## Seminars and Colloquia by Series

### Discussion of Gender Issues and Authority in Academics

Series
Other Talks
Time
Friday, March 4, 2011 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 257
Speaker
Open DiscussionsSchool of Mathematics, Georgia Tech
Are there gender differences in authority in mathematics? For instance, do students treat male and female professors differently and what can we do to overcome any negative consequences? Also, what might some positive differences be? We may also discuss issues surrounding respect and authority in research. All are welcome, but if possible, please let Becca Winarski rwinarski@math.gatech.edu know if you plan on attending, so she can get an approximate head count.

### Stability of vortex and wave flows from bifurcation diagrams exploiting a variational argument

Series
Other Talks
Time
Wednesday, February 9, 2011 - 16:15 for 1 hour (actually 50 minutes)
Location
Howey W505
Speaker
Paolo Luzzatto-FegizMechanical &amp;amp; Aerospace Engineering, Cornell University
Steady fluid solutions can play a special role in characterizing the dynamics of a flow: stable states might be realized in practice, while unstable ones may act as attractors in the unsteady evolution. Unfortunately, determining stability is often a process substantially more laborious than computing steady flows; this is highlighted by the fact that, for several comparatively simple flows, stability properties have been the subject of protracted disagreement (see e.g. Dritschel et al. 2005, and references therein). In this talk, we build on some ideas of Lord Kelvin, who, over a century ago, proposed an energy-based stability argument for steady flows. In essence, Kelvin’s approach involves using the second variation of the energy to establish bounds on the growth of a perturbation. However, for numerically obtained fluid equilibria, computing the second variation of the energy explicitly is often not feasible. Whether Kelvin’s ideas could be implemented for general flows has been debated extensively (Saffman & Szeto, 1980; Dritschel, 1985; Saffman, 1992; Dritschel, 1995). We recently developed a stability approach, for families of steady flows, which constitutes a rigorous implementation of Kelvin’s argument. We build on ideas from bifurcation theory, and link turning points in a velocity-impulse diagram to exchanges of stability. We further introduce concepts from imperfection theory into these problems, enabling us to reveal hidden solution branches. Our approach detects exchanges of stability directly from families of steady flows, without resorting to more involved stability calculations. We consider several examples involving fundamental vortex and wave flows. For all flows studied, we obtain stability results in agreement with linear analysis, while additionally discovering new steady solutions, which exhibit lower symmetry. Paolo is a candidate for J Ford Fellowship at CNS. To view and/or participate in the CNS Webinar from wherever you are: evo.caltech.edu/evoNext/koala.jnlp?meeting=MeMMMu2M2iD2Di9D9nDv9e

### Women's Group Meeting - Etiquette in Mathematics Discussion

Series
Other Talks
Time
Friday, February 4, 2011 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 257 (Math Lab)
Speaker
Group DiscussionSchool of Mathematics, Georgia Tech
All are welcome to discuss professionalism in math, including inviting a speaker, asking questions in talks, dress code at conferences and workshops, and sending polite requests to strangers. Some topics specifically pertaining to women's issues may be discussed. If possible, contact Becca Winarski (rwinarski@math.gatech.edu) if you plan to attend, however, note that everyone is welcome even if you do not respond.

### Joint Athens-Atlanta Number Theory - Oscillatory integrals in analytic and adelic geometry

Series
Other Talks
Time
Tuesday, February 1, 2011 - 17:00 for 1 hour (actually 50 minutes)
Location
Emory University, Math and Science Center W201
Speaker
Yuri TschinkelNew York University

Please Note: If you wish to drive your own car and park, the closest parking deck is attached to the Oxford Rd Building. There will be a charge for parking, which is $6 for 2-3 hours. Once you have parked, exit the parking garage into the building and there will be an elevator to your right. Take the elevator to level 3. You should take a left out of the elevator and proceed through the glass doors into the courtyard area. The Mathematics and Science Center will be the building to your left. Oscillatory integrals arising as Fourier transforms of local and global height functions play an important role in the spectral analysis of height zeta functions. I will explain a general geometric technique which allows to evaluate such integrals. This is joint work with A. Chambert-Loir. ### Joint Athens-Atlanta Number Theory - Moments of zeta and L-functions Series Other Talks Time Tuesday, February 1, 2011 - 16:00 for 1 hour (actually 50 minutes) Location Emory University, Math and Science Center W201 Speaker K. SoundararajanStanford University Please Note: If you wish to drive your own car and park, the closest parking deck is attached to the Oxford Rd Building. There will be a charge for parking, which is$6 for 2-3 hours. Once you have parked, exit the parking garage into the building and there will be an elevator to your right. Take the elevator to level 3. You should take a left out of the elevator and proceed through the glass doors into the courtyard area. The Mathematics and Science Center will be the building to your left.

An important theme in number theory is to understand the values taken by the Riemann zeta-function and related L-functions. While much progress has been made, many of the basic questions remain unanswered. I will discuss what is known about this question, explaining in particular the work of Selberg, random matrix theory and the moment conjectures of Keating and Snaith, and recent progress towards estimating the moments of zeta and L-functions.

