Jan 16-19 2018

Edit: This workshop was also featured in this story from the College of Science.

Workshop on introduction to dynamical systems methods for mission design

This workshop is designed to provide an introduction to recent methods to design orbits for spacecraft which use less fuel by taking advantage of natural gravitational forces. The analysis of such missions requires a deep understanding of the structure of phase space.

The workshop is part of a SURP grant by JPL Graduate and undergraduate students are encouraged to attend.

Some information on the workshop is available at: http://people.math.gatech.edu/~rll6/JPL/jpl.html

Date/Time:

## Huiling Yu

### Contact Information

The Tech Topology Conference brings together established and beginning researchers from around the country for a weekend of mathematics in Atlanta. Check back soon for more details. We are pleased to announce this year's speakers:

The 2017 conference features a session of five-minute lightning talks.

If you are interested in giving such a talk (on behalf of your work or someone else’s) please see the "Registration and Support" page.
Deadline for submitting proposals for Lightning Talks is October 31.

organizers: J. Etnyre, J. Hom, P. Lambert-Cole, J. Lanier, C. Leverson, D. Margalit, and B. Strenner
Supported by the NSF and the Georgia Institute of Technology

#### Event Details

Date/Time:

The "Quolloquium" series is a set of talks at the colloquium level intended to update the local mathematics community on the topics discussed at QMath13, an international conference that took place at Tech in October, 2016.   Qmath13 broadly covered the mathematical aspects of quantum mechanics, including such fields as models with randomness, quantum information, many-body theory, and models on graphs and similar structures, as well as an open-ended topic of current mathematical problems in theoretical physics.  It is taking place at approximately two-week intervals in Fall Semester, 2017 and may extend into Spring Semester, 2018.

Series: Math Physics Seminar
Title: Isoperimetric inequalities for convex cones
Speaker: Lotfi Hermi Florida International University lhermi@gmail.com
We use the weighted isoperimetric inequality of J. Ratzkin for a wedge domain in higher dimensions to prove new isoperimetric inequalities for weighted Lp-norms of the fundamental eigenfunction of a bounded domain in a convex cone-generalizing earlier work of Chiti, Kohler-Jobin, and Payne-Rayner. We also introduce relative torsional rigidity for such domains and prove a new Saint-Venant-type isoperimetric inequality for convex cones. Finally, we prove new inequalities relating the fundamental eigenvalue to the relative torsional rigidity of such a wedge domain thereby generalizing our earlier work to this higher dimensional setting, and show how to obtain such inequalities using the Payne interpretation in Weinstein fractional space. (Joint work with A. Hasnaoui)

Series: Math Physics Seminar
Title: Semiclassical Spectral Estimates with Renainder Terms
Starting from the classical Berezin- and Li-Yau-bounds onthe eigenvalues of the Laplace operator with Dirichlet boundaryconditions I give a survey on various improvements of theseinequalities by remainder terms. Beside the Melas inequalitywe deal with modifications thereof for operators with and withoutmagnetic field and give bounds with (almost) classical remainders.Finally we extend these results to the Heisenberg sub-Laplacianand the Stark operator in domains.

Vieri Mastropietro (Universita' di Milano, Italy)
will visit the SoM from November 26 to December 2. He will give a seminar on November 27. Exact time, title and abstract: TBA

Ian Jauslin (IAS, Princeton)
approximate dates November 27 to November 29/30. He will also give a seminar on November 27. Exact time, title and abstract: TBA

Date/Time:

## Oluwa Damilola Ojomo

### Contact Information

The 34th Southeastern Analysis Meeting will take place at Georgia Institute of Technology in March 23-25, 2018.

The tentative schedule is here. Here are the abstracts.

The list of confirmed participants is here.

