- Friday December 12: 13:15 - 15:00 Sal S1
- Geometry and Analysis (B.E.J. Dahlberg)
Luis Vega, Bilbao:
Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations.
Abstract: Consider the initial value problem (IVP) for nonlinear Schrödinger equations of the form:(1.1) (Click here to see the equations)
We are interested in the local solvability of the (IVP) (1.1). More precisely, we shall establish that (1.1) is locally well posed in the appropriate Sobolev spaces.
- Friday November 21: 13:15 - 15:00 Sal S1
- Geometry and Analysis (B.E.J. Dahlberg)
Jana Madjarova
An old paper on Dirichlet Spaces by A.Beurling and J.Deny.
Abstract: The paper contains an alternative and very general approach to potential theory. - Friday November 14: 13:15 - 15:00 Sal S1
- Geometry and Analysis (B.E.J. Dahlberg)
Mats Aigner
Taubes solution of the critical Ginzburg-Landau equations
Abstract: The Ginzburg-Landau equations are the variational equations of the Ginzburg-Land au action functional, which describes the state of a superconductor in a magneti c field. Following Taubes we will describe the space of solutions to these equat ions. - Friday November 07: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
Conformal Mappings and Deformation of Curves
Abstract: We shall use conformal mapping techniques to study deformations of curves. We will be especially interested in the case of curves with bounded total curvat ure. We begin by summarizing the smoothness properties of conformal mappings. - Friday October 24: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
A review of fiber bundles V
Abstract: I will give the basic definitions and discuss some properties of fiber bundles. The talk will focus on the covering homotopy properties. - Friday October 17: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
A review of fiber bundles IV
Abstract: I will give the basic definitions and discuss some properties of fiber bundles. The talk will focus on the covering homotopy properties. - Friday October 10: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
A review of fiber bundles III
Abstract: I will give the basic definitions and discuss some properties of fiber bundles. The talk will focus on the covering homotopy properties. - Friday October 3: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
A review of fiber bundles II
Abstract: I will give the basic definitions and discuss some properties of fiber bundles. The talk will focus on the covering homotopy properties. - Friday September 26: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
A review of fiber bundles
Abstract: I will give the basic definitions and discuss some properties of fiber bundles. The talk will focus on the covering homotopy properties. - Friday September 19: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
Sphere Bundles and Deformations of Closed, Regular Curves II. - Friday September 12: 13:15 - 15:00 Sal S1
- B.E.J. Dahlberg
Sphere Bundles and Deformations of Closed, Regular Curves I.
Abstract: This lecture will give the necessary background results on fiber spaces in order to present Smale's theory of sphere bundles and curve deformations. - Friday September 5: 13:15 - 15:00
- Björn Dahlberg
Deformations of Closed Curves
Abstract: Let M be a manifold. There are several natural families of closed curves associa ted to M. For instance, the family of immersions and the family of curves with n on-vanishing curvature.
We shall in this lecture show that the family of closed curves in R³ with a non-vanishing curvature has two components.
Seminars 1996/97:
Spring 1997 - Friday May 30: 10:15 - 12:00
- Björn Dahlberg
Geodesic curvature measures and the Gauss-Bonnet theorem
Abstract: We begin by introducing the concept of total curvature for curves on a Riemann manifold. For a curve on a Riemann surface with a bounded total curvature we def ine its geodesic curvature measure. We also establish the Gauss-Bonnet theorem in this setting. - Friday May 16: 13:15 - 15:00
- Björn Dahlberg
Curvature Measures
Abstract: Let
be a plane curve that is locally one-to-one and has
a
bounded total curvature.
We will in this lecture associate a canonical curvature measure to 
and establish some of its properties.
- Friday April 25: 13:15 - 15:00
- Björn Dahlberg
Curves with a bounded total curvature
Abstract: We will analyze the structure of curves with a bounded total curvature. We shall in particular show that they can be written as the union of Lipschitz graphs. - Friday April 18: 13:15 - 15:00
- Björn Dahlberg
Closed curves in R³ with a prescribed tangent image
Abstract: We shall prove that a closed curve on S² is the tangent image of a cl osed, non-planar curve in R³ if and only if its convex hull contains the or igin in its interior! This beautiful result is due to Fenchel. - Friday April 11: 13:15 - 15:00
- Valeri Golovitchev, Dep. of Thermo- and Fluid Dynamics, CTH
Simulation of Spray Combustion: Search for Effective Numerical Algorithms
Abstract: The numerical framework of the CFD codes used for spray combustion simulation is reviewed as well as some physical submodels requiring a special care in modeling . Several areas for potential improvement of numerical techniques increasing their algorithmic "smartness" are discussed. Among them, the locally adaptive schemes which automatically drop off the terms as they become insignificant in the course of calculations accounting for finite-rate chemistry, real gas and turbulence effects, droplet representation method reducing a total number of parcels in the spray equation formulation are rated among realized. The other improvements, (adaptive gridding, more robust numerics, massive parallel processing), are still rating among desirable. The illustrative results demonstrating the current modeling capabilities include simulation of spray ignition and combustion of oxygenated fuels in the DI (direct injection) Diesel engine. - Friday March 21: 13:15 - 15:00
- Alexei Heintz
Krökningsflöde i några fysiska modeller
Abstract: Vi kommer att diskutera några fysiska modeller som innehåller flödet av någon yta enligt ekvationen dr/dt = H(r), där r är en punkt på ytan och H(r) är dess krökning. Naturföreteelser som kommer att observeras är flödet av två vätskor, förbränning och olika fasövergånger. - Friday March 14: 13:15 - 15:00
- Gunnar Peters, KTH
Analytic aspects of knots
Abstract: We will review some results of Freedman et.al. on the Moebius energy for knots, and discuss possible generalizations. This will be an informal discussion of wor k in progress.
Autumn 1996 - 8 november 1996
- Björn Dahlberg
- Curvature frames and Frenet frames, (abstract, (ps-file))
- 25 october 1996
- Björn Dahlberg
- Frames and curvature flows, (abstract, (ps-file))
- 18 october 1996
- Björn Dahlberg
- A definition of curvature for space curves, (abstract, (ps-file))
- 11 october 1996
- Björn Dahlberg
- Curves with a bounded total curvature, (abstract, (ps-file))
- 4 october 1996
- Björn Dahlberg
- Rotation index for a normal plane curve, (abstract, (ps-file))
- 27 september 1996
- Björn Dahlberg
- Total curvature of space curves - theorems by Fenchel and Milnor, (abstract, (ps-file))
- 20 september 1996
- Björn Dahlberg
- Differential geometry and functions of bounded variation, (abstract, (ps-file))
- 13 september 1996
- Björn Dahlberg
- The differential geometry of plane curves, (abstract, (ps-file))