Seminars and Colloquia by Series

Algorithms in Combinatorial Topology

Series
Research Horizons Seminar
Time
Wednesday, October 5, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Dan Margalit – Department of Mathematics, Georgia Institute of Technology –

Please Note: Food and Drinks will be provided before the seminar.

For every surface (sphere, torus, etc.) there is an associated graph called the curve graph. The vertices are curves in the surface and two vertices are connected by an edge if the curves are disjoint. The curve graph turns out to be very important in the study of surfaces. Even though it is well-studied, it is quite mysterious. Here are two sample problems: If you draw two curves on a surface, how far apart are they as edges of the curve graph? If I hand you a surface, can you draw two curves that have distance bigger than three? We'll start from the beginning and discuss these problems and some related computational problems on surfaces.

Math research in the age of Google Scholar and the revolutionary library

Series
Research Horizons Seminar
Time
Wednesday, October 5, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Liz Holdsworth – Georgia Institute of Technology
If Google Scholar gives you everything you want, what could Georgia Tech Library possibly do for you? Come learn how to better leverage the tools you know and discover some resources you may not. Get to know your tireless Math Librarian and figure out how to navigate the changes coming with Library Next. This is also an opportunity to have a voice in the Library’s future, so bring ideas for discussion.

Geometric Small Cancellation

Series
Geometry Topology Working Seminar
Time
Wednesday, October 5, 2016 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shane Scott – Georgia Tech
In this lecture series, held jointly (via video conference) with the University of Buffalo and the University of Arkansas, we aim to understand the lecture notes by Vincent Guirardel on geometric small cancellation. The lecture notes can be found here: https://perso.univ-rennes1.fr/vincent.guirardel/papiers/lecture_notes_pcmi.pdf This week we will begin Lecture 4.

Boltzmann's equation and its entropy inequality

Series
Non-Equilibrium Statistical Mechanics Reading Group
Time
Monday, October 3, 2016 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zaher Hani – GeorgiaTech –
We continue our discussion, started last week, on what we called the "Boltzmann approach" to non-equilibrium statistical physics. We shall start with some remarks concerning the derivation and regimes of validity of the Boltzmann equation for rarefied gases (the Boltzmann-Grad limit). Then we will consider Boltzmann kinetic equation, and prove its H-principle. This corresponds mainly to Chapters 1 and 2 of Dorfman "An introduction to Chaos in Non-equilibrium Statistical Mechanics".

Hypersurfaces with central convex cross sections

Series
Geometry Topology Seminar
Time
Monday, October 3, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alper Gur – Indiana University –
The compact transverse cross-sections of a cylinder over a central ovaloid in Rn, n ≥ 3, with hyperplanes are central ovaloids. A similar result holds for quadrics (level sets of quadratic polynomials in Rn, n ≥ 3). Their compact transverse cross-sections with hyperplanes are ellipsoids, which are central ovaloids. In R3, Blaschke, Brunn, and Olovjanischnikoff found results for compact convex surfaces that motivated B. Solomon to prove that these two kinds of examples provide the only complete, connected, smooth surfaces in R3, whose ovaloid cross sections are central. We generalize that result to all higher dimensions, proving: If M^(n-1), n >= 4, is a complete, connected smooth hypersurface of R^n, which intersects at least one hyperplane transversally along an ovaloid, and every such ovaloid on M is central, then M is either a cylinder over a central ovaloid or a quadric.

Knudsen layer: coupling fluids with kinetics

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 3, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Qin Li – UW-Madison –
Many kinetic equations have the corresponding fluid limits. In the zero limit of the Knudsen number, one derives the Euler equation out of the Boltzmann equation and the heat equation out of the radiative transfer equation. While there are good numerical solvers for both kinetic and fluid equations, it is not quite well-understood when the two regimes co-exist. In this talk, we model the layer between the fluid and the kinetic using a half-space equation, study the well-posedness, design a numerical solver, and utilize it to couple the two sets of equations that govern separate domains. It is a joint work with Jianfeng Lu and Weiran Sun.

NumericalImplicitization for Macaulay2

Series
Algebra Seminar
Time
Friday, September 30, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Justin Chen – UC Berkeley

Please Note: Many varieties of interest in algebraic geometry and applications are given as images of regular maps, i.e. via a parametrization. Implicitization is the process of converting a parametric description of a variety into an intrinsic (i.e. implicit) one. Theoretically, implicitization is done by computing (a Grobner basis for) the kernel of a ring map, but this can be extremely time-consuming -- even so, one would often like to know basic information about the image variety. The purpose of the NumericalImplicitization package is to allow for user-friendly computation of the basic numerical invariants of a parametrized variety, such as dimension, degree, and Hilbert function values, especially when Grobner basis methods take prohibitively long.

Topology Optimization of Structures and Materials

Series
GT-MAP Seminar
Time
Friday, September 30, 2016 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 257
Speaker
Tomas Zegard – GT CE

Please Note: Bio: Tomas Zegard is a postdoctoral fellow in the School of Civil and Environmental Engineering at Georgia Tech. He received a PhD in Structural Engineering from the University of Illinois at Urbana-Champaign in 2014. Afterwards, he took a position at SOM LLP in Chicago, an Architecture + Engineering firm specializing in skyscrapers. He has made significant contributions to the field of topology optimization through research papers and free open-source tools. Xiaojia Zhang is a doctoral candidate in the School of Civil and Environmental Engineering at Georgia Tech. She received her bachelor’s and master’s degrees in structural engineering from the University of Illinois at Urbana-Champaign. Her major research interests are structural topology optimization with material and geometric nonlinearity, stochastic programming, and additive manufacturing.

Topology optimization, an agnostic design method, proposes new and innovative solutions to structural problems. The previously established methodology of sizing a defined geometry and connectivity is not sufficient; in these lie the potential for big improvements. However, topology optimization is not without its problems, some of which can be controlled or mitigated. The seminar will introduce two topology optimization techniques: one targeted at continuum, and one targeted at discrete (lattice-like) solutions. Both will be presented using state-of-the-art formulations and implementations. The stress singularity problem (vanishing constraints), the ill-posedness of the problem, the large number of variables involved, and others, continue to challenge researchers and practitioners. The presented concepts find potential applications in super-tall building designs, aircrafts, and the human body. The issue of multiple load cases in a structure, a deterministic problem, will be addressed using probabilistic methodologies. The proposed solution is built around a suitable damping scheme based on simulated annealing. A randomized approach with stochastic sampling is proposed, which requires a fraction of the computational cost compared to the standard methodologies.

Anisotropic Structures and Sparse Regularization of Inverse Problems

Series
Analysis Seminar
Time
Friday, September 30, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gitta Kutyniok – Technical University of Berlin –

Please Note: Note the unusual time.

Many important problem classes are governed by anisotropic structures such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images or shear layers in solutions of transport dominated equations. While the ability to reliably capture and sparsely represent anisotropic features for regularization of inverse problems is obviously the more important the higher the number of spatial variables is, principal difficulties arise already in two spatial dimensions. Since it was shown that the well-known (isotropic) wavelet systems are not capable of efficiently approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems. Among various suggestions, shearlets are the most widely used today. Main reasons for this are their optimal sparse approximation properties within a model situation in combination with their unified treatment of the continuum and digital realm, leading to faithful implementations. In this talk, we will first provide an introduction to sparse regularization of inverse problems, followed by an introduction to the anisotropic representation system of shearlets and presenting the main theoretical results. We will then analyze the effectiveness of using shearlets for sparse regularization of exemplary inverse problems such as recovery of missing data and magnetic resonance imaging (MRI) both theoretically and numerically.

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