MenuEvents for 10/05/2015 from all calendars
Geometry Seminar
Time: 3:00PM - 3:50PM
Location: BLOC 220
Speaker: Daniel Brake, Notre Dame
Title: Applications of Monodromy
Abstract: Monodromy action plays an important role in a number of mathematical theories. Stemming from a fundamental principle in complex analysis, the Cauchy integral formula, monodromy loops give all sorts of information about the interior of a region given boundary data. The uses include computing whether a pole is contained in the interior, and determining the breakup of the sheets coming together at a pole. As a consequence, monodromy is used in numerical algebraic geometry to decompose a pure-dimensional set into its irreducible components.
This talk will give an overview of monodromy, and some new connections to algebraic geometry. In particular, we will discuss how to use it to compute some local properties of algebraic varieties, as in the Numerical Local Irreducible Decomposition, and a new method for computing real tropical curves.
Student Working Seminar in Groups and Dynamics
Time: 3:00PM - 4:00PM
Location: BLOC 624
Speaker: Roman Kogan, Texas A&M University
Title: Induced measures of automaton groups acting on a binary tree I
Applied Math Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Dr. Mario Di Salvo, Mario E. Di Salvo - Universidad Nacional de Córdoba, Argentina
Title: Energetics and dynamics of the motion of self-propelled bacteria in aqueous media
Abstract: Marine bacteria often reach high swimming speeds, either to beat Brownian forces or to explore their surroundings in search of nutrients. Nutrients in the oceans are often present in the form of micropatches, point sources that are available within limited time and space. It is, therefore, very interesting to study how self-propelled organisms administer their energetic resources in order to optimize space exploration. To perform this task, we present a model to investigate the relation between bacterial dynamics and changes in the energy stored by a bacterium. Noting the existence of two very different time scales, we use a quasistatic approximation to obtain information about the speed of the bacterium and the variation on the available energy. We analyze the particular cases where the absorption is null for being the microorganism in a resource-depleted medium, and the possible enhancement in the motility of bacteria when the nutrient intake is a function of their speed. For the first case, it is possible to determine the volume of the region that a starving bacterium may visit until it stops its motion, which will depend on bacterial size. For the last case we conclude that a fast-moving microorganism can substantially increase its swimming speed by taking advantage of the advective uptake of nutrient molecules. We also discuss the dependence of the energy transfer rate to the bacterial motors, finding that the space exploration is optimized when this rate is a linear function on the speed of the microorganism.
Working Seminar on Quantum Groups
Time: 4:00PM - 5:00PM
Location: BLOC 624
Speaker: Branimir Ćaćić, Texas A&M University
Title: Introduction to Liberated Spheres (Continued)
Abstract: We will continue with Banica's "Liberations and Twists of Real and Complex Spheres."
