Department of

# Mathematics

Seminar Calendar
for events the day of Monday, January 30, 2006.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2005           January 2006          February 2006
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3    1  2  3  4  5  6  7             1  2  3  4
4  5  6  7  8  9 10    8  9 10 11 12 13 14    5  6  7  8  9 10 11
11 12 13 14 15 16 17   15 16 17 18 19 20 21   12 13 14 15 16 17 18
18 19 20 21 22 23 24   22 23 24 25 26 27 28   19 20 21 22 23 24 25
25 26 27 28 29 30 31   29 30 31               26 27 28



Monday, January 30, 2006

2:00 pm in 143 Altgeld Hall,Monday, January 30, 2006

#### States and completely positive maps

###### Florin Boca (UIUC)

Abstract: No session 4-5pm because of job-talks.

3:00 pm in 241 Altgeld Hall,Monday, January 30, 2006

#### Two generalizations of Khovanskii Theory over an o-minimal structure

###### Sergio Fratarcangeli (McMaster University)

Abstract: Khovanskii Theory is an important tool for identifying new o-minimal structures and for obtaining uniformity results within o-minimal structures. In this talk, we generalize Khovanskii Theory in two directions. In one case, we produce a version that holds within any expansion of an ordered field with the intermediate value property. In the other case, we generalize how sets may be obtained from Rolle leaves—beyond mere intersections—so that the number of their connected components is still uniformly bounded.

3:00 pm in 343 Altgeld Hall,Monday, January 30, 2006

#### Quantum Mechanics of Fermions

Abstract: We will continue the discussion of quantum mechanics by introducing fermions. Topics will include spin, actions for fermions, path integrals, and basic supersymmetry.

3:00 pm in 3405 Siebel Center,Monday, January 30, 2006

#### Computing Optimal Graphs on Surfaces

###### J. Erickson (UIUC Computer Science)

Abstract: The study of optimal subgraphs, such as minimum spanning trees and shortest paths, has been a staple of computer science for more than fifty years. Similarly, optimal straight-line geometric graphs, such as convex hulls and Voronoi diagrams, have been a standard object of study in computational geometry since its earliest beginnings. These optimal graph structures are critical components of countless graph and geometry algorithms. It is therefore natural to consider algorithms to compute optimal graphs in more general topological spaces. Even though embedded graphs have been a standard tool in topology for more than 100 years, relatively little is known about this class of algorithmic problem. This talk will survey algorithms for computing optimal graphs on topological surfaces, with an emphasis on open problems. For example: How quickly can we compute the shortest nontrivial cycle in a given surface? The shortest cycle in a given homotopy class? The shortest cycle that cuts the surface into two nontrivial components? The shortest graph that cuts the surface into a disk? The shortest pants decomposition? The shortest canonical homotopy basis? Neither efficient algorithms, approximations, or hardness results are known for most of these problems. For the few problems where algorithms are known, there is little reason to believe that are as fast as possible.

4:00 pm in 245 Altgeld Hall,Monday, January 30, 2006

#### On the homogenization of some free boundary problems

###### Antoine Mellet (University of Texas at Austin)

Abstract: Free boundary problems arise in the modeling of many natural phenomena such as the combustion of premixed gas or the shaping of capillary drops. Mathematically, these problems are well known to yield very challenging questions. In this talk, I will discuss the effects of homogenization on the free boundary condition. In particular, I will show that oscillations arising along the free boundary can explain hysteresis phenomena observed experimentally. Hosts: R. Sowers and E. Kirr