Weekly Bulletin

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Monday, 22 May
Time Speaker Title Location
09:15 - 11:00 Prof. Dr. Richard Schoen
University of California, Irvine
Topics in scalar curvature
HG G 43 
13:15 - 14:45 Prof. Dr. Gerard Freixas Montplet
Institut de Mathématiques de Jussieu
Oberseminar: Algebraische Geometrie (uzh)
Families of curves, flat line bundles and reciprocity laws.
Y27  H 25
15:15 - 16:15 Paolo Guasoni 
Dublin City University
Talks in Financial and Insurance Mathematics
Optimal Consumption and Investment with Healthcare Spending 
HG G 19.2 
Abstract: Health-care slows the natural growth of mortality, indirectly increasing utility from consumption through longer lifetimes. We solve the problem of optimal dynamic investment, consumption, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect the Gompertz' law and investment opportunities are constant. Optimal consumption and healthcare imply an endogenous mortality law that is asymptotically exponential in the old-age limit, with lower growth rate than natural mortality. Health spending steadily increases with age, both in absolute terms and relative to total spending. The optimal stochastic control problem reduces to a nonlinear ordinary differential equation with a unique solution, which has an explicit expression in the old-age limit. Differential access to healthcare can account for observed longevity gains across cohorts.
16:30 - 17:30 Dr. Andrea Baggio 
ETH Zurich, Switzerland
Optimization Seminar
Efficient Infrastructure Planning and Room Scheduling for a New Surgery Center
HG G 19.1 
17:15 - 18:15 Prof. Dr. Stefan Hell
MPI Göttingen & Heidelberg
Wolfgang Pauli Lectures
Lecture 1: How I Got to Break the Diffraction Barrier of Optical Microscopy
HG F 30 
Tuesday, 23 May
Time Speaker Title Location
13:30 - 14:30 Lavinia Heisenberg
ETH Institute for Theoretical Studies
ETH-ITS Fellows' Seminar
Our Mysterious Dark Universe 
CLV B 4 
Abstract: After giving an introduction into modern cosmology and the incredible progresses it witnessed, I will summarise the theoretical and observational challenges that we are facing in the standard model of cosmology. I will then introduce different ideas proposed in the literature to tackle these problems within modified gravity theories, among which I will pay special attention to massive gravity, scalar-tensor theories and generalised Proca theories on curved space-time.
15:15 - 16:15 Prof. Dr. Walter Craig
McMaster University
Analysis Seminar
Vortex filament dynamics 
HG G 43 
Abstract: The evolution of vortex filaments in three dimensions is a central problem in mathematical hydrodynamics, appearing in questions on solutions of the Euler equations as well as in the fine structure of vortex filamentation in a superfluid. It is also a setting in the analysis of partial differential equations with a compelling formulation as a Hamiltonian dynamical systems in an infinite dimensional phase space. I will give an analysis of a system of model equations for the dynamics of near-parallel vortex filaments in a three dimensional fluid. These equations can be formulated as Hamiltonian PDEs, and the talk will describe some aspects of a phase space analysis of solutions, including the construction of periodic and quasi-periodic orbits via a version of KAM theory for PDEs, and a topological principle to count multiplicity of solutions. This is ongoing joint work with L. Corsi (Georgia Tech), C.
17:15 - 18:15 Prof. Dr. Stefan Hell
MPI Göttingen & Heidelberg
Wolfgang Pauli Lectures
Lecture 2: Nanoscopy with Focused Light
HG F 30 
17:15 - 18:30 Merlin Incerti-Medici
Universität Zürich
Zurich Graduate Colloquium (uzh)
What is... Möbius geometry?
KO2  F 150
Wednesday, 24 May
Time Speaker Title Location
10:15 - 12:00 Prof. Dr. Eitan Tadmor
University of Maryland & ETH-ITS
Self-organized dynamics. From emerging consensus to hydrodynamic flocking
HG G 43 
13:30 - 15:00 Dr. Nicola Tarasca
Univ. of Georgia
Algebraic Geometry and Moduli Seminar
K-classes of Brill-Noether loci and a determinantal formula 
HG G 43 
Abstract: I will present a formula for the Euler characteristic of the structure sheaf of Brill-Noether loci of linear series on curves with prescribed vanishing at marked points. The formula recovers the classical Castelnuovo number in the zero-dimensional case, and previous results of Eisenbud-Harris, Pirola, Chan-López-Pflueger-Teixidor in the curve case. The result follows from a new determinantal formula for the K-theory class of certain degeneracy loci of maps of flag bundles. This is joint work with Dave Anderson and Linda Chen.
