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Series: Other Talks

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.

Series: Other Talks

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

Series: Other Talks

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.

Series: Other Talks

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.

Series: Other Talks

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.

Series: Other Talks

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.

Series: Other Talks

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.

Series: Other Talks

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 )

Series: Other Talks

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.

Series: Other Talks

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.