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Upcoming talks


Bob Eisenberg (U. Rush Chicago) WPI, OMP 1, Seminar Room 08.135 Fri, 11. Nov 16, 11:00
"Ions in Solutions and Channels: the plasma of life"
All of biology occurs in ionic solutions that are plasmas in both the physical and biological meanings of the word. The composition of these ionic mixtures has profound effects on almost all biological functions, whether on the length scale of organs like the heart or brain, of the length scale of proteins, like enzymes and ion channels. Ion channels are proteins with a hole down their middle that conduct ions (spherical charges like Na+ , K+ , Ca2+ , and Clƒ{ with diameter ~ 0.2 nm) through a narrow tunnel of fixed charge (¡¥doping¡¦) with diameter ~ 0.6 nm. Ionic channels control the movement of electric charge and current across biological membranes and so play a role in biology as significant as the role of transistors in computers: almost every process in biology is controlled by channels, one way or the other. Ionic channels are manipulated with the powerful techniques of molecular biology in hundreds of laboratories. Atoms (and thus charges) can be substituted a few at a time and the location of every atom can be determined in favorable cases. Ionic channels are one of the few living systems of great importance whose natural biological function can be well described by a tractable set of equations. Ions can be studied as complex fluids in the tradition of physical science although classical treatments as simple fluids have proven inadequate and must be abandoned in my view. Ion channels can be studied by Poisson-Drift diffusion equations familiar in plasma and semiconductor physics ¡X called Poisson Nernst Planck or PNP in biology. Ions have finite size and so the Fermi distribution must be introduced to describe their filling of volume. The PNP-Fermi equations form an adequate model of current voltage relations in many types of channels under many conditions if extended to include correlations, and can even describe ¡¥chemical¡¦ phenomena like selectivity with some success. My collaborators and I have shown how the relevant equations can be derived (almost) from stochastic differential equations, and how they can be solved in inverse, variational, and direct problems using models that describe a wide range of biological situations with only a handful of parameters that do not change even when concentrations change by a factor of 107. Variational methods hold particular promise as a way to solve problems outstanding for more than a century because they describe interactions of ¡¥everything with everything¡¦ else that characterize ions crowded into channels. An opportunity exists to apply the well established methods of computational physics to a central problem of computational biology. The plasmas of biology can be analyzed like the plasmas of physics.
  • Thematic program: Models in Biology and Medicine (MOBAM-16) (2016)

Talks of the past month


Chris Rogers (U. Cambridge) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Fri, 23. Sep 16, 17:30
"High-frequency data: why are we looking at this?"
High-frequency financial data is certainly a `big data' problem, with all of the associated issues: what are the stylized facts of the data? what are we trying to do with the data? what are appropriate models? Industry approaches get the first two of these questions, but do badly on the third. Most academic studies do badly on all three. For example, it is a fairy tale that we can propose a time-invariant model for the evolution of high-frequency data, estimate the parameters of this model, and then apply the conclusions of an analysis that assumes that the paramters were known with certainty. In this talk, I will try to identify what we might want to do with high-frequency data, critique some existing research agendas, and illustrate a possible way of dealing with the problem of optimally liquidating a given position before a given time.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Mark Podolskij (U. Aarhus) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Fri, 23. Sep 16, 16:30
"Testing for the maximal rank of the volatility process in noisy diffusion models"
In this talk we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high frequency observations we construct a test statistic for the maximal rank of the time varying stochastic volatility process. We will show the asymptotic mixed normality of the test statistic and obtain a consistent testing procedure. Finally, we demonstrate some numerical and empirical illustrations.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Albert Menkveld (VU. Amsterdam) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Fri, 23. Sep 16, 15:00
"High-Frequency Trading around Large Institutional Orders"
Liquidity suppliers lean against the wind. We analyze whether high-frequency traders (HFTs) lean against large institutional orders that execute through a series of child orders. The alternative is that HFTs go “with the wind” and trade in the same direction. We find that HFTs initially lean against orders but eventually turn around and go with them for long-lasting orders. This pattern explains why institutional trading cost is 46% lower when HFTs lean against the order (by one standard deviation) but 169% higher when they go with it. Further analysis supports recent theory, suggesting HFTs “back-run” on informed orders.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Philip Protter (U. Columbia) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Fri, 23. Sep 16, 14:00
"High Frequency Trading and Insider Trading"
The attorney general for New York State, Eric Schneiderman, said at one point that he believed that high frequency trading (in the sense of co-location, that is to say extremely high frequency trading) is used for insider trading. Inspired by his remarks we purport to indicate via a mathematical model how this could come to pass. We use the newly developed theory (by Y. Kchia and this speaker) on the enlargement of filtrations via a stochastic process to show how continual infinitesimal peaks at the order book can beget a type of insider trading, thereby explaining the casual observation of the attorney general.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Mathieu Rosenbaum (U. Paris VI) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Fri, 23. Sep 16, 11:30