15:30 - 16:30 Prof. Dr. Stefan Hell
MPI Göttingen & Heidelberg
Wolfgang Pauli Lectures
Lecture 3: Optical Nanoscopy: Concepts and Recent Advances
HCI G 3 
16:15 - 17:15 Prof. Dr. Mikhail Shashkov
Los Alamos National Laboratory
Zurich Colloquium in Applied and Computational Mathematics
Modern numerical methods for high-speed, compressible, multi-physics, multi-material flows 
KOL  G 201
Abstract: Computational experiment is among the most significant developments in the practice of the scientific inquiry in the 21th century. Within last four decades, computational experiment has become an important contributor to all scientific research programs. It is particular important for the solution of the research problems that are insoluble by traditional theoretical and experimental approaches, hazardous to study in the laboratory, or time consuming or expensive to solve by traditional means. Computational experiment includes several important ingredients: creating mathematical model, discretization, solvers, coding, verification and validation, visualization, analysis of the results, etc. In this talk we will describe some aspects of the modern numerical methods for high-speed, compressible, multi-physics, multi-material flows. We will address meshing issues, mimetic discretizations of equations of the Lagrangian gas dynamics and diffusion equation on general polygonal meshes, mesh adaptation strategies, methods for dealing with shocks, interface reconstruction needed for multi-material flows, closure models for multi-material cells, time discretizations, etc.
17:15 - 18:15 Fabio Martinelli
Università di Roma Tre
Seminar on Stochastic Processes
Bootstrap percolation and interacting particle systems with kinetic constraints: critical time and length scales 
Y27  H 12
Abstract: Recent years have seen a great deal of progress in understanding the behaviour of bootstrap percolation models, a particular class of monotone cellular automata. In the two dimensional lattice there is now a quite satisfactory understanding of their evolution starting from a random initial condition, with a strikingly beautiful universality picture for their critical behaviour (length and time scales). Mu ch less is known for their non-monotone stochastic counterpart, namely kinetically constrained models (KCM). In a KCM the state of each vertex which could be infected by the bootstrap percolation rules is resampled (independently among the vertices) at rate one by tossing a p-coin. In particular infection can also heal, hence the non-monotonicity. Besides their connection with bootstrap percolation, KCMs have an strong interest in their own : as p ↓ 0 they display some of the most striking features of the liquid/glass transition, a major and still largely open problem in condensed matter physics. In this talk, after an introductory first part, I shall discuss (i) some recent conjectures relating the universality behaviour of critical KCMs to their bootstrap percolation counterpart and (ii) some very recent progresses towards proving the above conjectures. Joint project with C. Toninelli (Paris VII) and R. Morris (IMPA).
Thursday, 25 May
— no events scheduled today —
Friday, 26 May
Time Speaker Title Location
14:00 - 14:55 José Carrillo
Imperial College London
Collective dynamics, control and imaging
Swarming models with local alignment effects: phase transition & hydrodynamics 
LEE E 101 
Abstract: I will make a review of swarming models with repulsive-attractive effects focusing on two new aspects: phase transitions for the local Cucker-Smale type model and self-organized hydrodynamics of the Vicsek model with fixed speed from asymptotic speed Cucker-Smale models by penalization. In short, we will show that the asymptotic speed Cucker-Smale model behaves in terms of hydrodynamics and phase transitions as the Vicsek model with fixed speed for large friction parameter.
14:15 - 15:15 Tiago Fonseca
Université Paris-Sud
Number Theory Seminar
Higher Ramanujan equations and periods of abelian varieties 
HG G 43 
Abstract: The Ramanujan equations are some algebraic differential equations satisfied by the classical Eisenstein series E_2, E_4, E_6. These equations play a pivotal role in the proof of Nesterenko's celebrated theorem on the algebraic independence of values of Eisenstein series, which gives in particular a lower bound on the transcendence degree of fields of periods of elliptic curves. Motivated by the problem of extending the methods of Nesterenko to other settings, we shall explain in this talk how to generalize Ramanujan's equations to higher dimensions via a geometric approach, and how the values of a particular solution of these equations relate with periods of abelian varieties.
15:15 - 16:10 Florian Dörfler
ETH Zürich
Collective dynamics, control and imaging
Almost global synchronization in complex oscillator networks with applications in power system 
LEE E 101 
Abstract: In this seminar we study the problem of almost global stability in networks of coupled and heterogeneous oscillators as well as applications thereof to power systems. We begin our investigation with networks of so-called phase oscillators, in particular the Kuramoto model for which the review the available results as well as the obstructions to almost global synchronization. Next we showcase the utility of phase oscillator models for analysis and control in power systems. This application motivates us to study more general state-space oscillator models which are useful for control in power grids dominated by renewable sources interfaced with power converters. We demonstrate how our oscillator-inspired and fully decentralized controllers for power converters achieve almost global synchronization on a common harmonic solution with synchronous frequency, pre-defined oscillation amplitudes, and desired phase angle differences.
16:30 - 17:25 Josselin Garnier
École Polytechnique, Paris
Collective dynamics, control and imaging
Stability of mean field model for opinion dynamics and collective motion 
LEE E 101 
Abstract: In this talk, we consider two models for opinion dynamics (consensus model) and for collective motion (Czirok model). In each model, each agent's opinion or velocity locally interacts with other agents' opinions or velocities in the system. The interaction tends to create consensus convergence or alignment of collective motion. By analyzing the associated nonlinear Fokker-Planck equation, we obtain the conditions for the existence of stationary states and the conditions for their stabilities. In both cases exogenous noise stabilizes the systems. This is a joint work with G. Papanicolaou and T.-W. Yang.

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