TBA
TBA
Seminar
TBA
TBA
The classification of one-manifolds: a take-home exam
The Geometry of the Conformal Vacuum Equations of Space-Time
Abstract:
Self-dual vacuum spacetimes are known to be integrable following the work of Ted Newman and Roger Penrose. We will discuss the question of integrability in the case that the self-duality condition is dropped.
Generalized Cross-Ratios and Transversals
Abstract:
After introducing the standard cross-ratio, we discuss a generalization of the cross-ratio to higher-dimensional Grassmannians. As an application, we give a short proof of the following theorem in projective geometry: Any four n-plane subspaces in general position in a projective space of dimension 2n+1 over an algebraically closed field have exactly n+1 common transversals.
“An introduction to fixed point theory in Banach spaces. 6.”
“Generalized limits with invariance properties.”
Milnor's construction of exotic seven-spheres
Polarizations of Powers of Maximal Ideals in a Polynomial Ring
Abstract:
We give a complete combinatorial characterization of all possible polarizations of powers of the maximal ideal $(x_1,x_2,\dotsc,x_n)$ in a polynomial ring of $n$ variables. We also give a combinatorial description of the Alexander duals of such polarizations. In the three variable case we show that every polarization defines a (shellable) simplicial ball. We conjecture that any polarization of an artinian monomial ideal defines a simplicial ball. This is joint work with Gunnar Fløystad.
Uniform Large Deviations Principles
Abstract: