## Critical Challenges at the Interface of Mathematics and Engineering

#### September 17-18, 2012

Organized by IMSE at the University of Illinois at Urbana-Champaign.

**Plenary Speakers: **

- François Baccelli, University of Texas at Austin,
*Multihop Routing in Mobile Ad hoc Networks and Navigation on Point Processes*The objective of this lecture is to illustrate the interplay between routing protocols used in networking and mathematical questions pertaining to the theory of point process and to Palm calculus.Consider a point process in the Euclidean space and a rule, either deterministic or random, defining the edges that exist between its points. This defines a random graph on the point process. Typical examples are the Delaunay graph of the point process, its Boolean graph, or its SIR (Signal to Interference Ratio) graph.A routing algorithm constructs, for all pairs of points of the point process, a route between these points, namely a path of this graph connecting them, when possible. Such an algorithm can be global, like in shortest path routing, or local, like in geographic routing which consists in making locally optimal hops on this random graph.Each route is a functional of the point process and is hence a random geometric object of the Euclidean space. This talk will discuss both local and asymptotic properties of routes defined on stationary point processes.We will show that shortest path routes can be analyzed in terms of first passage percolation and that some geographic routing algorithms on Poisson point processes can be analyzed using stochastic geometry and general state space Markov chains. We will also discuss the notions of spatial averages and route averages and show that they differ in general. We will show that this naturally leads to the definition of a mathematical object which extends the notion of Palm probability.We will finally describe dynamic extensions of these notions, namely routes built on a random graph whose edges vary over time. - Gunnar Carlsson, Stanford University,
*The Shape of Data*Science, engineering, and business are creating large databases at a rapidly increasing rate. Further, the complexity of the data is also increasing in many ways. However, our ability to analyze this data so as to extract usable knowledge is not keeping pace. In this talk we will describe some new methods being developed for data analysis, based on the idea that data has a kind of high dimensional shape, and that this shape is vital for our understanding of the data. This observation naturally brings up the mathematical subdiscipline called topology, which is the study of shape, and has helped to create an emerging area of mathematics called computational or applied topology. The talk will survey these developments, with examples.

#### Thematic sessions planned are: **Computing, Networked Systems, Risks and Decisions, **and** Stochastics & Dynamics.**

**Invited Speakers:**

- Mihai Anitescu, Argonne National Laboratory
- Jonathan Mattingly, Duke University
- Lek-Heng Lim, University of Chicago
- Vadim Linetsky, Northwestern University
- Andreea Minca, Cornell University
- Devavrat Shah, MIT
- Jeremy Staum, Northwestern University
- Aleksandr Stolyar, AT&T Alcatel-Lucent
- Dharma Kwon, University of Illinois at Urbana-Champaign
- Negar Kiyavash, University of Illinois at Urbana-Champaign
- Bruce Hajek, University of Illinois at Urbana-Champaign
- Maxim Raginsky, University of Illinois at Urbana-Champaign
- Prashant Mehta, University of Illinois at Urbana-Champaign
- Ali Abbas, University of Illinois at Urbana-Champaign
- Ahmed Sameh, Purdue University
- Wen-Mei Hwu, University of Illinois at Urbana-Champaign
- Narayan Aluru, University of Illinois at Urbana-Champaign
- Bill Gropp, University of Illinois at Urbana-Champaign
- Jinqiao Duan, Illinois Institute of Technology and IPAM
- Lee DeVille, University of Illinois at Urbana-Champaign
- Kay Kirkpatrick, University of Illinois at Urbana-Champaign
- Matt West, University of Illinois at Urbana-Champaign
- Alejandro Dominguez-Garcia, University of Illinois at Urbana-Champaign

*Registration is free but required*** - here.**

**- here.**

*For more information contact Carolyn Thomas, cdthoma2@illinois.edu.*

**Accommodations:**

A hotel block at the Hampton Inn has been held for this conference. If you are attending and need a hotel room, please book in this block by Thursday, August 23 using the link below.http://hamptoninn.hilton.com/en/hp/groups/personalized/C/CMIILHX-IMS-20120916/index.jhtml?WT.mc_id=POG

In need of a hotel after August 23? Here are links to other hotels in the area:

IMSE is supported by the Vice Chancellor for Research, the College of Liberal Arts and Sciences, and the College of Engineering at the University of Illinois at Urbana-Champaign.