| 27th of April, 2006. | Nir Avni |
Lecture : Exotic Spheres
Abstract: In 1956 Milnor discovered that on the seven dimensional sphere there is a differential structure that is not diffeomorphic to the standard one. This discovery was so surprising that at first he thought he found a counterexample to the Poincare conjecture (which roughly says that if you cannot distinguish a manifold from a sphere by using algebraic topology, then this manifold is in fact a sphere). I will try to give the construction assuming almost no background from the audience. Exotic cookies will be used to exemplify the talk. |
| 4th of May, 2006. (Time and place may change - please check the site before coming...) | Ofek Shilon |
Lecture : Novel approach to simulation of Bend and Twist of elastic 1D objects
Our motivation is the need for a fast and robust simulation of an endoscopic suturing thread. The traditional approach to modeling bending of a thread consists in adding springs connecting non-adjacent keypoints. An alternative is introduced, obtained by novel discretizations of a bending energy sampled at arbitrary joints. Significant visual appeal is thus gained, with negligable computational costs. We generlize to twist energy, further investigate the bending interaction of a spline with a connected rigid body, and mention several generalization directions. Short sample movie captures from the relevant software module: Demo 1 Demo 2 Demo 3 Demo 4 |
| 19 January, 2006. | Sasha Golubeva |
Lecture : Moment Map - continued
Last time we considered definitions and examples of symplectic manifolds. This time we will discuss poisson structures, hamiltonian actions, and moment maps. One of the examples of a moment map is so-called Springer's resolution that arises in geometric representation theory. |
| 12 January, 2006. | Boaz Karni |
Lecture : Super Mathematics (part II)
Following the talk in which I defined the category of supermanifolds, I will show how to properly define bundles on supermanifolds. I will define the objects that we integrate on supermanifolds, and how to integrate them. The talk is intended to people who attended my first talk, or to people familiar with the construction of a supermanifold. |
| 5 January, 2006. | Sasha Golubeva |
Lecture : Moment Map
We plan to consider definitions and examples of symplectic manifolds, poisson structures, hamiltonian actions, and moment maps. One of the examples of a moment map is so-called Springer's resolution that arises in geometric representation theory. |
| 29nd December, 2005. | Ofer Ron |
Lecture : Knot Theory, Surgery, and 3-Manifolds
I will present (in very basic terms) the fact that the set of orientable, connected, and closed (compact and boundaryless) 3-manifolds can be entirely described by combinatorial structures, namely links in the 3-sphere. This talk will be as self inclusive as possible, meaning that I will only assume knowledge of basic topological structures such as the fundamental group. Hopefully this talk will be a good (but very concise) introduction to the world of knot theory and low dimensional topology. |
| 22nd December, 2005. | Mike Hochman |
Lecture : Why tiling the plane is complicated.
A set of tiles in one/two dimensions is a set of segments/squares of the form [0,1] or [0,1]x[0,1] whose boundary faces (points in one dimension or segments in two diemensions) are colored using some finite set of colors. a legal tiling is a tiling of the line/plane by translates of the tiles such that every boundary face meets a face of the same color (like in the game of dominos). It turns out that tilings of the line are easy to understand, while tilings of the plane can be very, very complicated. i will explain various aspects of this phenomenon. the talk will be entirely elementary. |
| 15th December, 2005. | Boaz Karni |
Lecture: Super Manifolds and Super Mathematics
During the 70's a new theory in physics - supersymmetry, gave rise to new mathematical concepts, that were given the name of super-mathematics. In my talk I will define the basic objects of supermatematics - the super vectorspace, super algebra and supemanifold, and will show how to adjust the well known non-super operations and objects to the super-case. |
8th December, 2005. | Uri Shapira |
Lecture : Basic concepts in measurable and topological dynamics.
We will discuss the following subjects: -Measurable and topological dynamical systems -Ergodicity -Partitions and measure theoretical entropy -Covers and topological entropy -The variational principle -A short overview of my Ms.c thesis preliminaries: abisal'e measure theory and topology. |
| 1th December, 2005. | Shlomi Kotler |
Lecture : Quantum Mechanics for Mathematicians
A short introduction of the theory of Quantum Mechanics. What were the problems physics scientists had which led to the construction of the theory. Descriptions of wave equations. The behaviour of electrons as waves and as particles. The hydrogen atom. A "Derivation" of the famous Schrodinger equation. We assume no prior knowledge of physics. |
| 24th November, 2005. | Eran Nevo |
Lecture : The Face Ring
The purpose of this talk is to give a flavor of face rings (Stanley-Reisner rings). This is a meeting point of combinatorics, algebraic topology, commutative algebra and geometry. Some well known results which demonstrate it will be presented, and, time permitting, also new ones. |