**Title:** Pattern hunting in the prime numbers

**Abstract:** We will discuss patterns that have been found amongst the prime numbers, some of which we can prove are really there, and some of which are still a mystery….

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# Author: Lonette Stoddard

## Focus on Math: Andrew Granville (University of Montreal)

## Focus on Math: Jack Thompson (Deloitte Consulting)

## Math Biology Seminar: Chin Lin Guo

## Colloquium: Jared Whitehead

## Colloquium: Andrew Dittmer

## Colloquium: Peter Trapa

## Focus on Math: Robert Lang

## Colloquium: Matija Cencelj

## Colloquium: Donald Saari

## Colloquium: Donald Saari

**Title:** Pattern hunting in the prime numbers

**Abstract:** We will discuss patterns that have been found amongst the prime numbers, some of which we can prove are really there, and some of which are still a mystery….

**Speaker Profile:** Mr. Thompson leads Deloitte Consulting’s Federal supply chain practice. He has more than 30 years of experience in consulting and has worked for Deloitte in Europe, Africa and the USA. His areas of expertise are Supply Chain Strategy and Business Transformation.

Mr. Thompson has led many projects for clients in the public sector, consumer business, automotive, manufacturing, retail, healthcare, and energy industries. He led the project to outsource General Motors global logistics operations that culminated in the creation of 4 PL company, Vector SCM, a Joint Venture Company between CNF and GM. He has also led many efforts at GSA including the development and implementation of a new business model for the General Services Administration’s Office of Global Supply.

Prior to joining Deloitte Consulting in the US he was a vice president of the freight forwarding firm LEP Worldwide.

**Title:** Surviving the Data Deluge: How Data Analytics is Transforming Our Lives

**Abstract: **Analytics is the practice of using data to manage information and performance to make more effective decisions. It integrates capabilities in data management, statistics, change management, technology, automation, and governance into a powerful agent for making better, faster decisions. Sound familiar? It should, because analytics isn’t exactly new. What has changed is the speed at which decisions need to be made and the complex environment, including social, economic, environmental, and political currents, in which they are made. New data is being generated every day as a result of new sensors, the growth of mobile and digital technologies and an increasing ability to track individuals’ behaviors through a variety of technology platforms. The same old approaches to analytics just are not up to the job. At its highest use, analytics can deliver uncommon insights and breakout value. It all starts with asking crunchy questions and ends with getting answers you can use.

The challenge data analytics is not only to unlock the information, but also to represent and communicate it appropriately to the target audience. As data grows exponentially, traditional means of data interpretation are becoming a bottleneck for decision-making. Visual Analytics combines an analytical mindset with the power of visual perception. This means more than just charts and graphs, but applying powerful new methods of visualizing data in quick and useable ways.

Most available data we have yet to effectively capture. The future lies in harnessing the knowledge contained in unstructured data. The ability to collect, analyze, and extract insight from these data formats will exponentially catapult the power of analytics. The next generation of structured and unstructured data requires a unified approach to the mobile, social, analytics, cloud and cyber forces.

In this presentation we will discuss how to “Survive the Data Deluge” and how Data Analytics is transforming our lives. We will explore the reasons for the “Data Deluge”, from the ever-increasing volume to the disparate signals that create that volume. We will consider the many, varied and innovative uses of the data by organizations for research and predictive analysis. We will introduce the concept of visual analytics and finally we will discuss the next generation of analytics and the increasing ethical decisions that must be made. ;

**Title:** Multi-step self-organization of epithelial tubules at centimeter scales

**Abstract:** With lengths up to centimeter scales, tubules enable long-range transport and are essential for the homeostasis of our bodies. The current theory is that cells follow morphogen gradients to build long tubules. It remains undetermined whether interactions between cells and extracellular matrix molecules are sufficient to form long tubules at organ scales. Here, we show that with a limited supply of type I collagen in the liquid environment, epithelial cells can self-organize centimeter-long, hundred-micrometer-wide, unbranched tubules without preexisting spatial cues from biochemical factors or scaffolds. Formation of these tubules involves a sequential series of cell-collagen interactions including a cell-aided assembly of collagen fibers, collagen fiber-aided long-range (~ 600 micrometers) mechanical interactions between cells, and a collagen fiber-guided morphological switch of cells, which in turn form polarized, tubular lumens. We propose a simple free energy model to explain how collagen as a limiting factor provides a spatiotemporal collective effect for long tubule formation. Our findings suggest that cells can use mechanical forces to create large-scale self-organization (spatial scale: centimeters), which can be used for the engineering of functional organs.

