33 citations · 105 across the 34 of their papers we have counts for
36 papers
The homology of random simplicial complexes in the multi-parameter upper model
Michael Farber, Tahl Nowik
We study random simplicial complexes in the multi-parameter upper model. In this model simplices of various dimensions are taken randomly and independently, and our random simplici…
A systolic inequality with remainder in the real projective plane
Mikhail G. Katz, Tahl Nowik
The first paper in systolic geometry was published by Loewner's student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary…
Metric completions, the Heine-Borel property, and approachability
Vladimir Kanovei, Mikhail G. Katz, Tahl Nowik
We show that the metric universal cover of a plane with a puncture yields an example of a nonstandard hull properly containing the metric completion of a metric space. As mentioned…
Topological embeddings into random 2-complexes
Michael Farber, Tahl Nowik
We consider 2-dimensional random simplicial complexes in the multi-parameter model. We establish the multi-parameter threshold for the property that every 2-dimensional simplic…
Random Simplicial Complexes, Duality and The Critical Dimension
Michael Farber, Lewis Mead, Tahl Nowik
In this paper we discuss two general models of random simplicial complexes which we call the lower and the upper models. We show that these models are dual to each other with respe…
Universal Knot Diagrams
Chaim Even-Zohar, Joel Hass, Nati Linial +1
We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implic…