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).
Abstract: In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply connected groups which have since been proven, particularly Weil's conjecture on Tamagawa numbers over number fields. One easily deduces that this same formula holds for all linear algebraic groups over number fields. Sansuc's method still works to treat reductive groups in the function field setting, thanks to the recent resolution of Weil's conjecture in the function field setting by Lurie and Gaitsgory.
Hebrew University, Givat Ram, Ross Building, room 63
A natural question is whether there exists a continuous p-adic analogue
for the classical local Langlands correspondence for GL_n(F) .
Namely, for a finite extension F of Q_p, we want to associate continuous p -adic representations of GL_n(F) to n-dimensional p-adic representations of the Weil group of F.
The particular case, where F=Q_p and n=2 , is now known. One of the main tools for establishing this correspondence was the existence of GL_2(Q_p)-invariant norms in certain representations of GL_2(Q_p).
Abstract: This talk will be about joint work with Eyal Goren about the
structure of Picard modular surfaces at a prime p which is inert in the
underlying quadratic imaginary field. The main tool for studying the bad
reduction of Shimura varieties is the theory of local models (due to de
Jong and Rapoport-Zink). Our results concern global geometric questions
which go beyond the theory of global models. For example, we are able to
count supersingular curves on the Picard surface. We also study certain
foliations in its tangent bundle that have not been studied before, and
Repeats every week every Monday until Sun Feb 28 2016 .
10:30am to 12:30pm
B221 Rothberg (CS and Engineering building)
Speaker: Asaf Nachmias (TAU)
Title: The connectivity of the uniform spanning forest on planar graphs
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.
Speaker: Zuzana Patakova, HU
Title: Multilevel polynomial partitions
The polynomial partitioning method of Guth and Katz partitions a given finite point set P in R^d using the zero set Z(f) of a suitable d-variate polynomial f.
Applications of this result are often complicated by the problem, what should be done with the points of P lying within Z(f)? A natural approach is to partition these points with another polynomial and continue further in a similar manner.
As a main result, we provide a polynomial partitioning method with up to d polynomials
Title: Discrete Geometry in Minkowski Spaces
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.
Speaker: Eli Shamir, HUJI
Title :Completing partial Latin Square[LS] using 2-sided Hall marriage theorem
Evans conjectured in 1960 that nxn partial LS with n-1 dictated entries
can be completed. Smetaniuk gave an inductive, complicated proof in 1981 -
it is reproduced in the "Proofs from the Book".
My proof is direct-- filling row after row using a recent 2-sided extension of Hall
marriage conditions - which will be presented.
It gives all completions and also a generalized completion claim:
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:
Speaker: László Babai (University of Chicago)
Title: Finite permutation groups and the Graph Isomorphism problem
The Graph Isomorphism (GI) problem is the algorithmic problem
Title: Polynomials vanishing on Cartesian products
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?