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Upcoming Colloquia & Seminars

  1. Research Seminar: An approach to Nonlinear Evolution Equations via modified energy estimates

    Location: MSRI: Simons Auditorium
    Speakers: Nicola Visciglia (Università di Pisa)

    We present a strategy to solve globally in time some nonlinear PDEs at higher order Sobolev regularity, by relying exclusively on energy estimates. The main point is the introduction of suitable modified energies that allow us to control the higher order Sobolev norms for large times. We shall focus mainly on NLS and nonlinear Half-Wave. Moreover, by using some extra basic informations coming from the dispersion (when available), one can get new results on the polynomial growth of higher order Sobolev norms. The talk is based on a joint work with T. Ozawa (Waseda U.) and on a work in progress with F. Planchon (Nice U.).

    Updated on Aug 27, 2015 01:50 PM PDT
  2. UCB Probability Seminar: Weak Concentration for First Passage Percolation Times on Graphs and General Increasing Set-valued Processes

    Location: 344 Evans Hall UCB
    Speakers: David Aldous (University of California, Berkeley)

    A simple lemma bounds s.d.(T)/\ExT for hitting times T in Markov chains with a certain strong monotonicity property. We show how this lemma may be applied to several increasing set-valued processes. Our main result concerns a model of first passage percolation on a finite graph, where the traversal times of edges are independent Exponentials with arbitrary rates. Consider the percolation time X between two arbitrary vertices. We prove that s.d.(X)/\ExX is small if and only if Ξ/\ExX is small, where Ξ is the maximal edge-traversal time in the percolation path attaining X.

    Updated on Aug 28, 2015 05:23 PM PDT
  3. Graduate Student Lunch Seminar

    Location: MSRI: Baker Board Room
    Updated on Aug 28, 2015 03:58 PM PDT
  4. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 Evans Hall UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Updated on Aug 27, 2015 02:03 PM PDT
  5. Postdoc Symposium (Part I) - Initial and boundary value problems for the deterministic and stochastic Zakharov-Kuznetsov equation in a bounded domain

    Location: MSRI: Simons Auditorium
    Speakers: Chuntian Wang (University of California)
    In this talk I will focus on the well-posedness and regularity of the Zakharov- Kuznetsov (ZK) equation in the deterministic and stochastic cases, subjected to a rectangular domain in space dimensions 2 and 3. ZK equation is a multi-dimensional extension of the KdV equation.  
     
    Mainly we have established the existence, in 3D, and uniqueness, in 2D, of the weak solutions, and the local and global existence of strong solutions in 3D. Then we extend the results to the stochastic case and obtain in 3the existence of martingale solutions, and in 2the pathwise uniqueness and existence of pathwise solutions. The main focus is on the mixed features of the partial hyperbolicity, nonlinearity, nonconventional boundary conditions,anisotropicity and stochasticity, which requires methods quite different than those of the classical models in fluid dynamics, such as the Navier-Stokes equation, Primitive Equation and related equations.
    Created on Aug 28, 2015 02:31 PM PDT
  6. Postdoc Symposium (Part II) - Small Divisors and the NLSE

    Location: MSRI: Simons Auditorium
    Speakers: Bobby Wilson (MSRI - Mathematical Sciences Research Institute)

    We will discuss the classical small divisor problem, and connections to questions concerning Sobolev stability of solutions to the nonlinear Schrodinger equation on the d-dimensional torus. In particular, we will examine results concerning the arbitrarily long-time orbital stability of plane wave solutions under generic perturbations.

    Created on Aug 28, 2015 02:33 PM PDT
  7. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 EVANS HALL UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

     

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Created on Aug 28, 2015 02:38 PM PDT
  8. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 EVANS HALL UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

     

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Created on Aug 28, 2015 02:40 PM PDT
  9. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 EVANS HALL UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

     

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Created on Aug 28, 2015 02:41 PM PDT
  10. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 EVANS HALL UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

     

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Created on Aug 28, 2015 02:43 PM PDT
  11. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 EVANS HALL UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

     

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Created on Aug 28, 2015 02:46 PM PDT
  12. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 EVANS HALL UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

     

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Created on Aug 28, 2015 02:48 PM PDT
  13. Pierre Raphael Course (UCB) - On singularity formation in nonlinear PDE’s: a constructive approach

    Location: 740 EVANS HALL UCB

    This course will be an introduction to the problem of singularity formation in nonlinear evolution equations, both dispersive and parabolic, which has seen spectacular developments for the past ten years. We will start with reviewing some of the basis concepts in the field (local well posedness, global existence, scattering and blow up) and in particular the role of solitary waves in the qualitative description of the flow. We will then introduce some of the basic tools for the construction of blow up solutions. We will in particular detail the construction of minimal blow up elements and explain their role in describing the flow near solitary waves. This will give us the first keys to understand the differences between type I and type II blow up which we will illustrate on various problems, We will for example give partial answers to a very simple question: how fast do ice balls melt? Time permitting, we will conclude the class towards energy super critical models.

     

    The course will be completely self contained with the prior knowledge of basis functional analysis (Hilbert and Banach spaces), PDE’s (well posedness, energy estimates) and dynamical systems (perturbation theory), and will start with a crash course on the Sobolev H^s(\R^d) space and its embedding properties.

    Created on Aug 28, 2015 02:50 PM PDT