School of Mathematics

Extremal set theory II

Andrey Kupavskii
Member, School of Mathematics
November 5, 2019

Extremal set theory typically asks for the largest collection of sets satisfying certain constraints. In the first talk of these series, I'll cover some of the classical results and methods in extremal set theory. In particular, I'll cover the recent progress in the Erdos Matching Conjecture, which suggests the largest size of a family of k-subsets of an n-element set with no s pairwise disjoint sets.

Privacy via ill-posedness

Anna Gilbert
University of Michigan; Member, School of Mathematics
November 4, 2019

In this work, we exploit the ill-posedness of linear inverse
problems to design algoithms to release differentially private data or
measurements of the physical system. We discuss the spectral
requirements on a matrix such that only a small amount of noise is
needed to achieve privacy and contrast this with the poor conditioning
of the system. We then instantiate our framework with several
diffusion operators and explore recovery via l1 constrained
minimisation. Our work indicates that it is possible to produce

Pseudoholomorphic curves with boundary: Can you count them? Can you really?

Sara Tukachinsky
Member, School of Mathematics
November 4, 2019

Open Gromov-Witten (OGW) invariants should count pseudoholomorphic maps from curves with boundary to a symplectic manifold, with various constraints on boundary and interior marked points. The presence of boundary poses an obstacle to invariance. In a joint work with J. Solomon (2016-2017), we defined genus zero OGW invariants under cohomological conditions.