Events & Seminars

2018 Nov 08

Colloquium: Nathan Keller (Bar Ilan) - The junta method for hypergraphs and the Erdos-Chvatal simplex conjecture

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Numerous problems in extremal hypergraph theory ask to determine the maximal size of a k-uniform hypergraph on n vertices that does not contain an 'enlarged' copy H^+ of a fixed hypergraph H. These include well-known problems such as the Erdos-Sos 'forbidding one intersection' problem and the Frankl-Furedi 'special simplex' problem.
2019 Jan 03

Colloquium: Nati Linial (HUJI) - Graph metrics

2:30pm to 3:30pm

A finite graph is automatically also a metric space, but is there any interesting geometry to speak of? In this lecture I will try to convey the idea that indeed there is very interesting geometry to explore here. I will say something on the local side of this as well as on the global aspects. The k-local profile of a big graph G is the following distribution. You sample uniformly at random k vertices in G and observe the subgraph that they span. Question - which distributions can occur? We know some of the answer but by and large it is very open.
2018 Oct 25

Colloquium: Karim Adiprasito (HUJI) - Combinatorics, topology and the standard conjectures beyond positivity

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Consider a simplicial complex that allows for an embedding into R^d. How many faces of dimension d/2 or higher can it have? How dense can they be? This basic question goes back to Descartes. Using it and other rather fundamental combinatorial problems, I will motivate and introduce a version of Grothendieck's "standard conjectures" beyond positivity (which will be explored in detail in the Sunday Seminar). All notions used will be explained in the talk (I will make an effort to be very elementary)
2018 Dec 20

Colloquium: Assaf Rinot (Bar-Ilan) - Hindman’s theorem and uncountable Abelian groups

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
In the early 1970’s, Hindman proved a beautiful theorem in additive Ramsey theory asserting that for any partition of the set of natural numbers into finitely many cells, there exists some infinite set such that all of its finite sums belong to a single cell. In this talk, we shall address generalizations of this statement to the realm of the uncountable. Among other things, we shall present a negative partition relation for the real line which simultaneously generalizes a recent theorem of Hindman, Leader and Strauss, and a classic theorem of Galvin and Shelah.
2018 Nov 29

Colloquium: Chaya Keller (Technion) - Improved lower and upper bounds on the Hadwiger-Debrunner numbers

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A family of sets F is said to satisfy the (p,q)-property if among any p sets in F, some q have a non-empty intersection. Hadwiger and Debrunner (1957) conjectured that for any p > q > d there exists a constant c = c_d(p,q), such that any family of compact convex sets in R^d that satisfies the (p,q)-property, can be pierced by at most c points. Helly's Theorem is equivalent to the fact that c_d(p,p)=1 (p > d).
2018 Nov 15

Colloquium: Ari Shnidman (Boston College) - Rational points on elliptic curves in twist families

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The rational solutions on an elliptic curve form a finitely generated abelian group, but the maximum number of generators needed is not known. Goldfeld conjectured that if one also fixes the j-invariant (i.e. the complex structure), then 50% of such curves should require 1 generator and 50% should have only the trivial solution. Smith has recently made substantial progress towards this conjecture in the special case of elliptic curves in Legendre form. I'll discuss recent work with Lemke Oliver, which bounds the average number of generators for general j-invariants.

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