# Techmath - Math Seminars in Israel

*Abstract:*

Abstract: Semicocycles appear naturally in the study of the asymptotic behavior of non-autonomous differential equations. They play an important role in the theory of dynamical systems and are closely connected to semigroups of weighted composition operators. In this talk we consider semicocycles whose elements are either continuous or holomorphic mappings on a domain in a real/complex Banach space which take values in a unital Banach algebra. We study properties of semicocycles employing, in particular, their link with semigroups of nonlinear mappings. We show analogies as well as differences between the theory of semigroups and the theory of semicocycles. One of our main aims is to establish conditions for differentiability of a semicocycle and prove the existence of a "generator". The simplest semicocycles are those independent of the spatial variable. An interesting problem is to determine whether a given semicocycle is cohomologous to an independent one (in other words, is linearizable). We provide some criteria for a semicocycle to be linearizable as well as several easily verifiable sufficient conditions. This is joint work with Fiana Jacobzon and Guy Katriel.

*Abstract:*

**Advisor: **Prof**. **Amos Nevo

**Abstract: **Counting lattice points has a long history in number theory, that can be traced back to Gauss. I will introduce this subject, and its relation to questions regarding asymptotic properties of integral points in the plane. The main focus will be an arithmetic result regarding equidistribution of parameters that characterize primitive integral points. I will also present a similar result for rings of integers in C (e.g., Gaussian integers).

Both these results are achieved via counting lattice points w.r.t. the Iwasawa decomposition in certain simple rank-one Lie groups, a topic which I will discuss more generally, if time permits.

*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**

*Announcement:*

Title of lectures: **Virtual fibering theorem**.

Lecture 1: Monday, November 5, 2018 at 15:30 (about the statement, history and more)

Lecture 2: Wednesday, November 7, 2018 at 15:30

Lecture 3: Thursday, November 8, 2018 at 15:30

The other two lectures will be about the proof, following Prof. Friedl's paper with Takahiro Kitayama.

** Abstract**: In 2008 Agol showed that a 3-manifold with a certain condition on its fundamental group is virtually fibered, i.e. it has a finite covering that is a surface bundle over the circle. A few years later it was shown by Agol and Wise that the fundamental groups of most 3-manifold satisfy Agol's condition, i.e. most 3-manifodls are virtually fibered. We will outline a proof of Agol's theorem following an approach taken by myself and Kitayama.

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

*Announcement:*

Title of lectures: **Virtual fibering theorem**.

Lecture 1: Monday, November 2, 2018 at 15:30 (about the statement, history and more)

Lecture 2: Wednesday, November 4, 2018 at 15:30

Lecture 3: Thursday, November 5, 2018 at 15:30

The other two lectures will be about the proof, following Prof. Friedl's paper with Takahiro Kitayama.

**Abstract**: In 2008 Agol showed that a 3-manifold with a certain condition on its fundamental group is virtually fibered, i.e. it has a finite covering that is a surface bundle over the circle. A few years later it was shown by Agol and Wise that the fundamental groups of most 3-manifold satisfy Agol's condition, i.e. most 3-manifodls are virtually fibered. We will outline a proof of Agol's theorem following an approach taken by myself and Kitayama.

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

*Announcement:*

Title of lectures: **Virtual fibering theorem**.

Lecture 1: Monday, November 2, 2018 at 15:30 (about the statement, history and more)

Lecture 2: Wednesday, November 4, 2018 at 15:30

Lecture 3: Thursday, November 5, 2018 at 15:30

The other two lectures will be about the proof, following Prof. Friedl's paper with Takahiro Kitayama.

**Abstract**: In 2008 Agol showed that a 3-manifold with a certain condition on its fundamental group is virtually fibered, i.e. it has a finite covering that is a surface bundle over the circle. A few years later it was shown by Agol and Wise that the fundamental groups of most 3-manifold satisfy Agol's condition, i.e. most 3-manifodls are virtually fibered. We will outline a proof of Agol's theorem following an approach taken by myself and Kitayama.

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

*Announcement:*

Title: **Geometric structures in nonholonomic mechanics.**

Lecture 1: Monday, November 12, 2018 at 15:30

Lecture 2: Wednesday, November 14, 2018 at 15:30

Lecture 3: Thursday, November 15, 2018 at 15:30

*Announcement:*

Title: **Geometric structures in nonholonomic mechanics.**

Lecture 1: Monday, November 12, 2018 at 15:30

Lecture 2: Wednesday, November 14, 2018 at 15:30

Lecture 3: Thursday, November 15, 2018 at 15:30

*Announcement:*

Title: **Geometric structures in nonholonomic mechanics.**

Lecture 1: Monday, November 12, 2018 at 15:30

Lecture 2: Wednesday, November 14, 2018 at 15:30

Lecture 3: Thursday, November 15, 2018 at 15:30

*Announcement:*

Title & abstract of lectures: **TBA**.

Lecture 1: Monday, March 25, 2019 at 15:30

Lecture 2: Wednesday, March 27, 2019 at 15:30

Lecture 3: Thursday, March 28, 2019 at 15:30

*Announcement:*

Title & abstract of lectures: **TBA**.

Lecture 1: Monday, March 25, 2019 at 15:30

Lecture 2: Wednesday, March 27, 2019 at 15:30

Lecture 3: Thursday, March 28, 2019 at 15:30

*Announcement:*

Title & abstract of lectures: **TBA**.

Lecture 1: Monday, March 25, 2019 at 15:30

Lecture 2: Wednesday, March 27, 2019 at 15:30

Lecture 3: Thursday, March 28, 2019 at 15:30

*Announcement:*

**Title**: *The Double Bubble Problem*

**Abstract**: A single round soap bubble provides the least-perimeter way to enclose a given volume of air, as was proved by Schwarz in 1884. The Double Bubble Problem seeks the least-perimeter way to enclose and separate two given volumes of air. Three friends and I solved the problem in Euclidean space in 2000. In the latest chapter, Emanuel Milman and Joe Neeman recently solved the problem in Gauss space (Euclidean space with Gaussian density). The history includes results in various spaces and dimensions, some by undergraduates. Many open questions remain.

*Announcement:*

**Title**: *The Isoperimetric Problem*

**Abstract**: The isoperimetric problem seeks the least-perimeter way to enclose a given volume. Although the answer is well known to be the round sphere in Euclidean and some other spaces, many fascinating open questions remain. Is a geodesic sphere isoperimetric in CP^2? What is the least-perimeter tile of the hyperbolic plane of prescribed area?

*Announcement:*

**Title**: *The Isoperimetric Problem in Spaces with Density*

**Abstract**: Since their appearance in Perelman's 2006 proof of the Poincaré Conjecture, there has been a flood of interest in positive weights or densities on spaces and the corresponding isoperimetric problem. The talk will include recent results and open questions.

*Announcement:*