**Title:** In search of the ultimate state of slippery Rayleigh-Benard convection

**Abstract:** For decades, experiments (and more recently numerical simulations) have attempted to determine how the effective transport of heat (measured by the non-dimensional Nusselt number Nu) scales with the driving force (as measured by the Rayleigh number Ra) –when said driving force is asymptotically strong–in Rayleigh-Benard convection where an incompressible, Boussinesq fluid is driven by an imposed temperature gradient. To date the results are inconclusive for experiments, and finite limitations on computational resources restrict the potential usefulness of direct numerical simulation. In contrast to these approaches, we derive rigorous upper bounds on the heat transport for slippery convection in which the velocity satisfies a stress-free (or free-slip) boundary condition on the vertical boundary. For 2*d* convection as well as 3*d* convection for infinite (or even large) Prandtl number (ratio of kinematic viscosity to thermal diffusivity) this bound takes the form Nu < *C* Ra^{5/12}. At finite Prandtl numbers this scaling challenges some theoretical arguments regarding asymptotic high Rayleigh number heat transport by turbulent convection.

**Title:** How to Find Curves as Symmetric as the Klein Curve

**Abstract:** The complex curve *x*^{3}*y* + *y*^{3}*z* + *z*^{3}*x*=0 is a nonsingular genus 3 curve whose automorphism group is famously isomorphic to the simple group *G* = *PSL*_{2}(*F*_{7}) of order 168. These 168 automorphisms are induced by (the projectivization of) one of the irreducible degree 3 representations of *G*. It is natural to wonder whether or not there might be other plane curves that have this unexpected symmetry property, and, if so, whether these curves have other interesting geometric characteristics. It will be possible to show that the answers to these questions display surprising patterns, and that these patterns are capable of considerable generalization.

**Title:** Unitary representations of Lie groups

**Abstract:** Unitary representations of Lie groups appear everywhere in mathematics: in harmonic analysis (as generalizations of the sines and cosines appearing in classical Fourier analysis); in number theory (as spaces of modular and automorphic forms); in quantum mechanics and more modern physical theories (as solutions of differential equations admitting symmetries); and in many other places. They have been the subject of intense study for decades, but only recently has their classification emerged. The answer relies, perhaps surprisingly, on an essentially combinatorial object — the finite Hecke algebra — and its relation to certain singular algebraic varieties. The purpose of this talk is to explain a little bit about unitary representations and offer a few hints about how Hecke algebras and algebraic geometry enter into their study.

**Title:** Circles, Rivers, and Polygon Packing. Mathematical Methods in Origami

**Speaker biography:** Robert J. Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. With a Ph.D. in Applied Physics from Caltech, he has, during the course of work at NASA/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored over 80 papers and 45 patents in lasers and optoelectronics as well as authoring, co-authoring, or editing 14 books and a CD-ROM on origami. He is a full-time artist and consultant on origami and its applications to engineering problems and his origami artworks are shown and sold commercially in galleries in Santa Fe, NM and Jackson Hole, WY. He received Caltech’s highest honor, the Distiguished Alumni Award, in 2009 and has been selected as one of the inaugural Fellows of the AMS in January, 2013.

**Title:** Gropes and their fundamental groups

**Abstract:** We consider open infinite gropes which are 2-dimensional CW complexes introduced by Stan’ko and Cannon. Gropes are classifying spaces of their fundamental groups. We show some properties of these groups and present some recent results.

**Title:** Mathematics of Voting Procedures

**Abstract:** We vote, but will the outcome accurately reflect what the voters want? We make decisions, but does the conclusion accurately reflect the data? While the importance of these concerns is obvious, it turns out that these issues are mathematically complex. With an emphasis on voting rules, the severity of the problem will be illustrated and some of the underlying mathematical structures will be described.

**T****itle:** Mathematics and the ‘Dark Matter’ Mystery

**Abstract:** Even after spending billions of dollars on experiments, nobody has been able to find that elusive, mysterious thing hiding out there in the heavens that is called "dark matter." Sounds ominous! But, what is it? Why do we believe it is important? As described in this expository lecture, mathematics now is shedding significant new light on this darkness to illuminate the mystery. Part of this puzzle includes mathematical aspects about the evolution of Newton’s universe, which will be briefly discussed.