Update: The lectures this week are cancelled. They will be given at a later date.
Next week Igor Pak will give the 2018 Erdős Lectures
Monday Jun 18 2018
IIAS, Eilat hall, Feldman bldg (top floor), Givat Ram
I will survey various known and recent results on counting the number of linear extensions of finite posets. I will emphasize the asymptotic and complexity aspects for special families, where the problem is especially elegant yet remains #P-complete.
Wednesday Jun20, 2018
Rothberg (CS building) B-220
The number of standard Young tableaux of skew shape is a mesmerizing special case of the number of linear extensions of posets, that is important for applications in representation theory and algebraic geometry. In this case there is a determinant formula, but finding their asymptotics is a difficult challenge. I will survey some of the many beautiful result on the subject, explain some surprising product formulas, connections to Selberg integral, lozenge tilings and certain particle systems.
Thursday, Jun21, 2018
Manchester Building (Hall 2), Hebrew University Jerusalem
Given a convex polytope P, what is the number of integer points in P? This problem is of great interest in combinatorics and discrete geometry, with many important applications ranging from integer programming to statistics. From a computational point of view it is hopeless in any dimensions, as the knapsack problem is a special case. Perhaps surprisingly, in bounded dimension the problem becomes tractable. How far can one go? Can one count points in projections of P, finite intersections of such projections, etc.?