Abstract: my talk will be devoted to a basic theory of extensions of
complete real-valued fields L/K. Naturally, one says that L is
topologically-algebraically generated over K by a subset S if L lies
in the completion of the algebraic closure of K(S). One can then define
topological analogues of algebraic independence, transcendence degree, etc.
These notions behave much more wierd than their algebraic analogues. For example,
there exist non-invertible continuous K-endomorphisms of the completed
algebraic closure of K(x). In my talk, I will tell which part
Abstract: Inseparable morphisms proved to be
an important tool for the study of algebraic
varieties in characteristic p. In particular,
Rudakov-Shafarevitch, Miyaoka and Ekedahl
have constructed a dictionary between
"height 1" foliations in the tangent bundle
and "height 1" purely inseparable quotients
of a non-singular variety in characteristic p.
In a joint work with Eyal Goren we use this
dictionary to study the special fiber S of a
unitary Shimura variety of signature (n,m),
m < n, at a prime p which is inert in the
underlying imaginary quadratic field. We
I discuss some class of function of several elliptic variables,
this functions generalize multiple polylogarithms of D. Zagier.
I show some applications of developed formalism.
This is a joint work with F. Brown.
Repeats every week every Monday until Sun Feb 28 2016 .
10:30am to 12:30pm
Location:
B221 Rothberg (CS and Engineering building)
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.
Speaker: Zur Luria (ETH)
Title: Hamiltonian spheres in random hypergraphs
Abstract:
Hamiltonian cycles are a fundamental object in graph theory, and combinatorics in general. A classical result states that in the random graph model G(n,p), there is a sharp threshold for the appearance of a Hamiltonian cycle. It is natural to wonder what happens in higher dimensions - that is, in random uniform hypergraphs?
Title: Gaussian Random Links
Abstract: A model for random links is obtained by fixing an
initial curve in some n-dimensional Euclidean space and
projecting the curve on to random 3 dimensional subspaces. By
varying the curve we obtain different models of random
knots, and we will study how the second moment of the average crossing
number change as a function of the initial curve.
This is based on work of Christopher Westenberger.
Speaker: Thilo Weinert, BGU
Title: The Ramsey Theory of ordinals and its relation to finitary combinatorics
Abstract:
Ramsey Theory is a branch of mathematics which is often times summed up by the slogan “complete disorder is impossible”. An important branch of finitary Ramsey Theory lies in the determination of Ramsey Numbers. Infinitary Ramsey Theory on the other hand is an important branch of set theory. Whereas the Ramsey Theory of the Uncountable often times features independence phenomena, the Ramsey Theory of the Countably Infinite provides many interesting combinatorial challenges.
Speaker: Ehud Fridgut (Weizmann Institute)
Title: Almost-intersecting families are almost intersecting-families.
Abstract: Consider a family of subsets of size k from a ground set of size n (with k < n/2). Assume most (in some well defined sense) pairs of sets in the family intersect. Is it then possible to remove few (in some well defined sense) sets, and remain with a family where every two sets intersect?
We will answer this affirmatively, and the route to the answer will pass through a removal lemma in product graphs.
