# Mathematics Colloquia and Seminars

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### Longest Increasing Subsequence under Area Constraint

**Mathematical Physics & Probability**

Speaker: | Riddhi Basu, Stanford University |

Related Webpage: | https://web.stanford.edu/~rbasu/ |

Location: | 2112 MSB |

Start time: | Wed, May 24 2017, 4:10PM |

Motivated by extremal isoperimetric problems in percolation, I shall describe a

model which puts a global curvature constraint on the classical

Ulam's problem in the plane, and studies the longest increasing path

from (0,0) to (n,n) trapping atypically large area. As is typical in these

models, the first order behaviour of this random contour is determined by a

variational problem which we explicitly solve. More interesting are exponents

related to local fluctuation properties which capture the competition between the

global curvature constraint and the behaviour of an unconstrained path governed

by KPZ universality. These can be studied via maximal facet lengths of the convex

hull of the contour and the Hausdorff distance from the hull for which we identify

scaling exponents 3/4 and 1/2 respectively. I shall also discuss connections

to different models and several open problems.

Joint work with Shirshendu Ganguly and Alan Hammond.