### Southeast Geometry Seminar

Series
Other Talks
Time
Monday, December 13, 2010 - 08:30 for 8 hours (full day)
Location
University of Tennessee Knoxville
Speaker
Southeast Geometry SeminarUniversity of Tennessee Knoxville
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham;  The Georgia Institute of Technology;  Emory University;  The University of Tennessee Knoxville.  The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology. Catherine Williams (Columbia U);  Hugh Bray (Duke U);  Simon Brendle (Stanford U);  Spyros Alexakis (U of Toronto);  Alessio Figalli (U of Texas at Austin).   There will also be an evening public lecture by plenary speaker Hugh Bray (Duke U) entitled From Black Holes and the Big Bang to Dark Energy and Dark Matter: Successes of Einstein's Theory of Relativity.

### Nonlinear Science Seminar - Nearly perfect flows

Series
Other Talks
Time
Wednesday, December 8, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Physics Howey L5
Speaker
Wendy W. ZhangPhysics Department and the James Franck Institute, University of Chicago
In school, we learned that fluid flow becomes simple in two limits. Over long lengthscales and at high speeds, inertia dominates and the motion can approach that of a perfect fluid with zero viscosity. On short lengthscales and at slow speeds, viscous dissipation is important. Fluid flows that correspond to the formation of a finite-time singularity in the continuum description involve both a vanishing characteristic lengthscale and a diverging velocity scale. These flows can therefore evolve into final limits that defy expectations derived from properties of their initial states. This talk focuses on 3 familiar processes that belong in this category: the formation of a splash after a liquid drop collides with a dry solid surface, the emergence of a highly-collimated sheet from the impact of a jet of densely-packed, dry grains, and the pinch-off of an underwater bubble. In all three cases, the motion is dominated by inertia but a small amount of dissipation is also present. Our works show that dissipation is important for the onset of splash, plays a minor role in the ejecta sheet formation after jet impact, but becomes irrelevant in the break-up of an underwater bubble. An important consequence of this evolution towards perfect-fluid flow is that deviations from cylindrical symmetry in the initial stages of pinch-off are not erased by the dynamics. Theory, simulation and experiment show detailed memories of initial imperfections remain encoded, eventually controlling the mode of break-up. In short, the final outcome is not controlled by a single universal singularity but instead displays an infinite variety.

### Nonlinear Science Webminar - Multiple Time Scale Dynamics in Chemical Oscillators

Series
Other Talks
Time
Monday, December 6, 2010 - 10:00 for 1 hour (actually 50 minutes)
Location
Physics Howey 501
Speaker
Chris ScheperCenter for Applied Mathematics, Cornell University
Dynamical systems with multiple time scales have invariant geometric objects that organize the dynamics in phase space. The slow-fast structure of the dynamical system leads to phenomena such as canards, mixed-mode oscillations, and bifurcation delay. We'll discuss two projects involving chemical oscillators. The first is the analysis of a simple chemical model that exhibits complex oscillations. Its bifurcations are studied using a geometric reduction of the system to a one-dimensional induced map. The second investigates the slow-fast mechanisms generating mixed-mode oscillations in a model of the Belousov-Zhabotinsky (BZ) reaction. A mechanism called dynamic Hopf bifurcation is responsible for shaping the dynamics of the system. This webminar will be broadcast on evo.caltech.edu (register, start EVO, webminar link is evo.caltech.edu/evoNext/koala.jnlp?meeting=MMMeMn2e2sDDDD9v9nD29M )

### Sequences of problems, matrices, and solutions

Series
Other Talks
Time
Friday, November 12, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Klaus 1447
Speaker
Eric de SturlerDepartment of Mathematics, Virginia Tech
In a wide range of applications, we deal with long sequences of slowly changing matrices or large collections of related matrices and corresponding linear algebra problems. Such applications range from the optimal design of structures to acoustics and other parameterized systems, to inverse and parameter estimation problems in tomography and systems biology, to parameterization problems in computer graphics, and to the electronic structure of condensed matter. In many cases, we can reduce the total runtime significantly by taking into account how the problem changes and recycling judiciously selected results from previous computations. In this presentation, I will focus on solving linear systems, which is often the basis of other algorithms. I will introduce the basics of linear solvers and discuss relevant theory for the fast solution of sequences or collections of linear systems. I will demonstrate the results on several applications and discuss future research directions.

### Branched Covers in Contact Geometry

Series
Other Talks
Time
Wednesday, October 27, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Meredith CaseySchool of Mathematics, Georgia Tech

Please Note: This talk will be the oral examination for Meredith Casey.

I will first discuss the motivation and background information necessary to study the subjects of branched covers and of contact geometry. In particular we will give some examples and constructions of topological branched covers as well as present the fundamental theorems in this area. But little is understood about the general constructions, and even less about how branched covers behave in the setting of contact geometry, which is the focus of my research. The remainder of the talk will focus on the results I have thus far and current projects.