Robert Vandermolen -- This is Our Universe (As an Algebraic Geometer sees it)

In this talk we will show that Deligne-Mumford Stacks arise naturally as a description of our observable universe. We then discuss how experimentally one can only verify models of the universe up to an equivalence on the category of coherent sheaves of these stacks. Finally we will discuss recent and ongoing work studying this equivalence in the case where the stacks arise as quotients of the general linear group and n-dimensional tori.

If you are susceptible to motion sickness, please advise the organizer before participating in this colloquium.

Various -- Invitation to upcoming graduate courses

Professors will give meet-and-greet talks for what to expect in their courses coming up in the fall. Everyone is welcome.

Zack French -- The predicate completion of a partial information system

Originally, partial information systems were introduced as a means of providing a representation of the Smyth powerdomain in terms of order convex substructures of an information-based structure. For every partial information system $\mathbb{S}$, there is a new partial information system that is naturally induced by the principal lowersets of the consistency predicate for $\mathbb{S}$. In this paper, we show that this new system serves as a completion of the parent system $\mathbb{S}$ in two ways. First, we demonstrate that the induced system relates to the parent system $\mathbb{S}$ in much the same way as the ideal completion of the consistency predicate for $\mathbb{S}$ relates to the consistency predicate itself. Second, we explore the relationship between this induced system and the notion of $D$-completions for posets. In particular, we show that this induced system has a “semi-universal” property in the category of partial information systems coupled with the preorder analog of Scott-continuous maps that is induced by the universal property of the $D$-completion of the principal lowersets of the consistency predicate for the parent system $\mathbb{S}$.

Demmas Salim -- Riemann Zeta function (a brief introduction)

We will talk about the domain of analyticity of the zeta function, its analytic continuation through the functional equation (without any proof) and its trivial zeroes.

Wolfgang Dahmen -- Mathematics and the Little Valiant Tailor - Any Connection?

There is a rapidly intensifying, often overlooked, interaction between mathematics and a modern technology oriented world. This goes far beyond the educated use of a mathematical tool box but rather stimulates synergetic developments of new concepts in mathematics and applications. This talk attempts to highlight such synergies in several different application scenarios. Interested attendants with a minimum familiarity with Grimm’s Fairy Tales will in the end be able to answer the question in the title.

Various -- SIAM Career Panel

Applying for jobs is a very demanding and stressful task. From shortlisting positions, preparing CVs, to taking interviews, the list is long. Come learn about all these steps. Four of our current graduate students will share their experiences with the job application process. Light refreshments will be served.

Panel -- Everything you always wanted to know about exams (but were afraid to ask)

Graduate students in the 2nd, 3rd, and 4th year will talk about their experiences with qualifying and comprehensive exams and answer questions.