# Weekly Bulletin

Monday, 24 April
Time Speaker Title Location
13:15 - 14:45 Dr. Jean-Baptiste Teyssier
KU Leuven
Oberseminar: Algebraische Geometrie (uzh)
Skeletons and moduli of Stokes torsors
Y27  H 25
Tuesday, 25 April
Time Speaker Title Location
13:30 - 14:30 Jean-Michel Coron
ETH-ITS and Pierre-and-Marie-Curie University
ETH-ITS Fellows' Seminar
CLV B 4
Abstract: A control system is a dynamical system on which one can act thanks to what is called the control. For example, in a car, one can turn the steering wheel, press the accelerator pedal etc. These are the control(s). One of the main problems in control theory is the controllability problem. It is the following one. One starts from a given situation and there is a given target. The controllability problem is to see if, by using some suitable controls depending on time, one can move from the given situation to the prescribed target. We study this problem with a special emphasis on the case where the nonlinearities play a crucial role. We first recall some classical results on this problem for finite dimensional control systems. We explain why the main tool used for this problem in finite dimension, namely the iterated Lie brackets, is difficult to use for many important control systems modeled by partial differential equations. We present methods to avoid the use of iterated Lie brackets. We give applications of these methods to various physical control systems (Euler and Navier-Stokes equations of incompressible fluids, 1-D hyperbolic systems, heat equations, shallow water equations, Korteweg-de Vries equations, Schroedinger equations…).
15:15 - 16:15 Prof. Dr. Matteo Bonforte
Analysis Seminar
HG G 43
Abstract: We investigate quantitative properties of nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + \mathcal{L} F(u)=0$ posed in a bounded domain, $x\in\Omega\subset \mathbb{R}^N$\,, with appropriate homogeneous Dirichlet boundary conditions. As $\mathcal{L}$ we can use a quite general class of linear operators that includes the three most common versions of the fractional Laplacian $(-\Delta)^s$, $01$\,. We will shortly present some recent results about existence, uniqueness and a priori estimates for a quite large class of very weak solutions, that we call weak dual solutions. We will devote special attention to the regularity theory: decay and positivity, boundary behavior, Harnack inequalities, interior and boundary regularity, and asymptotic behavior. All this is done in a quantitative way, based on sharp a priori estimates. Although our focus is on the fractional models, our techniques cover also the local case s = 1 and provide new results even in this setting. A surprising instance of this problem is the possible presence of nonmatching powers for the boundary behavior: for instance, when $\mathcal{L}=(-\Delta)^s$ is a spectral power of the Dirichlet Laplacian inside a smooth domain, we can prove that, whenever $2s \ge 1 - 1/m$, solutions behave as $dist^{1/m}$ near the boundary; on the other hand, when $2s < 1 - 1/m$, different solutions may exhibit different boundary behaviors even for large times. This unexpected phenomenon is a completely new feature of the nonlocal nonlinear structure of this model, and it is not present in the elliptic case. The above results are contained on a series of recent papers in collaboration with A. Figalli, X. Ros-Oton, Y. Sire and J. L. Vazquez.
17:15 - 18:15 Prof. Dr. Gerhard Huisken
Universität Tübingen + MFO
Zurich Colloquium in Mathematics
„Properties and applications of inverse mean curvature flow“
KO2  F 150
Wednesday, 26 April
Time Speaker Title Location
09:00 - 18:30 Young Researcher Workshop on Robust Mathematical Finance
various talks
HG G 19.1
10:15 - 12:00 Prof. Dr. Eitan Tadmor
University of Maryland & ITS-ETH Zürich
Nachdiplomvorlesung
Self-organized dynamics. From emerging consensus to hydrodynamic flocking
HG G 43
13:30 - 15:00 Dr. Clément Dupont
Université de Montpellier
Algebraic Geometry and Moduli Seminar
HG G 43
Abstract: We will introduce Brown’s moduli spaces, which parametrize genus zero curves. The original motivation is arithmetic and lies in the algebro-geometric study of multiple zeta values. In this talk we will see how these spaces fit in the study of the operadic structures underlying the moduli spaces of genus zero curves. More precisely, we will explain the proof of two essentially equivalent results: the purity of the Hodge structure on the cohomology of Brown’s moduli spaces, and the freeness of the non symmetric operad underlying Getzler’s gravity operad. This is joint work with Bruno Vallette.
14:00 - 15:00 Michela Procesi
Sapienza University of Rome
Dynamics Seminar
CLV B 4
Abstract: I will discuss a recent result in collaboration with Alberto Maspero, concerning the stability of finite gap solutions of the NLS on T^2. More precisely we study the 2d NLS close to a "generic" finite gap solution of the 1d NLS and show that we may perform two steps of Birkhoff normal form.
