Shiing-shen Chern: 1911–2004

On Characteristic Classes of Determinantal Cremona Transformations

We compute the multidegrees and the Segre numbers of general determinantal Cremona transformations, with generically reduced base scheme, by specializing to the standard Cremona transformation and computing its Segre class via mixed volumes of rational polytopes. Dedicated to the memory of Shiing-Shen Chern

Yang-mills, Complex Structures and Chern’s Last Theorem

Recently Shiing-Shen Chern suggested that the six dimensional sphere S has no complex structure. Here we explore the relations between his arguments and Yang-Mills theories. In particular, we propose that Chern’s approach is widely applicable to investigate connections between the geometry of manifolds and the structure of gauge theories. We also discuss several examples of manifolds, both with...

Description of Amy Shen

Shen Substring - Searchable Symmetric Encryption

In this paper, we consider a setting where a client wants to outsource storage of a large amount of private data and then perform substring search queries on the data – given a data string s and a search string p, find all occurrences of p as a substring of s. First, we formalize an encryption paradigm that we call queryable encryption, which generalizes searchable symmetric encryption (SSE) an...

Chern numbers of Chern submanifolds

We present a solution of the generalized Hirzebruch problem on the relations between the Chern numbers of a stably almost complex manifold and the Chern numbers of its virtual Chern submanifolds.