Since the seminal work of Arnold on the Euler equations (1966), many equations in hydrodynamics were shown to be geodesic equations of diffeomorphism groups of manifolds, with respect to various Sobolev norms. This led to new ways to study these PDEs, and also initiated the study of of the geometry of those groups as (infinite dimensional) Riemannian manifolds.

Speaker: Joel Friedman, UBC
Title: Open Problems Related to the Zeta Functions
Abstract:
We express some open problems in graph theory in terms of Ihara graph zeta
functions, or, equivalently, non-backtracking matrices of graphs. We focus
on "expanders" and random regular graphs, but touch on some seemingly
unrelated problems encoded in zeta functions.
We suggest that zeta functions of sheaves on graphs may have relevance to
complexity theory and to questions of Stark and Terras regarding whether

Speaker: Michael Farber,  Queen Mary

Title: Multi-parameter random simplicial complexes

Read more about Combinatorics: Michael Farber (Queen Mary), "Multi-parameter random simplicial complexes"

Speaker: Zur Luria, ETH
Title: New bounds for the n-queen's problem
Abstract:
The famous n-queens problem asks: In how many ways can n nonattacking queens be placed on an n by n chessboard? This question also makes sense on the toroidal chessboard, in which opposite sides of the board are identified. In this setting, the n-queens problem counts the number of perfect matchings in a certain regular hypergraph. We give an extremely general bound for such counting problems, which include Sudoku squares and designs.

The miracle of entropy - that the entropy of a measure preserving transformation calculated forward in time (for T) and backwards in time (for T^{-1}) are equal - is, depending on point of view and the definition used, either a triviality or highly surprising. Entropy theory (of Z-actions) plays a key role in analyzing the rigidity of algebraic (diagonalizable) Z^k actions; I show how a strong version of this symmetry property of entropy is useful in studying the measure classification question for such actions.
Joint work with Manfred Einsiedler.

I will explain the notion of a homotopy quotient of an operad providing different examples of operads of compactified moduli spaces of genus zero curves with marked points: including the space of complex curves (math.arXiv:1206.3749), the real loci of the complex one (arXiv:math/0507514) and the noncommutative …

Salmon and Cayley proved the celebrated 19th century result that a smooth cubic surface over the complex numbers contains exactly 27 lines.  By contrast, the count over the real numbers depends on the surface, and these possible counts were classified by Segre.  A number of researchers have recently made the striking observation that Segre’s work shows a certain signed count is always 3.  In my talk, I will explain how to extend this result to an arbitrary field.