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Wednesday, January 20, 2010 - 11:00 ,
Location: SKiles 269 ,
Lee Childers ,
Georgia Tech, School of Applied Physiology ,
lee@gatech.edu ,
Organizer:

Cycling represents an integration of man and machine. Optimizing this integration through changes in rider position or bicycle component selection may enhance performance of the total bicycle/rider system. Increasing bicycle/rider performance via mathematical modeling was accomplished during the US Olympic Superbike program in preparation for the 1996 Atlanta Olympic Games. The purpose of this presentation is to provide an overview on the science of cycling with an emphasis on biomechanics using the track pursuit as an example. The presentation will discuss integration and interaction between the bicycle and human physiological systems, how performance may be measured in a laboratory as well as factors affecting performance with an emphasis on biomechanics. Then reviewing how people pedal a bicycle with attention focused on forces at the pedal and the effect of position variables on performance. Concluding with how scientists working on the US Olympic Superbike program incorporated biomechanics and aerodynamic test data into a mathematical model to optimize team pursuit performance during the 1996 Atlanta Olympic Games.

Series: Algebra Seminar

Weyl proved that if an N-dimensional real vector v has linearly independent coordinates over Q, then its integer multiples v, 2v, 3v, .... are uniformly distributed modulo 1. Stated multiplicatively (via the exponential map), this can be viewed as a Haar-equidistribution result for the cyclic group generated by a point on the N-dimensional complex unit torus. I will discuss an analogue of this result over a non-Archimedean field K, in which the equidistribution takes place on the N-dimensional Berkovich projective space over K. The proof uses a general criterion for non-Archimedean equidistribution, along with a theorem of Mordell-Lang type for the group variety G_m^N over the residue field of K, which is due to Laurent.

Series: PDE Seminar

I will discuss the intermediate and long time dynamics
of solutions of the nonlinear Schroedinger - Gross Pitaevskii equation,
governing nonlinear dispersive waves in a spatially
non-homogeneous background.
In particular, we present results (with B. Ilan)
on solitons with frequencies near a spectral band edge associated
with periodic potential, and results (with Z. Gang) on large
time energy distribution in systems with multiple bound states.
Finally, we discuss how such results can inform strategies
for control of soliton-like states in optical and quantum systems.

Series: Job Candidate Talk

The Edrei-Thoma theorem characterizes totally positive functions, and plays an important role in character theory of the infinite symmetric group. The Loewner-Whitney theorem characterizes totally positive elements of the general linear group, and is fundamental for Lusztig's theory of total positivity in reductive groups. In this work we derive a common generalization of the two theorems. The talk is based on joint work with Thomas Lam.

Friday, January 15, 2010 - 14:00 ,
Location: Skiles 269 ,
Mohammad Ghomi ,
Georgia Tech ,
Organizer:

We study the topology of the space bd K^n of complete convex
hypersurfaces of R^n which are homeomorphic to R^{n-1}. In particular,
using Minkowski sums, we construct a deformation retraction of bd K^n
onto the Grassmannian space of hyperplanes. So every hypersurface in bd
K^n may be flattened in a canonical way. Further, the total curvature
of each hypersurface evolves continuously and monotonically under this
deformation. We also show that, modulo proper rotations, the subspaces
of bd K^n consisting of smooth, strictly convex, or positively curved
hypersurfaces are each contractible, which settles a question of H.
Rosenberg.

Series: ACO Colloquium

Refreshments at 4:00PM in Skiles 236

I will talk about new approximation algorithms for the Asymmetric Traveling Salesman Problem (ATSP) when the costs satisfy the triangle inequality. Our approach is based on constructing a "thin" spanning tree from the solution of a classical linear programming relaxation of the problem and augmenting the tree to an Eulerian subgraph. I will talk about Goddyn's conjecture on the existence of such trees and its relations to nowhere-zero flows. I will present an O(log n/log log n) approximation algorithm that uses a new randomized rounding method. Our rounding method is based on sampling from a distribution and could be of independent interest. Also, I will talk about the special case where the underlying undirected graph of the LP relaxation of the problem has bounded genus. This is the case for example, when the distance functions are shortest paths in a city with few bridges and underpasses. We give a constant factor approximation algorithm in that case. The first result is a joint work with A. Asadpour, M. Goemans, A. Madry and S. Oveis Gharan, and the second result is a joint work with S. Oveis Gharan.

Series: Analysis Seminar

Sandro Levi and I have investigated variational strengthenings of uniform continuity and uniform convergence of nets or sequences of functions with respect to a family of subsets of the domain. Out of our theory comes an answer to this basic question: what is the weakest topology stronger than the topology of pointwise convergence in which continuity is preserved under taking limits? We argue that the classical theory constitues a misunderstanding of what is fundamentally a variational phenomenon.

Monday, January 11, 2010 - 13:00 ,
Location: Skiles 255 ,
Peter Blomgren ,
San Diego State University ,
Organizer: Sung Ha Kang

We describe two computational frameworks for the assessment of contractileresponses of enzymatically dissociated adult and neonatal cardiac myocytes.The proposed methodologies are variants of mathematically sound andcomputationally robust algorithms very well established in the imageprocessing community. The physiologic applications of the methodologies areevaluated by assessing the contraction in enzymatically dissociated adultand neonatal rat cardiocytes. Our results demonstrate the effectiveness ofthe proposed approaches in characterizing the true 'shortening' in thecontraction process of the cardiocytes. The proposed method not onlyprovides a more comprehensive assessment of the myocyte contraction process,but can potentially eliminate historical concerns and sources of errorscaused by myocyte rotation or translation during contraction. Furthermore,the versatility of the image processing techniques makes the methodssuitable for determining myocyte shortening in cells that usually bend ormove during contraction. The proposed method can be utilized to evaluatechanges in contractile behavior resulting from drug intervention, diseasemodeling, transgeneity, or other common applications to mammaliancardiocytes.This is research is in collaboration with Carlos Bazan, David Torres, andPaul Paolini.

Series: Geometry Topology Seminar

Series: Job Candidate Talk

Attached to every homeomorphism of a surface is a real number called its dilatation. For a generic (i.e. pseudo-Anosov) homeomorphism, the dilatation is an algebraic integer that records various properties of the map. For instance, it determines the entropy (dynamics), the growth rate of lengths of geodesics under iteration (geometry), the growth rate of intersection numbers under iteration (topology), and the length of the corresponding loop in moduli space (complex analysis). The set of possible dilatations is quite mysterious. In this talk I will explain the discovery, joint with Benson Farb and Chris Leininger, of two universality phenomena. The first can be described as "algebraic complexity implies dynamical complexity", and the second as "geometric complexity implies dynamical complexity".