Events & Seminars

2018 May 17

Colloquium - Tzafriri lecture: Amitay Kamber (Hebrew university) "Almost-Diameter of Quotient Spaces and Density Theorems"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A recent result of Lubetzky and Peres showed that the random walk on a $q+1$-regular Ramanujan graph has $L^{1}$-cutoff, and that its “almost-diameter” is optimal. Similar optimal results were proven by other authors in various contexts, e.g. Parzanchevski-Sarnak for Golden Gates and Ghosh-Gorodnik-Nevo for Diophantine approximations. Those results rely in general on a naive Ramanujan conjecture, which is either very hard, unknown, or even false in some situations. We show that a general version of those results can be proven using the density hypothesis of Sarnak-Xue.
2017 Mar 23

Colloquium: Asaf Shapira (Tel Aviv) - "Removal Lemmas with Polynomial Bounds"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A common theme in many extremal problems in graph theory is the relation between local and global properties of graphs. We will consider the following variant of this theme: suppose a graph G is far (in some well defined sense) from satisfying property P. Must G contain a small proof of this fact? We will show that for many natural graph properties the answer is Yes. In particular, we will show that the answer is Yes whenever P is a semi-algebraic graph property, thus conforming a conjecture of Alon. Joint work with L. Gishboliner
2017 Jun 22

Colloquium: Zohovitzki prize lecture - Ariel Rapaport, "Self-affine measures with equal Hausdorff and Lyapunov dimensions"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A measure on the plane is called self-affine if it is stationary with respect to a finitely supported measure on the affine group of R^2. Under certain randomization, it is known that the Hausdorff dimension of these measures is almost surely equal to the Lyapunov dimension, which is a quantity defined in terms of the linear parts of the affine maps. I will present a result which provides conditions for equality between these two dimensions, and connects the theory of random matrix products with the dimension of self-affine measures.
2017 Jun 15

Colloquium: Alexander Logunov (Tel Aviv), "0,01% Improvement of the Liouville property for discrete harmonic functions on Z^2"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Let u be a harmonic function on the plane. The Liouville theorem claims that if |u| is bounded on the whole plane, then u is identically constant. It appears that if u is a harmonic function on a lattice Z^2, and |u| < 1 on 99,99% of Z^2, then u is a constant function.   Based on a joint work(in progress) with L.Buhovsky, Eu.Malinnikova and M.Sodin.  
2015 Nov 25

Topology & geometry: Lara Simone Suárez (HUJI), "Exact Lagrangian cobordism and pseudo-isotopy"

11:00am to 12:45pm

Location: 

Ross building, Hebrew University (Seminar Room 70A)
Abstract: Consider two Lagrangian submanifolds L, L′ in a symplectic manifold (M,ω). A Lagrangian cobordism (W;L,L′) is a smooth cobordism between L and L′ admitting a Lagrangian embedding in (([0,1]×R)×M,(dx∧dy)⊕ω) that looks like [0,ϵ)×{1}×L and (1−ϵ,1]×{1}×L′ near the boundary. In this talk we will show that under some topological constrains, an exact Lagrangian cobordism (W;L,L′) with dim(W)>5 is diffeomorphic to [0,1]×L.
2017 Apr 20

Basic notions: Raz Kupferman (HUJI) - A geometric framework for continuum mechanics

4:00pm to 5:15pm

Abstract: The “geometrization" of mechanics (whether classical, relativistic or quantum) is almost as old as modern differential geometry, and it nowadays textbook material. The formulation of a mathematically-sound theory for the mechanics of continuum media is still a subject of ongoing research. In this lecture I will present a geometric formulation of continuum mechanics, starting with the definition of the fundamental physical observables, e.g., force, deformation, stress and traction. The outcome of this formulation is a generalization of Newton’s "F=ma” equation for continuous media.
2017 Jun 01

Group actions:Lei Yang - badly approximable points on curves and unipotent orbits in homogeneous spaces

10:30am to 11:30am

We will study n-dimensional badly approximable points on curves. Given an analytic non-degenerate curve in R^n, we will show that any countable intersection of the sets of weighted badly approximable points on the curve has full Hausdorff dimension. This strengthens a previous result of Beresnevich by removing the condition on weights. Compared with the work of Beresnevich, we study the problem through homogeneous dynamics. It turns out that the problem is closely related to the study of distribution of long pieces of unipotent orbits in homogeneous spaces.
2016 Mar 17

Colloquium-Landau Lectures: Ravi Vakil (Stanford) "Cutting and pasting in algebraic geometry, and the motivic zeta function"

3:30pm to 4:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Given some class of "geometric spaces", we can make a ring as follows. 1. (additive structure) When U is an open subset of such a space X, [X] = [U] + [(X \ U)] 2. (multiplicative structure)} [X x Y] = [X] [Y]. In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising structure, connecting geometry to arithmetic and topology.
2015 Nov 26

Colloquium: Shai Evra (HUJI), "Topological Expanders"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Title: Topological Expanders. Abstract: A classical result of Boros-Furedi (for d=2) and Barany (for d>=2) from the 80's, asserts that given any n points in R^d, there exists a point in R^d which is covered by a constant fraction (independent of n) of all the geometric (=affine) d-simplices defined by the n points. In 2010, Gromov strengthen this result, by allowing to take topological d-simplices as well, i.e. drawing continuous lines between the n points, rather then straight lines and similarly continuous simplices rather than affine.
2016 Dec 29

Colloquium: Jordan Ellenberg (University of Wisconsin) "The cap set problem"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A very old question in additive number theory is: how large can a subset of Z/NZ be which contains no three-term arithmetic progression? An only slightly younger problem is: how large can a subset of (Z/3Z)^n be which contains no three-term arithmetic progression? The second problem was essentially solved in 2016, by the combined work of a large group of researchers around the world, touched off by a brilliantly simple new idea of Croot, Lev, and Pach.

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