"How to predict the consequences of a tick value change? Evidence from the Tokyo Stock Exchange pilot program"
The tick value is a crucial component of market design and is often considered the most suitable tool to mitigate the effects of high frequency trading. The goal of this paper is to demonstrate that the approach introduced in Dayri and Rosenbaum (2015) allows for an ex ante assessment of the consequences of a tick value change on the microstructure of an asset. To that purpose, we analyze the pilot program on tick value modifications started in 2014 by the Tokyo Stock Exchange in light of this methodology. We focus on forecasting the future cost of market and limit orders after a tick value change and show that our predictions are very accurate. Furthermore, for each asset involved in the pilot program, we are able to de ne (ex ante) an optimal tick value. This enables us to classify the stocks according to the relevance of their tick value, before and after its modification. This is joint work with Charles-Albert Lehalle and Weibing Huang.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Hung Luong (U. Wien) WPI, OMP 1, Seminar Room 08.135 Fri, 23. Sep 16, 10:30
"Zakharov-Rubenchik/Benney-Roskes system on the background of a line soliton"
In order to study the transverse (in) stability of a line soliton, we consider the 2-d Zakharov-Rubenchik/Benney-Roskes system with initial data localized by a line soliton. The new terms in perturbed system lead to some diculties, for example, the lack of mass conservation. In this talk, I will present our recent work on this problem. This is a joint work with Norbert Mauser and Jean-Claude Saut. 1
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Torben G. Andersen (U. Northwestern) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Fri, 23. Sep 16, 10:00
"Intraday Trading Invariance in Foreign Exchange Futures"
Prior work of Andersen, Bondarenko, Kyle and Obizhaeva (2015) establishes that the intraday trading patterns in the E-mini S&P 500 futures contract are consistent with the following invariance relationship: The return variation per transaction is log-linearly related to trade size, with a slope coefficient of -2. This association applies both across the intraday diurnal pattern and across days in the time series. The factor of proportionality deviates sharply from prior hypotheses relating volatility to transactions count or trading volume. This paper documents that a similar invariance relation holds for foreign exchange futures. However, the log-linear association is not fixed, but shifts over time reflecting an, all else equal, declining trend in the average trade size. The findings are remarkably robust across the full set of currency contracts explored, providing challenges to market microstructure research to rationalize these tight intraday and intertemporal interactions among key market activity variables. Co-authored with Oleg Bondarenko, University of Illinois at Chicago.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Felipe Linares (IMPA) WPI, OMP 1, Seminar Room 08.135 Fri, 23. Sep 16, 9:30
"On special regularity properties of solutions to the k-generalized Korteweg-de Vries equation"
We will discuss special regularity properties of solutions to the IVP associated to the k-generalized KdV equations. We show that for data u0 2 H3=4+(R) whose restriction belongs to Hk((b;1)) for some k 2 Z+ and b 2 R, the restriction of the corresponding solution u(; t) belongs to Hk(( ;1)) for any 2 R and any t 2 (0; T). Thus, this type of regularity propagates with in nite speed to its left as time evolves. This kind of regularity can be extended to a general class of nonlinear dispersive equations. Recently, we proved that the solution ow of the k-generalized KdV equation does not preserve other kind of regularities exhibited by the initial data u0.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Pete Kyle (U. Maryland) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Fri, 23. Sep 16, 9:00
"Dimensional Analysis and Market Microstructure Invariance"
In this talk we focus on the combination of dimensional analysis, leverage neutrality, and a principle of market microstructure invariance to derive scaling laws expressing transaction costs functions, bid-ask spreads, bet sizes, number of bets, and other financial variables in terms of dollar trading volume and volatility. The scaling laws are illustrated using data on bid-ask spreads and number of trades for Russian stocks. These scaling laws provide useful metrics for risk managers and traders; scientific benchmarks for evaluating controversial issues related to high frequency trading, market crashes, and liquidity measurement; and guidelines for designing policies in the aftermath of financial crisis.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Jean-Philippe Bouchaud (CFM, Paris) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 22. Sep 16, 18:00
"The square root law of Price Impact and the intrinsic fragility of financial markets"
We will review the accumulating empirical evidence for an approximately square-root impact of a metaorder. Interestingly, this square-root law appears to be universal, i.e. to a large extent ndependent of markets (futures, equities, volatility, Bitcoin), microstructure and epochs (pre and post HFT). This suggests that this law must originate from a simple and robust statistical mechanism. We propose a dynamical theory of the latent market liquidity that predicts that the average supply/demand profile is V shaped and vanishes around the current price, leading to the square-root impact. This result only relies on mild assumptions about the order flow and on diffusive prices. We test our arguments numerically using a minimal model of order flow and provide further theoretical predictions that can be compared to further experimental observations. Our scenario suggests that markets are intrinsically prone to liquidity crises and puts in perspective the recent debate on the role of HFT liquidity.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Frank Hatheway (NASDAQ) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 22. Sep 16, 17:00
"We have all become High-Frequency Traders: What are some implications?"
