Abstract:
Motivated by understanding the action of Hecke operators on special sub-varieties of Shimura varieties, we consider the simplest possible case: the action of Hecke operators on the j-line, namely on the moduli space of elliptic curves, and in particular the action on singular moduli. Our interest is in this action considered in the p-adic topology. The emerging picture is surprisingly rich and the answers involve Serre-Tate coordinates, the Gross-Hopkins period map and finally involves random walks on GL_n.
This is joint work with Payman Kassaei (King's College).
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:
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.
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?
Speaker: Doron Puder, TAU
Title: Meanders and Non-Crossing Partitions
Abstract: Imagine a long river and a closed (not self-intersecting) racetrack that crosses the river by bridges 2n times. This is called a meander. How many meanders are there with 2n bridges (up to homeomorphisms of the plane that stabilizes the river)? This challenging question, which is open for several decades now, has connections to several fields of mathematics.
