2018/2019

2019 March 12th

Asahi Tsuchida

Title: On frontals for sub-Riemannian manifolds

2019 March 5th

Mariusz Zając

Title: Homogeneous polynomials in some discrete problem

2019 January 15th

Vincent Grandjean

Title: Equisingularity at infinity of real polynomials

Abstract: In this work, jointly with N. Dutertre, given a real polynomial function F in n variables, we are looking at the regularity of the functions "total curvature" and a "absolute total curvature" attached to F. The function "total curvature" is defined as the integral, over any given level of F, of the Gauss-Kronecker curvature of the given level. The function "absolute total curvature" is given by the integral, over the given level, of the absolute value of the Gauss-Kronecker curvature over the given level. The Total absolute curvature of a Given Level is related to Gauss-Bonnet formula; We show an equisingularity result of this nature; both functions "total curvature" are continuous at any regular value which satisfies Malgrange Condition.

2018 October 30th

Wojciech Kryński (IM PAN)

Title: Geometric approach to the multipeakon solutions to the Camassa-Holm equation

Abstract: Multipeakons are special solutions to the Camassa-Holm equation. They can be described by an integrable geodesic flow on a Riemannian manifold. Singular points of the Riemannian metric correspond to collisions of the multipeakons. We consider a bi-Hamiltonian formulation of the system and exploit its first integrals in order to analyse geodesics near a singular point of the metric. We present a novel approach to the problem of the dissipative prolongations of multipeakons after the collision time.

2018 October 16th (at 4 pm)

poster

Jun-Muk Hwang (Korea Institute for Advanced Study, Seoul)

Title: Rigidity of Legendrian singularities

Abstract: Let (M, D) be a holomorphic contact manifold, i.e. a complex manifold M of dimension 2m+1 equipped with a holomorphic contact structure D.

An m-dimensional complex analytic subvariety V in M is called a Legendrian subvariety if the smooth locus of V is tangent to D. A Legendrian singularity means the germ of a Legendrian subvariety at a point.

We discuss conditions under which a Legendrian singularity becomes a cone singularity and explain how they are related to the geometry of Fano contact manifolds.

2018 October 2nd

Shyuichi Izumiya (Sapporo)

Title: Singularities of Cauchy horizons in Lorentz-Minkowski space