February 2017 |

4:00 pm Monday, March 20, 2017 Topology Seminar: Concordance in 3-manifolds and satellitesPatrick Orson (UQAM) in HBH 427- The knot cobordism group C of knots in the 3-sphere has long been an important object of study in low-dimensional topology. A less intensely studied problem is cobordism of knots in a general 3-manifold Y, perhaps due to a lack of an obvious algebraic structure in this general case. To impose some algebraic structure, one can consider the action of the group C on the set of knot cobordism classes in Y. I will discuss some recent work which makes substantial progress towards proving the orbit sets of this action are all infinite (except for two notable examples, which I will also describe).
Submitted by dk27@rice.edu |

4:00 pm Tuesday, March 21, 2017 AGNT: Zero-Cycles on Torsors under Linear Algebraic Groups
Reed Leon Gordon-Sarney (Emory University) in HBH 227- Let G be a smooth connected linear algebraic group over a field, and let X be a G-torsor. If X admits a zero-cycle of degree 1, does X have a rational point? This question is attributed to Serre, dates back to the `60s, and is still open. In 2004, Totaro generalized Serre's question: if X admits a zero-cycle of positive degree d, does X have a closed etale point of degree dividing d? The speaker will discuss his thesis work (with some very recent results) on Totaro's question.
Submitted by ar76@rice.edu |

12:00 pm Wednesday, March 22, 2017 Spectral Theory Brown Bag Seminar: From 'Operators With a Soul' to Certain Forms of Dynamical Localization IValmir Bucaj (Rice University) in HBH 427- In these talks we will first briefly talk about the 'stability' of operators with SULE under local pertubations. Then, we will describe how SULE is related to other conditions. Finally, the goal is to give some suggestions on how one could show some (weaker) form of SULE for the Bernoulli-Anderson model, and how one could could use it to obtain some (soft) forms of Dynamical Localization.
Submitted by damanik@rice.edu |

4:00 pm Wednesday, March 22, 2017 Geometry-Analysis Seminar: Mixing and un-mixing by incompressible flowsYao Yao (Georgia Tech.) in HBH 227- Abstract: In this talk, we consider the questions of efficient mixing and un-mixing by incompressible flows, under the constraint that the W^{1,p} Sobolev norm of flow is uniformly bounded in time. We construct some explicit flows to show that for any bounded initial density, it can be mixed to scale epsilon in time C|log(epsilon)| for 1
Host Department: Rice University-Mathematics |

4:00 pm Thursday, March 23, 2017 Colloquium: Applications of optimization and optimal control to some fundamental problems in mathematical fluid dynamicsCharlie Doering (University of Michigan) in HBH 227- Optimization and optimal dynamical control are used to investigate the accuracy of analytical estimates for solutions of some basic nonlinear partial differential equations of mathematical hydrodynamics. Even though many mathematical estimates are demonstrably sharp, the result of a sequence of applications of such estimates need not be sharp leaving uncertainty in the ultimate result of the analysis. We examine the classical analysis bounding enstrophy and palinstrophy amplification in Burgers’ and the Navier-Stokes equations and discover that the best known instantaneous growth rates estimates are indeed sharp. Integrating the estimates in time may (as in the 2D Navier-Stokes case) but does not always (as in the Burgers case) produce sharp estimates in which case optimal control techniques must be brought to bear to determine the actual extreme behavior of the nonlinear dynamics. Regularity of solutions to the 3D Navier-Stokes remains unresolved although work is in progress to apply these tools to the question.
Submitted by ml28@rice.edu |

4:00 pm Friday, March 24, 2017 Undergraduate Colloquium: Planning robot motion using configuration spacesDavid Krcatovich (Rice University) in HBH 227- Geometry and topology, loosely speaking, are fields of math which study shapes. Any time a question can be rephrased as “what kind of shape is this?”, these fields provide tools to get an answer. One instance of this is Einstein’s theory of general relativity – if you want to understand motion of objects under the influence of gravity, you can do so by understanding the shape of 4-dimensional ‘space-time’. We will discuss how to rephrase the following question into one about shape: “Suppose you would like to plan and execute the simultaneous motion of robots on a warehouse floor (imagine an Amazon warehouse, with robots finding, packing and shipping items). How can you do so efficiently, while making sure that the robots don’t collide?”
Submitted by sswang@rice.edu |