Seminars and Colloquia by Series

Dynamical Path Planning Methods For Control Problems in Unknown Environment

Series
SIAM Student Seminar
Time
Monday, November 27, 2017 - 15:10 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Haoyan Zhai – School of Mathematics, Georgia Institute of Technology –
In this talk, we provide a deterministic algorithm for robotic path finding in unknown environment and an associated graph generator use only potential information. Also we will generalize the algorithm into a path planning algorithm for certain type of optimal control problems under some assumptions and will state some approximation methods if certain assumption no longer holds in some cases. And we hope to prove more theoretical results for those algorithms to guarantee the success.

Vologodsky and Coleman integration on curves with semi-stable reduction

Series
Algebra Seminar
Time
Monday, November 27, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skyles006
Speaker
Amnon Besser – Georgia Tech/Ben-Gurion University –
Let X be a curve over a p-adic field K with semi-stable reduction and let $\omega$ be a meromorphic differential on X. There are two p-adic integrals one may associated to this data. One is the Vologodsky (abelian, Zarhin, Colmez) integral, which is a global function on the K-points of X defined up to a constant. The other is the collection of Coleman integrals on the subdomains reducing to the various components of the smooth locus. In this talk I will prove the following Theorem, joint with Sarah Zerbes: The Vologodsky integral is given on each subdomain by a Coleman integrals, and these integrals are related by the condition that their differences on the connecting annuli form a harmonic 1-cocyle on the edges of the dual graph of the special fiber.I will further explain the implications to the behavior of the Vologodsky integral on the connecting annuli, which has been observed independently and used, by Stoll, Katz-Rabinoff-Zureick-Brown, in works on global bounds on the number of rational points on curves, and an interesting product on 1-forms used in the proof of the Theorem as well as in work on p-adic height pairings. Time permitting I will explain the motivation for this result, which is relevant for the interesting question of generalizing the result to iterated integrals.

Central and Central Discontinuous Galerkin (DG) Schemes on Overlapping Cells of Unstructured Grids for Solving Ideal MHD Equations with Globally Divergence-Free Magnetic Field

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 27, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Zhiliang Xu – Applied and Computational Mathematics and Statistics Dept, U of Notre Dame –
In this talk, we will present new central and central DG schemes for solving ideal magnetohydrodynamic (MHD) equations while preserving globally divergence-free magnetic field on triangular grids. These schemes incorporate the constrained transport (CT) scheme of Evans and Hawley with central schemes and central DG methods on overlapping cells which have no need for solving Riemann problems across cell edges where there are discontinuities of the numerical solution. The schemes are formally second-order accurate with major development on the reconstruction of globally divergence-free magnetic field on polygonal dual mesh. Moreover, the computational cost is reduced by solving the complete set of governing equations on the primal grid while only solving the magnetic induction equation on the polygonal dual mesh.

1-d Cubic NLS with several Dirac deltas as initial condition: Talbot effect and Intermittency

Series
PDE Seminar
Time
Tuesday, November 21, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Luis Vega – University of the Basque Country UPV/EHU –
The aim of talk is threefold. First, we solve the cubic nonlinear Schr\"odinger equation on the real line with initial data a sum of Dirac deltas. Secondly, we show a Talbot effect for the same equation. Finally, we prove an intermittency phenomena for a class of singular solutions of the binormal flow, that is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. If time permits some questions concerning the transfer of energy and momentum will be also considered.

Tropical Dolbeault cohomology of non-archimedean analytic spaces

Series
Algebra Seminar
Time
Monday, November 20, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Philipp Jell – Georgia Tech
Real-valued smooth differential forms on Berkovich analytic spaces were introduced by Chambert-Loir and Ducros. They show many fundamental properties analogous to smooth real differential forms on complex manifolds, which are used for example in Arakelov geometry. In particular, these forms define a real valued bigraded cohomology theory for Berkovich analytic space, called tropical Dolbeault cohomology. I will explain the definition and properties of these forms and their link to tropical geometry. I will then talk about results regarding the tropical Dolbeault cohomology of varietes and in particular curves. In particular, I will look at finite dimensionality and Poincar\'e duality.

