Monday, July 31, 2017 - 09:00 , Location: Clough 152 (plenary talks), Skiles (parallel sessions) , SIAM AG 2017 , Georgia Tech , Organizer: Anton Leykin
Georgia Tech is the site of the 2017 SIAM Conference on Applied Algebraic Geometry (July 31 to August 4). This biennial meeting is an activity of the Activity Group in Applied Geometry of SIAM, the Society for Industrial and Applied Mathematics. The SIAM Activity Group in Algebraic Geometry aims to bring together researchers who use algebraic geometry in industrial and applied mathematics. "Algebraic geometry" is interpreted broadly to include at least algebraic geometry, commutative algebra, noncommutative algebra, symbolic and numeric computation, algebraic and geometric combinatorics, representation theory, and algebraic topology. These methods have already seen applications in biology, coding theory, cryptography, combustion, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear partial differential equations, optimization, robotics, and statistics. School of Mathematics professors Greg Blekherman, Anton Leykin, and Josephine Yu lead the local organizing committee.
Thursday, July 27, 2017 - 09:00 , Location: Skiles 005 and 006 , Macaulay2 , Georgia Tech , Organizer: Anton Leykin
Dates: July 27-29 (Thu-Sat). Schedule will appear here. These tutorials are intended to appeal to participants with any level of prior M2 experience. The topics will range from the basic functionality of M2 to modeling problems in the M2 language to more specialized tutorials on algebraic statistics and numerical algebraic geometry. We will also reserve ample time for practice and Q&A sessions. Registration is free, but please fill the form here.
Series: CDSNS Colloquium
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.
Series: Dissertation Defense
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.
Friday, July 7, 2017 - 10:30 , Location: Skiles 006 , Nick Vlamis , Michigan , Organizer: Justin Lanier
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.
Tuesday, June 27, 2017 - 14:05 , Location: Skiles 006 , Lei Chen , University of Chicago , Organizer: Dan Margalit
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.
Friday, June 23, 2017 - 10:00 , Location: Skiles 006 , William Worden , Temple University , email@example.com , Organizer: Justin Lanier
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.
Series: Analysis Seminar
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
Tuesday, June 20, 2017 - 14:05 , Location: Skiles 006 , Dan Margalit and Justin Lanier , Georgia Tech , Organizer: Justin Lanier
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.