The meeting is partially sponsored by the College of Science at Georgia Tech and the NSF. Some funds will be available for travel and lodging. The speakers will receive reimbursement at the maximal amount for $400.00. As for the non-speakers, some additional funds may be available, but there is no guarantee at this point. If you are interested in participating in the dinner in honor for Joe Ball, please fill out this form: https://goo.gl/forms/X4uQaI5W3qIHrO7n2. The dinner will most likely take place at Le Fat and is organized by Quanlei Fang, QuanLei.Fang@bcc.cuny.edu Plenary speakers: Dmitriy Bilyk (University of Minnesota) Marianna Csiornei (University of Chicago) Benjamin Jaye (Clemson University) Yumeng Ou (MIT) Stefan Richter (University of Tennessee) Krystal Taylor (The Ohio State University) Elisabeth Werner (Case Western Reserve University) Brett Wick (Washington University at St. Louis) A special session on topics related to system theory will be used to celebrate Joe Ball's contribution in the area in the occasion of his 70th birthday. Joe has been the leading expert in the area for more than thirty years and he has influenced generations of mathematicians to enter this exciting area in the intersection of System Theory and Operator Theory. Lodging: Georgia Tech has some rooms with discounted rate at Renaissance Atlanta Midtown Hotel. Reservations for the Event will be made by individual attendees directly with Marriott reservations at 1 (800) 468-3571 or (678) 412-2400. The discounted rooms must be booked before March 1, 2018. Please contact the organizers if you have any questions. Some of the other hotels near campus include Georgian Terrace, Crowne plaza, Hilton Garden Inn Atlanta Midtown, Hyatt Atlanta Midtown. The Southeastern Analysis Meetings has established a strong tradition in the US as one of the prime venues to bring together seasoned and novel researchers, including graduate students, to exchange recent progress and advances in various areas of Analysis. These areas include, in particular, the subfields of Harmonic Analysis, Convex Analysis, Complex Analysis, Operator Theory and Probability, as well as many others. Past conference locations: • University of Tennessee, Knoxville (2017) • University of Southern Florida, Tampa (2016) • University of Georgia, Athens (2015) • Clemson University, Clemson (2014) • Virginia Tech, Blacksburg (2013) • University of Alabama, Tuscaloosa (2012) • University of Florida, Gainesville (2011) • Georgia Tech, Atlanta (2010) • University of South Florida, Tampa, (2009) • Vanderbilt University, Nashville (2008) • University of Richmond, Richmond (2007) • University of Florida, Gainesville (2006) • Washington and Lee University, Lexington (2005) • University of Alabama, Tuscaloosa (2004) • University of Tennessee, Knoxville (2003) • University of North Carolina, Chapel Hill (2002) • University of Georgia, Athens (2001) • University of Virginia, Charlottesville (2000) • Vanderbilt University, Nashville (1999) • University of Alabama, Tuscaloosa (1998) • University of Florida, Gainesville (1997) • University of Richmond, Richmond (1996) • Georgia Institute of Technology, Atlanta (1995) • Virginia Tech, Blacksburg (1994) • Memphis State University, Memphis (1993) • University of Tennessee, Knoxville (1992) • University of North Carolina, Chapel Hill(1991) • University of South Carolina, Columbia (1990) • University of Georgia, Athens (1989) • University of Virginia, Charlottesville (1988) • University of Alabama, Tuscaloosa (1987) • University of North Carolina, Chapel Hill (1986) • Virginia Tech, Blacksburg (1985) #### Event Details Date/Time: ## Philipp Jell ### Contact Information ## Jacob Smith ### Contact Information The workshop is a part of GTMAP activities of the thematic semester on Dynamics (Fall 2017) This is a half day workhop on a panorama of mathematical questions in Dynamical Systems, presented by some people in the school of Mathematics and Physics. 2-2:30 Chongchun Zeng on "Wind-driven water waves and hydrodynamic instability" 2:30-3 Leonid Bunimovich on "Isospectral compression of multidimensional systems and networks" 3-3:30 Roman Grigoriev on "Streamwise Localization of Traveling Wave Solutions in Channel Flow" 3:30-4 BREAK 4-4:30 Albert Fathi on "The Pageault barrier: a tool to find the recurrent part of a dynamical system" 4:30-5 Rafael de la Llave on "Perturbations of quasi-periodic orbits: From Theory to computations." Prof. Chongchun Zeng (GT MATH) Talk title: Wind-driven water waves and hydrodynamic instability Abstract: In this talk, we consider the mathematical theory of wind-generated water waves in the framework of the interface problem between two incompressible inviscid fluids under the influence of gravity. This entails the careful study of the stability of the shear flow solutions to the interface problem of the two-phase Euler equation. Based on a rigorous derivation of the linearized equations about shear flow solutions, we obtained rigorously the linear instability criterion of Miles due to the presence of the critical layer in the steady shear flows. Our analysis is valid even in the presence of surface tension and a vortex sheet (discontinuity in the tangential velocity across the air--sea interface). We are thus able to give a unified equation including the Kelvin--Helmholtz and quasi-laminar models of wave generation put forward by Miles. Prof. Leonid Bunimovich (GT MATH) Talk title: Isospectral compression of multidimensional systems and networks Abstract: When dealing with large networks it is tempting to compress such object