# Techmath - Math Seminars in Israel

*Abstract:*

Multi-finger caging offers a robust approach to object grasping. To securely grasp an object, the fingers are first placed in caging regions surrounding a desired immobilizing grasp. This prevents the object from escaping the hand, and allows for great position uncertainty of the fingers relative to the object. The hand is then closed until the desired immobilizing grasp is reached. While efficient computation of two-finger caging grasps for polygonal objects is well developed, the computation of three-finger caging grasps has remained a challenging open problem. We will discuss the caging of polygonal objects using three-finger hands that maintain similar triangle finger formations during the grasping process. While the configuration space of such hands is four dimensional, their contact space which represents all two and three finger contacts along the grasped object's boundary forms a two-dimensional stratified manifold. We will present a caging graph that can be constructed in the hand's relatively simple contact space. Starting from a desired immobilizing grasp of the object by a specific triangular finger formation, the caging graph is searched for the largest formation scale value that ensures a three-finger cage about the object. This value determines the caging regions, and if the formation scale is kept below this value, any finger placement within the caging regions will guarantee a robust object grasping.

*Abstract:*

Commutator length is a group theoretical analogue of genus. By taking a limit, stable commutator length, scl, is obtained. This is a group invariant that can be studied topologically. As scl detects surface subgroups, it is thought to be an important invariant for the study of 3-manifolds, however, there are open questions regarding its computability and its unit norm ball. This talk will give some background on scl in low dimensional topology, and will outline some work in progress of the speaker towards resolving these questions for 3-manifold groups.

***Double feature: please note the special time***

*Abstract:*

Commutator length is a group theoretical analogue of genus. By taking a limit, stable commutator length, scl, is obtained. This is a group invariant that can be studied topologically. As scl detects surface subgroups, it is thought to be an important invariant for the study of 3-manifolds, however, there are open questions regarding its computability and its unit norm ball. This talk will give some background on scl in low dimensional topology, and will outline some work in progress of the speaker towards resolving these questions for 3-manifold groups.

*Abstract:*

I will describe joint work with Sergei Lanzat.

Tropical geometry provides a new piece-wise linear approach to algebraic geometry. The role of algebraic curves is played by tropical curves - planar metric graphs with certain requirements of balancing, rationality of slopes and integrality. A number of classical enumerative problems can be easily solved by tropical methods. Lately is became clear that a more general approach also makes sense and seem to appear in other areas of mathematics and physics. We consider a generalization of tropical curves, removing requirements of rationality of slopes and integrality and discuss the resulting theory and its interrelations with other areas. Balancing conditions are interpreted as criticality of a certain action functional. A generalized Bezout theorem involves Minkowsky sum and mixed areas. A problem of counting curves passing through an appropriate collection of points turns out to be related to quadratic Plücker relations in Gr(2,4) and some nice Lie algebra. If time permits, we will also discuss new recursive relations for this count (in the spirit of Kontsevich and Gromov-Witten).

*Abstract:*

About 15 years ago, Bourgain, Brezis and Mironescu proposed a new characterization of BV and W^(1,q) spaces (for q > 1) using a certain double integral functional involving radial mollifiers. We study what happens when one changes the power of |x-y| in the denominator of the integrand from q to 1. It turns out that for q > 1 the corresponding functionals "see" only the jumps of the BV-function. We further identify the function space relevant to the study of these functionals as an appropriate Besov space. We also present applications to the study of singular perturbation problems of Aviles-Giga type.

*Abstract:*

A long line of research studies the space complexity of estimating a norm l(x) in the data-stream model, i.e., when x is the frequency vector of an input stream consisting of insertions and deletions of items of n types. I will focus on norms l (in R^n) that are *symmetric*, meaning that l is invariant under sign-flips and coordinate-permutations, and show that the streaming space complexity is essentially determined by the measure-concentration characteristics of l. These characteristics are known to govern other phenomena in high-dimensional spaces, such as the critical dimension in Dvoretzky's Theorem. The family of symmetric norms contains several well-studied norms, such as all l_p norms, and indeed we provide a new explanation for the disparity in space complexity between p<=2 and p>2. We also obtain bounds for other norms that are useful in applications. Joint work with Jaroslaw Blasiok, Vladimir Braverman, Stephen R. Chestnut, and Lin F. Yang.

*Abstract:*

Using technical language, the Navier-Stokes equations with measure initial data (such as "point vortices"), in two (spatial) dimensions, have attracted much mathematical interest in the last twenty years. There are still many basic open problems, such as well-posedness in bounded domains, Hopf bifurcation into time-periodic solutions and many more. The talk will be non-technical, the only expected analytical background is advanced calculus. It will touch on the theoretical aspects as well as the indispensable accompanying numerical simulations. The general topic has fascinated many poets: "Waves, undulaing waves, liquid, uneven, emulous waves... laughing and buoyant" (Walt Whitman). However, the talk will be much more prosaic.

