Seminars and Colloquia by Series

Invariant manifolds in energy harvesting coupled oscillators

Series
CDSNS Colloquium
Time
Tuesday, July 25, 2017 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Albert Granados – Department of Applied Mathematics and Computer Science, Technical University of Denmark
When perturbed with a small periodic forcing, two (or more) coupledconservative oscillators can exhibit instabilities: trajectories thatbecome unstable while accumulating ``unbounded'' energy from thesource. This is known as Arnold diffusion, and has been traditionallyapplied to celestial mechanics, for example to study the stability ofthe solar system or to explain the Kirkwood gaps in the asteroid belt.However, such phenomenon could be extremely useful in energyharvesting systems as well, whose aim is precisely to capture as muchenergy as possible from a source.In this talk we will show a first step towards the application ofArnold diffusion theory in energy harvesting systems. We will consideran energy harvesting system based on two piezoelectric oscillators.When forced to oscillate, for instance when driven by a small periodicvibration, such oscillators create an electrical current which chargesan accumulator (a capacitor or a battery). Unfortunately, suchoscillators are not conservative, as they are not perfectly elastic(they exhibit damping).We will discuss the persistence of normally hyperbolic invariantmanifolds, which play a crucial role in the diffusing mechanisms. Bymeans of the parameterization method, we will compute such manifoldsand their associated stable and unstable manifolds. We will alsodiscuss the Melnikov method to obtain sufficient conditions for theexistence of homoclinic intersections.

Multilinear Dyadic Operators and Their Commutators

Series
Dissertation Defense
Time
Tuesday, July 18, 2017 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ishwari Kunwar – Georgia Tech
In this thesis, we introduce multilinear dyadic paraproducts and Haar multipliers, and discuss boundedness properties of these operators and their commutators with locally integrable functions in various settings. We also present pointwise domination of these operators by multilinear sparse operators, which we use to prove multilinear Bloom’s inequality for the commutators of multilinear Haar multipliers. Along the way, we provide several characterizations of dyadic BMO functions.

Algebraic and topological properties of big mapping class groups

Series
Geometry Topology Seminar
Time
Friday, July 7, 2017 - 10:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nick Vlamis – Michigan
There has been a recent interest in studying surfaces of infinite type, i.e. surfaces with infinitely-generated fundamental groups. In this talk, we will focus on their mapping class groups, often called big mapping class groups. In contrast to the finite-type case, there are many open questions regarding the basic algebraic and topological properties of big mapping class groups. I will discuss several such questions and provide some answers. In particular, I will discuss automorphism groups of mapping class groups as well as relations between topological invariants of a surface and algebraic invariants of its mapping class group. The results in the talk are based on recent joint work with Priyam Patel and ongoing joint work with Javier Aramayona and Priyam Patel.

Surjective homomorphism between surface braid groups

Series
Geometry Topology Seminar
Time
Tuesday, June 27, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lei Chen – University of Chicago
I will talk about homomorphisms between surface braid groups. Firstly, we will see that any surjective homomorphism from PB_n(S) to PB_m(S) factors through a forgetful map. Secondly, we will compute the automorphism group of PB_n(S). It turns out to be the mapping class group when n>1.

Experimental statistics of veering triangulations.

Series
Geometry Topology Seminar
Time
Friday, June 23, 2017 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
William Worden – Temple University –
Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. We present experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. We will begin by discussing essential background material, including hyperbolic manifolds and ideal triangulations, and more particularly fibered hyperbolic manifolds and the construction of the veering triangulation.

Self-similar tilings of General Fractal Blow-ups and Anderson Putnam Theory

Series
Analysis Seminar
Time
Wednesday, June 21, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael F. Barnsley – Australian National University
In this seminar I will discuss current work, joint with AndrewVince and Alex Grant. The goal is to tie together several related areas, namelytiling theory, IFS theory, and NCG, in terms most familiar to fractal geometers.Our focus is on the underlying code space structure. Ideas and a conjecture willbe illustrated using the Golden b tilings of Robert Ammann

Normal closures of mapping classes

Series
Geometry Topology Seminar
Time
Tuesday, June 20, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dan Margalit and Justin Lanier – Georgia Tech
We give a simple geometric criterion for an element to normally generate the mapping class group of a surface. As an application of this criterion, we show that when a surface has genus at least 3, every periodic mapping class except for the hyperelliptic involution normally generates. We also give examples of pseudo-Anosov elements that normally generate when genus is at least 2, answering a question of D. Long.

Parallel Connections of Bilinear Systems

Series
Other Talks
Time
Thursday, May 25, 2017 - 11:00 for 1 hour (actually 50 minutes)
Location
TSRB 132
Speaker
Guenther Dirr – University of Wuzburg
First, we present a necessary and sufficient conditions for accessibility of bilinear systems evolving on semisimple (matrix) Lie groups. From this, we derive a controllability criterion for parallel connections of bilinear systems which gets a if-and-only-if condition in the case of compact Lie groups. Finally, we present a key application from quantum control.

Elusive problems in extremal graph theory

Series
Graph Theory Seminar
Time
Thursday, May 18, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel Kral – University of Warwick
We study the uniqueness of optimal configurations in extremal combinatorics. An empirical experience suggests that optimal solutions to extremal graph theory problems can be made asymptotically unique by introducing additional constraints. Lovasz conjectured that this phenomenon is true in general: every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints such that the resulting set is satisfied by an asymptotically unique graph. We will present a counterexample to this conjecture and discuss related results. The talk is based on joint work with Andrzej Grzesik and Laszlo Miklos Lovasz.

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