Competitive and regulatory forces in the U.S. have resulted in almost all equity executions being handled using sophisticated electronic trading systems. Empirical evidence from Nasdaq shows that order submission patterns once restricted to proprietary trading firms, the prototypical High Frequency Trader, are now observed in orders originating from almost all types of market participants. One aspect of the widespread automation of trading is that the use of "price taker" algorithms has become increasingly prevalent. The implications for the market where each algorithm's order placement decision is dependent on other algorithms' order placement decisions is not well understood. Some consequences of widespread "price taking" behavior are seen every trading day as well as on occasional events such as the May 6, 2010 and August 24, 2015 market breaks. The public policy discussion around market structure needs a better understanding of how the automated price setting mechanism works under the current structure and would work under future alternative market structure designs.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Francois Golse (U.Ecole Polytechnique) WPI, OMP 1, Seminar Room 08.135 Thu, 22. Sep 16, 15:30
"The Mean-Field Limit for the Quantum N-Body Problem: Uniform in Convergence Rate"
The Hartree equation can be derived from the N-body Heisenberg equation by the mean-field limit assuming that the particle number N tends to infinity. The first rigorous result in this direction is due to Spohn (1980) (see also [Bardos-Golse-Mauser, Meth. Applic. Anal. 7:275-294, (2000)] for more details), and is based on analyzing the Dyson series representing the solution of the BBGKY hierarchy in the case of bounded interaction potentials.This talk will (1) provide an explicit convergence rate for the Spohn method, and (2) interpolate the resulting convergence rate with the vanishing h bound obtained in [Golse-Mouhot-Paul, Commun. Math. Phys. 343:165-205 (2016)] by a quantum variant of optimal transportation modulo O(h) terms. The final result is a bound for a Monge-Kantorovich-type distance between the Husimi transforms of the Hartree solution and of the first marginal of the N-body Heisenberg solution which is independent of h and vanishes as N tends to infinity. (Work in collaboration with T. Paul and M. Pulvirenti).
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Terrence Hendershott (UC. Berkeley) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 22. Sep 16, 15:30
"Price Discovery Without Trading: Evidence from Limit Orders"
Adverse selection in financial markets is traditionally measured by the correlation between the direction of market order trading and price movements. We show this relationship has weakened dramatically with limit orders playing a larger role in price discovery and with high-frequency traders’ (HFTs) limit orders playing the largest role. HFTs are responsible for 60–80% of price discovery, primarily through their limit orders. HFTs’ limit orders have 50% larger price impact than non-HFTs’ limit orders, and HFTs submit limit orders 50% more frequently. HFTs react more to activity by non-HFTs than the reverse. HFTs react more to messages both within and across stock exchanges.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Mathieu Colin (U. Bordeaux I) WPI, OMP 1, Seminar Room 08.135 Thu, 22. Sep 16, 14:30
"Stability properties for a Maxwell-Schrödinger System"
The aim of this talk is to present some qualitative properties of a coupled Maxwell-Schrödinger system. First, I will describe conditions for the existence of minimizers with prescribed charge in terms of a coupling constant e. Secondly, I will study the existence of ground states for the stationary problem, the uniqueness of ground states for small e and finish with the orbital stability for the quadratic nonlinearity. This is a joint work with Tatsuya Watanabe.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Thierry Foucault (HEC Paris) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 22. Sep 16, 14:30
"Data Abundance and Asset Price Informativeness"
Investors can acquire either raw or processed information about the payoff of risky assets. Information processing filters out the noise in raw information but it takes time. Hence, investors buying processed information trade with a lag relative to investors buying raw information. As the cost of raw information declines, more investors trade on it, which reduces the value of processed information, unless raw information is very unreliable. Thus, a decline in the cost of raw information can reduce the demand for processed information and, for this reason, the informativeness of asset prices in the long run.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Rama Cont (Imperial College London) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 22. Sep 16, 12:00