*Abstract:*

Spectral theory for general classes of first order systems has been less popular since 1990's. In this talk, I would like to propose a new class of first order systems which generalize both Maxwell and Dirac equations. In this new class, we can treat these two equations in a unified manner, although their physical backgrounds are very different from each other. The main point of my talk is space-time estimates for the new class of first order systems. The essential part of the idea is to derive uniform boundedness of the spectral densities. This talk is based on joint work with Matania Ben-Artzi.

*Abstract:*

Understanding the ways in which the Brain gives rise to the Mind (memory, behavior, cognition, intelligence, language) is the most challengingproblem facing science today. As the answer seems likely to be at least partly computational, computer scientists should work on this problem --- except there is no obvious place to start. I shall recount recent work (with W. Maass and S. Vempala) on a model for the formation and association of memories in humans, and reflect on why it may be a clue about language.

*Abstract:*

Numerous optimization problems are solved using the tools of distributionally robust optimization. In this framework, the distribution of the problem's random parameter $z$ is assumed to be known only partially in the form of, for example, the values of its first moments. The aim is to minimize the expected value of a function of the decision variables $x$, assuming that Nature maximizes this expression using the worst-possible realization of the unknown probability measure of $z$. In the general moment problem approach, the worst-case distributions are atomic. We propose to model smooth uncertain density functions using sum-of-squares polynomials with known moments over a given domain. We show that in this setup, one can evaluate the worst-case expected values of the functions of the decision variables in a computationally tractable way. This is joint work with Etienne de Klerk (TU Delft) and Daniel Kuhn (EPFL Lausanne).

*Announcement:*

Lecture 1: April 23, 2018 at 15:30

Lecture 2: April 25, 2018 at 15:30

Lecture 3: April 26, 2018 at 15:30

Light refreshments will be given before the talks in the lounge of the Faculty of Mathematics on the 8th floor.

*Announcement:*

Lecture 1: April 23, 2018 at 15:30

Lecture 2: April 25, 2018 at 15:30

Lecture 3: April 26, 2018 at 15:30

Light refreshments will be given before the talks in the lounge of the Faculty of Mathematics on the 8th floor.

*Announcement:*

Lecture 1: April 23, 2018 at 15:30

Lecture 2: April 25, 2018 at 15:30

Lecture 3: April 26, 2018 at 15:30

Light refreshments will be given before the talks in the lounge of the Faculty of Mathematics on the 8th floor.

*Announcement:*

Title of lectures: *Billiard paths on polygons: Where do they lead?*

LECTURE 1: Monday, April 30, 2018 at 15:30

LECTURE 2: Tuesday, May 1, 2018 at 15:30

LECTURE 3: Thursday, May 3, 2018 at 15:30

*Announcement:*

Title of lectures: *Billiard paths on polygons: Where do they lead?*

LECTURE 1: Monday, April 30, 2018 at 15:30

LECTURE 2: Tuesday, May 1, 2018 at 15:30

LECTURE 3: Thursday, May 3, 2018 at 15:30

*Announcement:*

Title of lectures: *Billiard paths on polygons: Where do they lead?*

LECTURE 1: Monday, April 30, 2018 at 15:30

LECTURE 2: Tuesday, May 1, 2018 at 15:30

LECTURE 3: Thursday, May 3, 2018 at 15:30

*Announcement:*

Technion–Israel Institute of Technology

Center for Mathematical Sciences

Supported by the Mallat Family Fund for Research in Mathematics

invite you to a workshop on the topic of

**Nonpositively Curved Groups on the Mediterranean**

**Nahsholim, 23-29.5.18**

**Organizers:**

Kim Ruane,Tufts University

Michah Sageev, Technion–Israel Institute of Technology

Daniel Wise, McGill University

**For more information:**

** http://cms-math.net.technion.ac.il/nonpositively-curved-groups-on-the-mediterranean/ **

*Announcement:*

**TBA....**

For further information please click the link below:

http://cms-math.net.technion.ac.il/summer-school-the-complex-math-of-the-real-world/

*Announcement:*

**SUMMER PROJECTS IN MATHEMATICS AT THE TECHNION**

**Sunday-Friday, September 2-7, 2018**

**PLEASE CLICK HERE FOR FURTHER DETAILS**

**Organizers: Ram Band, Tali Pinsky, Ron Rosenthal**