15:00 - 16:00 Dr. Thijs Laarhoven
IBM Research - Zurich
Arbeitsgemeinschaft in Codierungstheorie und Kryptographie (uzh)
Sieving for shortest lattice vectors using near neighbor techniques
Y27  H 28
15:30 - 16:30 Riccardo Montalto

Dynamics Seminar
CLV B 4
Abstract: I discuss some recent results concerning the existence and linear stability of Cantor families of quasi-periodic solutions of the water waves equations under periodic boundary conditions. The proof is based on several arguments: (i) Nash-Moser iterative scheme (ii) Reduction to constant coefficients of the linearized equation (at any approximate quasi-solutions), which requires to use pseudo-differential calculus (due to the non-local nature of the water waves equations) and a KAM reducibility scheme (iii) Degenerate KAM theory, in order to verify the non-resonance conditions (zeroth, first and second Melnikov conditions) required along the KAM-reducibility scheme.
15:45 - 16:45 Romain Tessera
CNRS-Université Paris-Sud
Geometry Seminar
HG G 43
Abstract: A group has property H_FD if the first reduced cohomology of unitary representations is supported on finite sub-representations. Shalom has proved that this property is stable under quasi-isometry among amenable groups. We generalize this notion to the class of WAP representations, and we prove that this stronger property holds for a class of locally compact solvable groups including algebraic groups over local fields and their lattices. As a by-product we prove a conjecture of Shalom, namely that solvable finitely generated subgroups of GL(Q) have H_FD. This is joint work with Yves Cornulier
16:00 - 17:00 Veronica Estrada Galinanes
Universite de Neuchatel
Arbeitsgemeinschaft in Codierungstheorie und Kryptographie (uzh)
Practical erasure codes for storage systems
Y27  H 28
16:15 - 17:15 Prof. Dr. Xue-Mei Li
University of Warwick
Zurich Colloquium in Applied and Computational Mathematics
Y27  H 25
Abstract: Gaussian upper and lower bounds for heat kernels are the basic tools for large deviation estimates. There are two well known characterisations on the derivatives of heat semi-grouops: the lower bound of the Ricci curvature by gradient bounds on the heat semi-group; and the validity of the Logarithmic Sobolev inequality for the distributions of the Brownian motion by bounds on the Ricci curvature. What can we say about their second order derivatives? What can we say about the kernels of the self-adjoint operator, which is the sum of the Laplace-Beltrami operator plus a gradient vector field and a potential function? This talk will not be technical. We will discuss why the stochastic damped parallel translation and the doubly damped stochastic parallel translation equation are the natural companions for the heat equations, we will also discuss the associated estimates, the second order Feynman-Kac formulas, and the role of the Brownian bridges and the semi-classical Brownian bridges.
17:15 - 18:15 Charles Bordenave
Université de Toulouse
Seminar on Stochastic Processes
Y27  H 12
Abstract: In this general talk, we will review the notion of spectral measures of a graph. We will then explore some of the connections between the local geometry of a random graph and its spectrum. The talk will be partially based on the lecture notes available at http://www.math.univ-toulouse.fr/~bordenave/coursSRG.pdf.
Thursday, 27 April
Time Speaker Title Location
09:00 - 18:15 Young Researcher Workshop on Robust Mathematical Finance
various talks
HG G 19.1
09:15 - 11:00 Prof. Dr. Richard Schoen
University of California, Irvine
Nachdiplomvorlesung
Topics in scalar curvature
HG G 43
16:15 - 17:00 Marjolein Fokkema
Department of Methods and Statistics der Universität Leiden, NL
ZüKoSt Zürcher Kolloquium über Statistik
HG G 19.1
Abstract: Most statistical prediction methods provide a trade-off between accuracy and interpretability. For example, single classification trees may be easy to interpret, but likely provide lower predictive accuracy than many other methods. Random forests, on the other hand, may provide much better accuracy, but are more difficult to interpret, sometimes even termed black boxes. Prediction rule ensembles (PREs) aim to strike a balance between accuracy and interpretability. They generally consist of only a small set of prediction rules, which in turn can be depicted as very simple decision trees, which are easy to interpret and apply. Friedman and Popescu (2008) proposed an algorithm for deriving PREs, which derives a large initial ensemble of prediction rules from the nodes of CART trees and selects a sparse final ensemble by regularized regression of the outcome variable on the prediction rules. The R package ‘pre’ takes a similar approach to deriving PREs and offers several additional advantages. For example, it employs an unbiased tree induction algorithm, allows for a random-forest type approach to deriving prediction rules, and allows for plotting of the final ensemble. In this talk, I will introduce PRE methodology and package 'pre', illustrate with examples based on psychological research data, and discuss some future directions.
16:15 - 17:15 Prof. Dr. Marco Hutter
ETHZ, Inst. f. Robotik u. Intell. Syst.
