Yuval Dor will speal about Transformal Valued Fields.
Abstract: Abraham Robinson characterized the existentially closed valued fields as those which are algebraically closed and nontrivially valued. This theorem is somewhat surprising: it makes no assumption on the topology of the field other than the fact that it is not discrete, and immediately implies a strong from of the Nullstellensatz, asserting that the only obstruction to the solvability of a system of polynomial equations in a neighborhood of a point is the obvious one.
A countable group is said to be homogeneous if whenever tuples of elements u, v satisfy the same first-order formulas there is an automorphism of the group sending one to the other. We had previously proved with Rizos Sklinos that free groups are homogeneous, while most surface groups aren't. In a joint work with Ayala Dente-Byron, we extend this to give a complete characterization of torsion-free hyperbolic groups that are homogeneous.
Abstract. We investigate the approximation rate of a typical element of the Cantor set by dyadic rationals. This is a manifestation of the times two times three phenomenon, and is joint work with Demi Allen and Han Yu.
Driven by recent technological advancements, behavior and brain activity can now be measured at an unprecedented resolution and scale. This “big-data” revolution is akin to a similar revolution in biology. In biology, the wealth of data allowed systems-biologists to uncover the underlying design principles that are shared among biological systems. In my studies, I apply design principles from systems-biology to cognitive phenomena. In my talk I will demonstrate this approach in regard to creative search.
Motivated by three-dimensional N=4 superconformal field theory, in 2016 Beem, Peelaers and Rastelli considered short even star-products for homogeneous symplectic singularities (more precisely, hyper-Kahler cones) and conjectured that they exist and depend on finitely many parameters. We prove the dependence on finitely many parameters in general and existence for a large class of examples, using the connection of this problem with zeroth Hochschild homology of quantizations suggested by Kontsevich.
In the mid-18th century,Euler derived his famous equations of motion of an incompressible fluid, one ofthe most studied equations in hydrodynamics. More than 200 years later, in1966, Arnold observed that they are, in fact, geodesic equations on the(infinite dimensional) Lie group of volume-preserving diffeomorphisms of amanifold, endowed with a certain right-invariant Riemannian metric.
In the mid-18th century, Euler derived hisfamous equations of motion of an incompressible fluid, one of the most studiedequations in hydrodynamics. More than 200 years later, in 1966, Arnold observedthat they are, in fact, geodesic equations on the (infinite dimensional)Lie group of volume-preserving diffeomorphisms of a manifold, endowed with acertain right-invariant Riemannian metric.