Events & Seminars

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 Nov 24

Colloquium: Dan Freed (University of Texas) "Bordism and topological phases of matter"

2:00pm to 3:00pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Topological ideas have at various times played an important role in condensed matter physics. This year's Nobel Prize recognized the origins of a particular application of great current interest: the classification of phases of a quantum mechanical system. Mathematically, we would like describe them as path components of a moduli space, but that is not rigorously defined as of now. In joint work with Mike Hopkins we apply stable homotopy theory (Adams spectral sequence) to compute the group of topological phases of "invertible" systems. We posit a continuum field
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.
2016 Mar 03

Colloquium: Sara Tukachinsky (Hebrew University) "Counts of holomorphic disks by means of bounding chains"

3:30pm to 4:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Over a decade ago, Welschinger defined invariants of real symplectic manifolds of complex dimensions 2 and 3, which count pseudo-holomorphic disks with boundary and interior point constraints. Since then, the problem of extending the definition to higher dimensions has attracted much attention.
2016 May 05

Colloquium: Daniel Wise (McGill) "The Cubical Route to Understanding Groups"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that have recently culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many infinite groups.

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