Seminars and Colloquia by Series

Algebraic Geometry for Applications (IMA PI summer program; June 18th - July 6th)

Series
Other Talks
Time
Monday, June 18, 2012 - 09:30 for 8 hours (full day)
Location
Klaus 1116
Speaker
Greg Blekherman, Anton Leykin, and Josephine Yu – Georgia Tech
This is a summer school (June 18th - July 6th) in computational algebraic geometry intended for graduate students, however, everyone is welcome to attend. For details and schedule see aga.gatech.edu. The first day's schedule has been slightly altered; we will give introductory lectures at 9:30 (Anton Leykin -- Computer Algebra and Numerical Algebraic Geometry), 11:30 (Greg Blekherman -- Convexity), and 2:00 (Josephine Yu -- Tropical Geometry).

Slow feature analysis and decorrelation filtering for separating correlated images

Series
Applied and Computational Mathematics Seminar
Time
Wednesday, June 13, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Minh Ha-Quang – Italian Institute of Technology
Slow Feature Analysis (SFA) is a method for extracting slowly varying features from input signals. In this talk, we generalize SFA to vector-valued functions of multivariables and apply it to the problem of blind source separation, in particular image separation. When the sources are correlated, we apply the following technique called decorrelation filtering: use a linear filter to decorrelate the sources and their derivatives, then apply the separating matrix obtained on the filtered sources to the original sources. We show that if the filtered sources are perfectly separated by this matrix, then so are the original sources.We show how to numerically obtain such a decorrelation filter by solving a nonlinear optimization problem. This technique can also be applied to other linear separation methods, whose output signals are uncorrelated, such as ICA.This is joint work with Laurenz Wiskott (Proceedings of the 13th IEEE International Conference in Computer Vision, ICCV 2011, Barcelona, Spain).

"Open book decompositions of S^3"

Series
Geometry Topology Seminar
Time
Thursday, June 7, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Will Kazez – UGA
I will talk briefly about how the study of fibred knots and Thurston's classification of automorphisms of surfaces in the 70's lead to Gabai and Oertel's work on essential laminations in the 80's. Some of this structure, for instance fractional Dehn twist coefficients, has implications in contact topology. I will describe results and examples, both old and new, that emphasize the special nature of S^3. This talk is based on joint work with Rachel Roberts.

ACO/CS Theory Seminar - Solving maximum flows in O(nm) time, and less

Series
Other Talks
Time
Wednesday, May 23, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Jim Orlin – MIT Sloan Management
Over the past 30 years, researchers have developed successively faster algorithms for the maximum flow problem. The best strongly polynomial time algorithms have come very close to O(nm) time. Many researchers have conjectured that O(nm) time is the "true" worst case running time. We resolve the issue in two ways. First, we show how to solve the max flow problem in O(nm) time. Second, we show that the running time is even faster if m = O(n). In this case, the running time is O(n^2/log n).

A Cop and Robber Solve the Kakeya Needle Problem

Series
ACO Seminar
Time
Tuesday, May 22, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter Winkler – Dartmouth College, Hanover, NH
We derive optimal strategies for a pursuit-and-evasion game and show that when pitted against each other, the two strategies construct a small set containing unit-length line segments at all angles. Joint work with Y. Babichenko, Y. Peres, R. Peretz, and P. Sousi.

Symmetric Groebner bases

Series
Algebra Seminar
Time
Monday, May 21, 2012 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chris Hillar – UC Berkeley
We discuss the theory of symmetric Groebner bases, a concept allowing one to prove Noetherianity results for symmetric ideals in polynomial rings with an infinite number of variables. We also explain applications of these objects to other fields such as algebraic statistics, and we discuss some methods for computing with them on a computer. Some of this is joint work with Matthias Aschenbrener and Seth Sullivant.

Forbidden Subgraphs and 3-Colorability

Series
Dissertation Defense
Time
Monday, May 21, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tianjun Ye – School of Mathematics, Georgia Tech
Classical vertex coloring problems ask for the minimum number of colors needed to color the vertices of a graph, such that adjacent vertices use different colors. Vertex coloring does have quite a few practical applications in communication theory, industry engineering and computer science. Such examples can be found in the book of Hansen and Marcotte. Deciding whether a graph is 3-colorable or not is a well-known NP-complete problem, even for triangle-free graphs. Intutively, large girth may help reduce the chromatic number. However, in 1959, Erdos used the probabilitic method to prove that for any two positive integers g and k, there exist graphs of girth at least g and chromatic number at least k. Thus, restricting girth alone does not help bound the chromatic number. However, if we forbid certain tree structure in addition to girth restriction, then it is possible to bound the chromatic number. Randerath determined several such tree structures, and conjectured that if a graph is fork-free and triangle-free, then it is 3-colorable, where a fork is a star K1,4 with two branches subdivided once. The main result of this thesis is that Randerath's conjecture is true for graphs with odd girth at least 7. We also give an outline of a proof that Randerath's conjecture holds for graphs with maximum degree 4.

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