Activities This Week
Logic, Set Theory and Topology
Tight stationarity and pcf theory - part two
Nov 15, 12:30—13:45, 2016, Math -101
Speaker
Bill Chen (BGU)
Abstract
I will introduce the definitions of mutual and tight stationarity due to Foreman and Magidor. These notions generalize the property of stationarity from subsets of a regular cardinal to sequences of subsets of different regular cardinals (or, by some interpretations, to singular cardinals). Tight stationarity will then be related to pcf theory, and from a certain pcf-theoretic assumption we will define a ccc forcing which arranges a particularly nice structure in the tightly stationary sequences.
Colloquium
Combinatorial Hodge theory
Nov 15, 14:30—15:30, 2016, Math -101
Speaker
Karim Adiprasito (Hebrew University of Jerusalem)
Abstract
I will discuss how Hodge theory, and positivity phenomena from algebraic geometry in general, can be used to resolve fundamental conjectures in combinatorics, including Rotas conjecture for log-concavity of Whitney numbers and beyond. I will also discuss how combinatorics can in turn be used to explain and prove such phenomena, such as the Hodge-Riemann relations for matroids.
Operator Algebras
p-Summable Integral Formula for Spectral Flow
Nov 15, 16:00—17:00, 2016, Math -101
Speaker
Magdalena Georgescu (BGU)
Abstract
During the last two weeks, we discussed the definition of spectral flow and its connection to noncommutative geometry. This week, we will go over a proof of the integral formula for spectral flow which calculates the index pairing between (the equivalence classes of) a unitary and a p-summable semifinite Fredholm module.
Algebraic Geometry and Number Theory
A general theory of fields with operators
Nov 16, 15:10—16:30, 2016, Math -101
Speaker
Moshe Kamensky (BGU)
Special lecture in Geometry and Physics
Nov 21, 11:00—12:00, 2016, Math building (58), room 201, BGU
Dynamics of Spacetime — Einstein’s equations as a geometric flow.
Speaker: Dr. David Fajman (Vienna)
The interpretation of Einstein’s equations as a geometric flow (the Einstein flow) allows to study the evolution of spacetimes from a dynamical point of view. Two types of initial data are mainly considered: Firstly, asymptotically flat data describing initial states of isolated self-gravitating systems and secondly, data on closed manifolds describing initial states for cosmological spacetimes. Studying the evolution of data under the flow we aim to understand its long-time behavior and the global geometry of its time-development. We are interested in the construction of static solutions (or static up to a time-rescaling) as potential attractors of the flow and their nonlinear stability, completeness and incompleteness properties of spacetimes and singularity formation. We present new methods to construct and study solutions by geometric and analytical tools as well as several results in the directions mentioned above. We consider in particular the case of matter models coupled to the Einstein equations, which turns out to provide several interesting phenomena and new classes of solutions.