"Algorithmic trade execution and intraday market Dynamics"
''Optimal execution'' are typically derived assuming an exogenous Price process which is unaffected by the trading behaviour of market participants. On the other hand, in intraday price behavior in electronic markets reveals evidence of the price impact of algorithmic order flow, an extreme example being the 'Flash Crashes' repeatedly observed in such markets. We propose a simple model for analyzing the feedback effects which arise in a market where participants use market signals to minimize the impact of their trade execution. We show that commonly used execution algorithms which aim at reducing market impact of trades can actually lead to unintended synchronization of participants' order flows, increase their market impact and generate large « self-exciting » intraday swings in volume and volatility. We show that such bursts may occur even in absence of large orders, and lead to a systematic underperformance of 'optimal execution' strategies. These results call for a critical assessment of "optimal execution" algorithms and point to a notion of order flow toxicity distinct from information asymmetry or adverse selection.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Evelyne Miot (U. Grenoble Alpes) WPI, OMP 1, Seminar Room 08.135 Thu, 22. Sep 16, 11:30
"Collision of vortex Filaments"
In this talk we will present some results on the dynamics of vortex filaments according to a model introduced by Klein, Majda and Damodaran, focusing on the issue of collisions. This is a joint work with Valeria Banica and Erwan Faou.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Oana Ivanovici (U. Nizza) WPI, OMP 1, Seminar Room 08.135 Thu, 22. Sep 16, 10:30
"Dispersion for the wave and the Schrödinger Equations outside strictly convex Domains and counterexamples"
We consider the linear wave equation and the linear Schr dingier equation outside a compact, strictly convex obstacle in R^d with smooth boundary. In dimension d = 3 we show that for both equations, the linear flow satises the (corresponding) dispersive estimates as in R^3. For d>3, if the obstacle is a ball, we show that there exists at least one point (the Poisson spot) where the dispersive estimates fail. This is joint work with Gilles Lebeau.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Jonathan Brogaard (U. Washington) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 22. Sep 16, 10:30
"High-Frequency Trading Competition"
Using a firm-identified limit-order book dataset we show that competition among high-frequency trading firms (HFT) influences liquidity. HFT entries increase liquidity. The reverse is true for exits. Market participants’ behavioral changes are consistent with competitive pressure. HFT entries increase total HFT market share and take market share from incumbents. After HFT entry (exit), incumbent HFT spreads tighten (widen). Trading revenue suggests competition reduces HFT firm profitability. Impacts are larger in markets with fewer incumbents. The results show that part of the value of HFT comes from its competitiveness.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Thomas Duyckaerts (U. Paris XIII) WPI, OMP 1, Seminar Room 08.135 Thu, 22. Sep 16, 9:30
"Dynamics of the energy-critical wave equation"
It is conjectured that bounded solutions of the focusing energy-critical wave equation decouple asymptotically as a sum of a radiation term and a finite number of solitons . In this talk, I will review recent works on the subject, including the proof of a weak form of this conjecture (joint work with Hao Jia, Carlos Kenig and Frank Merle)
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Andrei Kirilenko (Imperial College London) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 22. Sep 16, 9:30
"Latency in Automated Trading Systems"
Time in an automated trading system does not move in a constant deterministic fashion. Instead, it is a random variable drawn from a distribution. This happens because messages enter and exit automated systems though different gateways and then race across a complex infrastructure of parallel cables, safeguards, throttles and routers into and out of the central limit order books. Add to it market fragmentation and you get a pretty complex picture about the effects of latency on price formation.