ITS Science Colloquium
HG E 5
Abstract: Legged robotics is the future when it comes to versatile machines that can move across any terrain. In contrast to classical wheeled or tracked vehicles, they have the potential to move with unperceived agility and grace. In this talk, I will give an insight into our work on legged robots that are used in the field for autonomous inspection and exploration. This includes novel compliant actuators that enable dynamic interaction, model based control algorithms to balance the machine in dynamic gaits, and optimization tools to learn motion trajectory and feedback control parameters. Moreover, I will show how these machines can perceive their environment to localize themselves and to create accurate maps of the surrounding. An overview about our work and the newest robot ANYmal is available on www.rsl.ethz.ch and on our youtube channel: www.youtube.com/leggedrobotics
17:15 - 18:15 Scott Robertson
Boston University
Talks in Financial and Insurance Mathematics
HG G 43
Abstract: We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated Garrtner-Ellis theorem. To highlight the robustness of our main price convergence assumption, we analyze a number of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, the Black-Scholes-Merton model with vanishing transaction costs, and the price impact recently introduced by Bank and Kramkov in the limit of vanishing market maker risk aversion. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models. This is joint work with Constantinos Spilioupoulos (Boston Unviersity) and Michalis Anthropelos (University of Pireaus).
18:10 - 19:30 Prof. Dr. Daniel Tataru
University of California
PDE and Mathematical Physics (uzh)
[Video] The threshold theorem for the hyperbolic Yang-Mills flow
Y27  H 35/36
Friday, 28 April
Time Speaker Title Location
09:00 - 13:00 Young Researcher Workshop on Robust Mathematical Finance
various talks
HG G 19.1
14:00 - 14:55 Georges Bastin
Université Catholique de Louvain
Collective dynamics, control and imaging
LEE E 101
Abstract: The operation of many physical networks having an engineering relevance can be represented by 1-D hyperbolic systems of balance laws. Typical example are hydraulic networks (for water supply, irrigation or navigation), road traffic networks, electrical line networks, gas transportation networks, blood flow networks etc … From an engineering perspective, for such networks, the exponential stability of the steady-states is a fundamental issue. As a matter of fact, the exponential stability closely depends on the so-called dissipativity of the boundary conditions which, in many instances, is a natural physical property of the system. If the boundary conditions are dissipative and if the smooth initial conditions are sufficiently close to the steady state, the system trajectories are guaranteed to remain smooth for all time and to exponentially converge locally to the steady state. In this talk, we shall see how robust dissipativity tests can be derived by using a Lyapunov stability approach. Surprisingly enough, it appears that, even for smooth solutions, the various function norms that can be used to measure the deviation with respect to the steady state are not may give rise to different stability tests. There are also many engineering applications where the dissipativity of the boundary conditions, and consequently the stability, is obtained by using boundary feedback control with actuators and sensors located at the boundaries. The control may be implemented with the goal of stabilization when the system is physically unstable, or simply because boundary feedback control is required to achieve an efficient regulation with disturbance attenuation. Obviously, the challenge in that case is to design the boundary control devices in order to have a good control performance with dissipative boundary conditions. In this talk, this issue will be addressed through a case-study devoted to the control of navigable rivers when the river flow is described by hyperbolic shallow water equations (Saint-Venant equations), illustrated with a real life application of the control of the Sambre and Meuse rivers in Belgium.
15:15 - 16:10 Massimo Fornasier
Technische Universität Münich
Collective dynamics, control and imaging
LEE E 101
Abstract: In the past decade there has been a large scope of studies on mathematical models of social dynamics. Self-organization, i.e., the autonomous formation of patterns, has been so far the main driving concept. Usually first or second order models are considered with given predetermined nonlocal interaction potentials, tuned to reproduce, at least qualitatively, certain global patterns (such as flocks of birds, milling school of fish or line formations in pedestrian flows etc.). However, often in practice we do not dispose of a precise knowledge of the governing dynamics. In the first part of this talk we present a variational and optimal transport framework leading to an algorithmic solution to the problem of learning the interaction potentials from the observation of the dynamics of a multiagent system. Moreover, it is common experience that self-organization of a society does not always spontaneously occur. In the second part of the talk we address the question of whether it is possible to externally and parsimoniously influence the dynamics, to promote the formation of certain desired patterns. In particular we address the issue of finding the sparsest control strategy for finite agent models in order to lead the dynamics optimally towards a given outcome. We eventually mention the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints to an infinite dimensional sparse mean-field optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of the agent population.
16:30 - 17:25 Ron Kimmel
Technion, Haifa
Collective dynamics, control and imaging
LEE E 101
Abstract: We explore the power of the Laplace Beltrami Operator (LBO) in processing and analyzing geometric information. The decomposition of the LBO at one end, and the heat operator at the other end provide us with efficient tools for dealing with images and shapes. Denoising, segmenting, filtering, exaggerating are just few of the problems for which the LBO provides an efficient solution. We will review the optimality of a truncated basis provided by the LBO, and a selection of relevant metrics by which such optimal bases are constructed. Specific example is the scale invariant metric for surfaces that we

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25.04.2017
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