DIMACS REU 2011 Schedule

Let's say we have a graph. No, not the kind with X and Y axes, the kind that has edges and vertices. A cycle in this graph is a sequence of distinct edges so that traversing them in order brings us back to the starting vertex. We will see an algorithm that lets us quickly count the number of cycles in any graph. We will then start trying to count cycles in structures that are slightly more complicated than the graphs than you have already seen. Along the way, we will alsoencounter simplicial complexes, boundary operators and some elementary computational homology.

A short presentation followed by discussion. The topic will be how to prepare a short research presentation, which REU students will be required to do. Topics may include scope, audience, presentation style, "dos and don'ts," etc.

A short presentation followed by discussion. Students will be introduced to ethics in a research context, and will discuss case-studies and general questions pertaining to topics in mathematics and the mathematical sciences.

To promote cultural exchange and socialization, students will present cultural information as a component of the DIMACS/DIMATIA program. Czech students will present information about the Czech Republic, while domestic students will present information about life in the United States or about their own cultural background.

Companies invest in R&D to create new, innovative products to help grow revenues. Research and innovation has historically followed the Olympics motto of "Citius, Altius, Fortius" of pushing faster, higher and stronger, the limits of what is feasible as the means for disruption. However, studies appear not to show any correlation between the size of R&D investments and growth of revenues.

We will argue that the primary cause of this discrepancy is the enormous technology advances over the last decade which has fundamentally scrambled the nature of innovation. The availability of (relatively) cheap, off-the-shelf computing and communication components has enabled commercial solutions that were, heretofore, simply not technically feasibly and/or financially attractive (such as a mobile payments system for users with ARPU of a few dollars, or, a wireless glucose monitoring system for diabetic patients that eliminates pin pricks). However, disruption in this new environment requires not technical superiority but technical agility that can balance complex business, customer needs and other societal factors. In effect, for R&D to be effective going forward, the more appropriate model for innovation is not Olympics but the X-Games, where the rules for sports such as BMX Bike Racing and Snowboarding are rough and tumble and success requires multi-faceted excellence. We will provide examples of such innovation and also highlight new opportunities for wireless access in emerging markets where by rethinking how to innovate for local conditions, one can fundamentally disrupt the market.

What are the most uniformly distributed point sets and infinite sequences in the unit square, cube, sphere, torus (donut surface), and so on? What are the most uniform motions (parametrized curves)? The subject of my talk is to make these vague questions precise, and to give an answer to the precise questions.

After giving an overview of the recent discoveries of non-Earth-like planets around other stars, I will explain what is hard about finding Earth-like ones. Then, I will describe the various approaches that are being considered to solve this challenging engineering problem and the role that Princeton researchers are playing in this endeavor. Hopefully, given adequate funding, we will soon (i.e., in our lifetimes) have a catalog of stars that are known to have Earth-like planets.

There are many environments — such as large-scale markets, social networks, and Internet protocols — in which computational agents repeatedly interact. In considering the dynamic behavior of these interactions, an important (and interesting) question is whether the system is can be guaranteed to converge to a stable state (or solution). After providing some background on game theory and its interaction with computer science, I'll discuss recent work on a couple of problems in which we find that having multiple stable states either guarantees that a system might never converge or breaks a guarantee of convergence. This work connects to classic results in distributed computing, and it has applications to game theory, circuit design, social networks, and network protocols.

My aim is to introduce you to notion of crossing numbers. Crossing numbers was introduced by Paul Turán, originally Turán was interested in one specific graph class (complete bipartite graphs) but later it was shown importance of crossing number parameter in combinatorics with many applications. I would like to show you some structural properties (Hanani-Tutte theorem), also some algorthmic aspects and in the end some application in combinatorial geometry.

Two panel discussions will introduce students to the graduate school admissions process and answer questions about applying to grad school, as well as graduate student life. One panel will consist of faculty representing REU-related departments; the other will consist of graduate students.

Faculty Panelists: Eric Allender, Gyan Bhanot, Endre Boros, Zheng-Chao Han, John Kolassa
Student Panelists: Taylor Burmeister, Ed Chien, Priyam Patel, Thom Tyrrell, Brent Young

Abstract TBA

Abstract TBA.