  • Thematic program: Mathematical Finance (FINANCE-16) (2016)
  • Event: High-Frequency Trading - Curse or Blessing (2016)

Mauser, Norbert (Inst. CNRS Pauli c/o Fak. Mathematik U. Wien) OMP 1, Fakultät für Mathematik, 1090 Wien Wed, 21. Sep 16, 19:00
Austro - Französische Mathematik: ein Diskurs
Warum ist Frankreich das weltweit führende Land in Mathematik ? Warum gibt es in Frankreich eine Sektion 25 und eine Sektion 26 - und in Österreich eine Sektion Forschung und eine Sektion Universitäten ?! Warum gibt es 2 französische Fields-Medaillen zur Boltzmanngleichung ? Warum ist eines der nur 3 europäischen CNRS Institute « extra muros » am WPI in Wien ? Warum kommen viele österreichische Spitzenmathematiker vom Lycée français de Vienne ? Diese und andere interessante Fragen wird uns Herr Prof. Mauser in seinem Vortrag (in deutscher Sprache) beantworten.
Note:   Click here for further information

Mats Ehrnström (NTNU) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Sep 16, 15:30
"Existence of a Highest Wave in a Full-Dispersion Shallow Water Model"
We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full two-way dispersion relation from the incompressible Euler equations with a canonical quadratic shallow water nonlinearity. Of particular interest is the existence of a highest, cusped, traveling wave solution, which we obtain as a limiting case at the end of the main bifurcation branch of $2pi$-periodic traveling wave solutions. Unlike the unidirectional Whitham equation, containing only one branch of the full Euler dispersion relation, where such a highest wave behaves like $|x|^{1/2}$ near its peak, the cusped waves obtained here behave like $|xlog|x||$ at their peak and are smooth away from their highest points. This is joint work with Mathew A. Johnson and Kyle M. Claassen at University of Kansas.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Eric Wahlen (NTNU) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Sep 16, 14:30
"On the highest wave for Whitham’s wave equation"
In the 1960’s G. B. Whitham suggested a non-local version of the KdV equation as a model for water waves. Unlike the KdV equation it is not integrable, but it has certain other advantages. In particular, it has the same dispersion relation as the full water wave problem and it allows for wave breaking. The equation has a family of periodic, travelling wave solutions for any given wavelength. Whitham conjectured that this family contains a highest wave which has a cusp at the crest. I will outline a proof of this conjecture using global bifurcation theory and precise information about an integral operator which appears in the equation. Joint work with M. Ehrnström.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Thomas Alazard (ENS) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Sep 16, 11:30
"Control and stabilization of the incompressible Euler equation with free surface"
The incompressible Euler equation with free surface dictates the dynamics of the interface separating the air from a perfect incompressible fluid. This talk is about the controllability and the stabilization of this equation. The goal is to understand the generation and the absorption of water waves in a wave tank. These two problems are studied by two different methods: microlocal analysis for the controllability (this is a joint work with Pietro Baldi and Daniel Han-Kwan), and study of global quantities for the stabilization (multiplier method, Pohozaev identity, hamiltonian formulation, Luke’s variational principle, conservation laws…).
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Hajer Bahouri (UPEC) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Sep 16, 10:30
"Qualitative study of 2D Schrodinger equation with exponential nonlinearity"
In this lecture, we investigate the behavior of the solutions to the nonlinear Schrodinger equation: (1) ( i@tu + u = f(u); ujt=0 = u0 2 H1 rad(R2); where the nonlinearity f : C ! C is de ned by (2) f(u) = p( p 4 juj) u with p > 1 and p(s) = es2 􀀀 pX􀀀1 k=0 s2k k!  Recall that the solutions of the Cauchy problem (1)-(2) formally satisfy the conservation laws: (3) M(u; t) = Z R2 ju(t; x)j2dx = M(u0) and (4) H(u; t) = Z R2  jru(t; x)j2 + Fp(u(t; x))  dx = H(u0) ; where Fp(u) = 1 4 p+1 􀀀p 4 juj   It is known (see [4], [6] and [2]) that global well-posedness for the Cauchy problem (1)-(2) holds in both subcritical and critical regimes in the functional space C(R;H1(R2)) L4(R;W1;4(R2)). Here the notion of criticity is related to the size of the initial Hamiltonian H(u0) with respect to 1. More precisely, the concerned Cauchy problem is said to be subcritical if H(u0) < 1, critical if H(u0) = 1 and supercritical if H(u0) > 1. Structures theorems originates in the elliptic framework in the studies by H. Brezis and J.