Abstract: Calabi conjectured that the complex Monge-Ampère equation on compact Kaehler manifolds has a unique solution. This was solved by Yau in 1978. In this talk, we present a non-archimedean version on projective Berkovich spaces. In joint work with Burgos, Jell, Künnemann and Martin, we improve a result of Boucksom, Favre and Jonsson in the equicharacteristic 0 case. We give also a result in positive equicharacteristic using test ideals.
In this talk we present a database of rational elliptic curves with
good reduction outside certain finite sets of primes, including the
set {2, 3, 5, 7, 11}, and all sets whose product is at most 1000.
In fact this is a biproduct of a larger project, in which we construct
practical algorithms to solve S-unit, Mordell, cubic Thue, cubic
Thue--Mahler, as well as generalized Ramanujan--Nagell equations, and
to compute S-integral points on rational elliptic curves with given
Mordell--Weil basis.
Our algorithms rely on new height bounds, which we obtained using the
Speaker: Asaf Nachmias (TAU)
Title: The connectivity of the uniform spanning forest on planar graphs
Abstract:
The free uniform spanning forest (FUSF) of an infinite connected graph G is obtained as the weak limit uniformly chosen spanning trees of finite subgraphs of G. It is easy to see that the FUSF is supported on spanning graphs of G with no cycles, but it need not be connected. Indeed, a classical result of Pemantle ('91) asserts that when G=Z^d, the FUSF is almost surely a connected tree if and only if d=1,2,3,4.
Repeats every week every Monday until Mon Nov 23 2015 .
11:00am to 1:00pm
11:00am to 1:00pm
Location:
B221 Rothberg (CS and Engineering building)
Speaker: Clara Shikhelman, TAU
Title: Many T copies in H-free graphs.
Abstract:
For two graphs T and H and for an integer n, let ex(n,T,H) denote
the maximum possible number of copies of T in an H-free graph on n
vertices. The study of this function when T=K_2 (a single edge) is
the main subject of extremal graph theory. We investigate the general
function, focusing on the cases of triangles, complete graphs and trees.
In this talk the main results will be presented as will sketches of
proofs of some of the following:
(i) ex(n,K_3,C_5) < (1+o(1)) (\sqrt 3)/2 n^{3/2}.
Title: Discrete Geometry in Minkowski Spaces
Abstract:
In recent decades, many papers appeared in which typical problems of Discrete Geometry are investigated, but referring to the more general setting of finite dimensional real Banach spaces (i.e., to Minkowski Geometry). In several cases such problems are investigated in the even more general context of spaces with so-called asymmetric norms (gauges).
In many cases the extension of basic geometric notions, needed for posing these problems in non-Euclidean Banach spaces, is already interesting enough.
I will talk about the three objects and the two inclusions mentioned in the title from a tropical viewpoint. Possible generalizations will be speculated.
There are exponentially many triangulations of a fixed manifold extremely distant from each other in some natural metric. I will discuss similar results for contractible 2-complexes. In order to prove these for the manifold being the sphere (or a contractible complex) one needs to create topology out of nothing. This is done by studying group theory of the trivial group.
Speaker: Ilan Karpas, HU
Tilte: Families with forbidden intersection patterns
Abstract:
Let l, n be even natural numbers. A pattern p of length l is an element
p = (p1, . . . , pl) ∈ {−, +}^l. Given such a pattern and two sets A, B ⊂ [n], we say that the pair (A, B) forms pattern p if the following conditions are satisfied:
1. A \Delta B = {i_1, . . . , i_l}, where i_1 < i_2 < . . . < i_l,
2. For 1 ≤ j ≤ l, we have i_ j ∈ A \ B if p_ j = + and i_ j ∈ B \ A if p_ j = −.
Israel Institute for Advanced Studies, Safra campus, Givat Ram
* This talk is joint with the 20th Midrasha Mathematicae: 60 faces to groups, celebrating Alex Lubotzky's 60th birthday.
The full program for AlexFest, Nov. 6--11, is detailed here:
http://www.as.huji.ac.il/ias/public/121/the20thMidrashaMa2016/program.pdf
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Speaker: László Babai (University of Chicago)
Title: Finite permutation groups and the Graph Isomorphism problem
Updated abstract:
The Graph Isomorphism (GI) problem is the algorithmic problem
Title: Polynomials vanishing on Cartesian products
Abstract:
Let F(x,y,z) be a real trivariate polynomial of constant degree, and let A,B,C be three sets of real numbers, each of size n. How many roots can F have on A x B x C?