A large abelian quotient of the level 4 braid group

Series
Geometry Topology Seminar
Time
Monday, November 20, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kevin Kordek – Georgia Institute of Technology
It is generally a difficult problem to compute the Betti numbers of a given finite-index subgroup of an infinite group, even if the Betti numbers of the ambient group are known. In this talk, I will describe a procedure for obtaining new lower bounds on the first Betti numbers of certain finite-index subgroups of the braid group. The focus will be on the level 4 braid group, which is the kernel of the mod 4 reduction of the integral Burau representation. This is joint work with Dan Margalit.

A partial Laplacian as an infinitesimal generator on the Wasserstein space

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 20, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yat Tin Chow – Mathematics, UCLA –
In this talk, we will introduce a family of stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes is modeled after Brownian motion and plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel probability measures, taken as a partial trace of a Hessian. We study the eigenfunction of this partial Laplacian and develop a theory of Fourier analysis. We also consider the heat flow generated by this partial Laplacian on the Wasserstein space, and discuss smoothing effect of this flow for a particular class of initial conditions. Integration by parts formula, Ito formula and an analogous Feynman-Kac formula will be discussed. We note the use of the infinitesimal generators in the theory of Mean Field Games, and we expect they will play an important role in future studies of viscosity solutions of PDEs in the Wasserstein space.

Bistable gaits and wobbling induced by pedestrian-bridge interactions

Series
CDSNS Colloquium
Time
Monday, November 20, 2017 - 11:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Igor Belykh – Georgia State University
Several modern footbridges around the world have experienced large lateral vibrations during crowd loading events. The onset of large-amplitude bridge wobbling has generally been attributed to crowd synchrony; although, its role in the initiation of wobbling has been challenged. In this talk, we will discuss (i) the contribution of a single pedestrian into overall, possibly unsynchronized, crowd dynamics, and (ii) detailed, yet analytically tractable, models of crowd phase-locking. The pedestrian models can be used as "crash test dummies" when numerically probing a specific bridge design. This is particularly important because the U.S. code for designing pedestrian bridges does not contain explicit guidelines that account for the collective pedestrian behavior. This talk is based on two recent papers: Belykh et al., Science Advances, 3, e1701512 (2017) and Belykh et al., Chaos, 26, 116314 (2016).

Sage

Series
AMS Club Seminar
Time
Friday, November 17, 2017 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 001
Speaker
Maxie Schmidt – Georgia Tech –
Sage is widely considered to be the defacto open-source alternative to Mathematica that is freely available for download to users on most standard platforms at sagemath.org. New users to Sage are also able to use its capabilities from any webbrowser and other useful Linux-only software by registering for a free account on the Sage Math Cloud platform (SMC). In addition to providing users with excellent documentation, Sage allows its users to develop spohisticated mathematics applications using Python and other excellent open-source developer tools that are well tested under both Unix / Linux and Windows environments. In this two-week workshop we provide a user-friendly introduction to Sage for beginners starting from first principles in Python, though some coding experience in other languages will of course be helpful to participants. The main project we will be focusing on over the course of the workshop is an extension of the open-source library provided by the Tilings Gap Distributions and Pair Correlation Project developed by the workshop guide at the University of Washington this and last year. This application will allow participants in the workshop to hone their coding skills in Sage by working on an extension of a real-world computational mathematics application in statistics and geometry. Prospective participants can gain a heads-up on the workshop by visiting the syllabus webpage freely available for modification online at https://github.com/maxieds/WXMLTilingsHOWTO/wiki. The workshop guide will also offer continued free technical support on Sage, Python programming, and Linux to participants in the workshop after the two-week session is complete. Future AMS workshop sessions focusing on other Sage programming topics may be run later based on feedback from this proto-session. Faculty and postdocs are welcome to attend. See you all there on Friday!

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