- M. Coron in [3] and M. Struwe in [8]. The approach that we shall adopt in this article consists in comparing the evolution of oscillations and concentration e ects displayed by sequences of solutions of the nonlinear Schrodinger equation (1)-(2) and solutions of the linear Schrodinger equation associated to the same sequence of Cauchy data. Our source of inspiration here is the pioneering works [1] and [7] whose aims were to describe the structure of bounded sequences of solutions to semilinear defocusing wave and Schrodinger equations, up to small remainder terms in Strichartz norms. The analysis we conducted in this work emphasizes that the nonlinear e ect in this framework only stems from the 1-oscillating component of the sequence of the Cauchy data, using the terminology introduced in [5]. This phenomenon is strikingly di erent from those obtained for critical semi linear dispersive equations, such as for instance in [1, 7] where all the oscillating components induce the same nonlinear e ect, up to a change of scale. To carry out our analysis, we have been led to develop a pro le decomposition of bounded sequences of solutions to the linear Schrodinger equation both in the framework of Strichartz and Orlicz norms. The linear structure theorem we have obtained in this work highlights the distinguished role of the 1-oscillating component of the sequence of the Cauchy data. It turns out that there is a form of orthogonality between the Orlicz and the Strichartz norms for the evolution under the ow of the free Schrodinger equation of the unrelated component to the scale 1 of the Cauchy data (according to the vocabulary of [5]), while this is not the case for the 1-oscillating component.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Vincent Duchêne (U. Rennes I) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Sep 16, 9:30
"On the well-posedness of the Green-Naghdi System"
The Green-Naghdi system is an asymptotic model for the water-waves system, describing the propagation of surface waves above a layer of ideal, homogeneous, incompressible and irrotational fluid, when the depth of the layer is assumed to be small with respect to wavelength of the flow. It can be seen as a perturbation of the standard quasilinear (dispersionless) Saint-Venant system, with additional nonlinear higher-order terms. Because of the latter, the well-posedness theory concerning the GN system is not satisfactory, in particular outside of the one-dimensional framework. We will discuss novel results, obtained with Samer Israwi, that emphasize the role of the irrotationality assumption.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Christian Klein (U.Bourgogne) WPI, OMP 1, Seminar Room 08.135 Tue, 20. Sep 16, 15:30
"Numerical study of break-up in Kadomtsev-Petviashvili equations"
The onset of a dispersive shock in solutions to the Kadomtsev-Petviashvili (KP) equations is studied numerically. First we study the shock formation in the dispersionless KP equation by using a map inspired by the characteristic coordinates for the one-dimensional Hopf equation. This allows to numerically identify the shock and to unfold the singularity. A conjecture for the KP solution near this critical point in the small dispersion limit is presented. It is shown that dispersive shocks for KPI solutions can have a second breaking where modulated lump solutions appear.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Thomas Kappeler (U. Zürich) WPI, OMP 1, Seminar Room 08.135 Tue, 20. Sep 16, 14:30
"Analytic extensions of frequencies of integrable PDEs and applications"
In form of a case study for the mKdV and the KdV2 equation we discuss a novel approach of representing frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include wellposedness results in spaces of low regularity as well as properties of the actions to frequencies map. This is joint work with Jan Molnar.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Laurent Thomann (U. Lorraine) WPI, OMP 1, Seminar Room 08.135 Tue, 20. Sep 16, 11:30
"Invariant measures for NLS in dimension two"
We consider the defocusing nonlinear Schrödinger equations on a two-dimensional compact Riemannian manifold without boundary or a bounded domain in dimension two. In particular, we discuss the Wick renormalization in terms of the Hermite polynomials and the Laguerre polynomials and construct the Gibbs measures corresponding to the Wick ordered Hamiltonian. Then, we construct global-in-time solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Nicola Visciglia (U. Pisa) WPI, OMP 1, Seminar Room 08.135 Tue, 20. Sep 16, 10:30
"Existence and Stability of Standing Waves for NLS in a partial confinement"
I will discuss a joint work with Bellazzini, Boussaid, Jeanjean about the existence and orbital stability of standing waves for NLS with a partial confinement in a supercritical regime. The main point is to show the existence of local minimizers of the constraint energy.
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)

Philippe Gravejat (U. Cergy-Pontoise) WPI, OMP 1, Seminar Room 08.135 Tue, 20. Sep 16, 9:30
"Stability of solitons for the Landau-Lifshitz equation with an easy-plane anisotropy"
We describe recent results concerning the orbital and asymptotic stability of dark solitons and multi- solitons for the Landau-Lifshitz equation with an easy-plane anisotropy. This is joint work with André de Laire (University of Lille Nord de France), and by Yakine Bahri (Nice Sophia Antipolis University).
  • Thematic program: Classical and Quantum Transport (TRANSPORT-16) (2016)
  • Event: Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems" (2016)
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