while keeping, as much as possible, information about it. for a great majority of real world networks all information about them is contained in their weighted adjacency. Laplace or some other matrix. I will talk about theory of isospectral transformations which in particular allows to compress a network keep all information about spectrum and eigenvectors of these matrices. Applications of this theory allowed to advance several areas of research and extract more information from real data than various other methods. It also allows to get new types of visualization of networks via building various their skeletons. This approach/theory is applicable to undirected and to directed networks. Prof. Roman Grigoriev (GT PHYSICS) Talk Title: Streamwise Localization of Traveling Wave Solutions in Channel Flow Abstract: Channel flow of an incompressible fluid at Reynolds numbers above 2400 possesses a number of different spatially localized solutions which approach the laminar flow far upstream and downstream. We use one such relative time-periodic solution that corresponds to a spatially localized version of a Tollmien-Schlichting wave to illustrate how the upstream and downstream asymptotics can be computed analytically. In particular, we show that for these spanwise uniform states the asymptotics predict exponential localization that has been observed for numerically computed solutions of several canonical shear flows but never properly understood theoretically. Prof. Albert Fathi (GT MATH) Talk Title: The Pageault barrier: a tool to find the recurrent part of a dynamical system Abstract: If f is a (invertible) dynamical system on a (compact) space X. Usually one is interested in the behavior of the sequence f^n(x), for n -> infinity, but also in control problems in the Lyapunov stable states (for example a stable attracting equilibrium) and sometime in the Lyapunov saddle state (like a saddle point of a gradient system). To find these states Conley introduced an approach through chain recurrence and Lyapunov functions. The purpose of this lecture is to introduce the Pageault barrier to study these problems. This a more metric approach, meaning that we can introduce a kind of distance that allows to locate the pieces where the recurrent dynamics is occurring. Prof. Rafael de la Llave (GT MATH) Talk Title: Perturbations of quasi-periodic orbits: From Theory to computations. Abstract: Since the time if Hyparco, it was known that the motion of celestial bodies is approximately given by epicycles. In modern language, expressed in Fourier series of a few frequencies, which we now call quasi-periodic. In modern language, these quasi-periodic solutions are landmarks that organize the behavior of a Hamiltonian system. The mathematically rigorous theory of persistence of quasi-periodic solutions is rather recent. Late 50's, early 60's with the work of Kolmogorov, Arnold, Moser (KAM). The theory is rather subtle since it involves high regularity as well as number theory. We will describe some new proofs that lead to very efficient algorithms as well as provide condition numbers that guarantee that the computations are correct. Bio] 1) Prof. Chongchun Zeng: After post-docs at NYU, and 5 years at Univ of Virginia, Chongchun Zeng joined the School of Mathematics in 2005, where he has been professor since 2009. Zeng is a leader in use of dynamical systems tools to study PDEs. 2) Prof. Leonid Bunimovich: After training at Moscow University and the Institute of Theoretical Physics in Moscow, Bunimovich joined the School of Mathematics, where he is a Regents' professor. World famous for the discovery of a fundamental mechanism of chaos, Bunimovch has wide ranging interests in ergodic theory, statistical mechanics, mathematical biology, and probability. 3) Prof. Roman Grigoriev obtained his MS from Moscow State University and PhD from Caltech. After two years as a postdoc at the University of Chicago, he joined the School of Physics in 2000. His research group studies a variety of topics related to nonlinear dynamics and pattern formation in out-of-equilibrium systems. Iinterests include deterministic modeling of fluid turbulence, phase change and heat transfer in fluids, and dynamical and topological description of cardiac arrhythmias. 4) Prof. Albert Fathi was educated in Paris and Orsay. He held positions in Paris (France), Gainesville (Florida) and Lyon (France). His mathematical interests are Topology, Geometry, Dynamical Systems and PDE. 5) Prof. Rafael de la Llave joined the School of Mathematics in August 2010, after having held positions at Princeton and the Univ. of Texas at Austin. He has wide ranging interests in dynamical systems and mathematical physics, spanning from KAM theory and hyperbolic dynamics to stability of matter and optics. He also has interest in combining analytical and numerical techniques to study dynamics. #### Event Details Date/Time: The Georgia Institute of Technology is launching the new Transdisciplinary Research Institute for Advancing Data Science (TRIAD), a cross-disciplinary institute established with a$1.5 million National Science Foundation (NSF) award. TRIAD includes faculty from across Georgia Tech in a collaborative effort to develop the foundations of data science.

The TRIAD Kickoff event includes a panel discussion featuring TRIAD leadership and remarks from special guests including Executive Vice President for Research Stephen Cross and Provost and Executive Vice President for Academic Affairs Rafael Bras, as well as talks from participating faculty members.

Buffet lunch served at 11 am.