1 Characteristic 0 We start with a basic question: given a polynomial f ∈ C[z1, · · · , zn] with a singularity at 0, how can we measure the “singularness” of this polynomial in a precise way? In other words: we can look at various singularities and see intuitively that some singularities are worse than others. For instance, it feels like a transverse self-intersection is probably not as bad as ...

Strictly enforced encapsulation is a key concept for modular software designs. However, in many situations like unanticipated reuse, productivity can be raised by a more flexible approach to encapsulation. Also the discussion about the role of “obliviousness” in aspect-oriented programming is one instance of a general conflict between strictness and flexibility. Here, different technologies tak...

We study multi-period college admission problems where, at each period, a matching is computed and students have the option to either finalize their matches or participate in next period. Students participating an additional run of mechanism can submit new rank order list clearinghouse. Such gradual systems adequately account for source heterogeneity among participants, like withdrawals. identi...

Abstract Gradually typed languages are designed to support both dynamically and statically programming styles while preserving the benefits of each. Sound gradually check types at runtime boundary between modules. However, there is much disagreement in gradual typing literature over how enforce complex such as tuples, lists, functions objects. In this paper, we propose a new perspective on desi...