Basic Notions seminar

Organizer: Uzi Vishne

Lectures will be self-contained. Talks are usually delivered in Hebrew.
Outline. Our BASIC NOTIONS seminar presents to undergraduate students some mathematical topics which are not normally covered in courses, and gives them better perspective on topics they do meet in class. The seminar aims at the third-year undergraduate level, but we do allow graduate students to sneak in.

Academic year   2010-11

Initial invitation.
Meeting time and place: Sundays, 15:00-16:00, Room 4 in "building" 502.

DATE: 2/1/2011, 15:00-16:00

Speaker: Prof. Eugene Plotkin
Title: Chevalley groups: why are they so important.

Abstract. We intend to give an introduction to Chevalley group theory, and to show how to extend the intuition from linear groups to Chevalley groups.

DATE: 19/12/2010, 15:00-16:00

Speaker: Dr. Gil Ariel
Title: Monte-Carlo simulations

Abstract. Monte-Carlo simulations are a type of computational methods for calculating averaged quantities of complex systems such as fluids, proteins and many others. These methods are also used for numerical integration of multidimensional integrals for which a uniform discritization of the domain of integration is unpractical. From the mathematical point of view, Monte-Carlo simulations are nothing but a clever application of the asymptotic properties of ergodic Markov chains. The talk will review the relevant properties of Markov chains and demonstrate their applications in a few example Monte-Carlo computational schemes.

DATE: 12/12/2010, 15:00-16:00

Speaker: Dr. Michael Schein
Title: Elliptic curves
Abstract. An elliptic curve is a curve defined by a polynomial equation of degree 3. We will consider the set of rational points, and see that it can be endowed with a group structure. We will discuss the groups obtained in this manner (theorems of Mordell and Mazur), and applications to this interaction of geometry and abstract algebra.

DATE: 5/12/2010

Chanukka vacation

DATE: 28/11/2010, 15:00-16:00

Speaker: Prof. Ely Merzbach
Title: Brownian motion: some properties and applications

DATE: 21/11/2010, 15:00-16:00

Speaker: Prof. Yoram Louzon
Title: How can an algorithm know what it sees by being probably approximately correct - An introduction to machine learning

Machine learning is the field of hypotheses development based on a limited set of observations. Very significant progress was performed in this field in the last twenty years with the introduction of new theoretical limits on the learning possibilities of machines and the development of algorithms reaching these limits. We will study the PAC (Probably approximately correct) framework of machine learning, as well as the VC dimension limiting the possibility of applying such learning. We will then discuss some machine learning algorihtms that can produce a hypothesis from a sample of data and understand the family of kernel machines.

DATE: 14/11/2010, 15:00-16:00

Speaker: Dr. Moshe Cohen
Title: An introduction to Knot Theory via the Jones polynomials

A knot is an embedding of the circle in three-dimensional space, but knot theorists prefer to look at the projection of the knot onto the plane along with the data at each crossing of which strand goes over and which goes under. This combinatorial picture is called a diagram.
The primary goal in Knot Theory is distinguishing knots. By a theorem of Reidemeister, two diagrams represent the same knot if one can be transformed into the other by a sequence of three local moves.
This will be a hands-on talk proving that the Jones polynomial is in fact invariant under these three Reidemeister moves and so can be used to distinguish knots.

DATE: 7/11/2010, 15:00-16:00

Speaker: Dr. Reuven Cohen
Title: Fourier transforms in physics and engineering

Fourier transforms are one the most important tools in applied mathematics. In my lecture, I will discuss various appliactions in physics and engineering; explain what is the frequency space and why is it so convenient to use; and try to explain bandwidth and its connections to third generation cellular communication and radio and television broadcasting. I will aslo present uses of the Fourier transform in classical and (in particular) quantum physics. If time permits, I will discuss generalizations to other families with applications, and the connection to Lie groups.

DATE: 31/10/2010, 15:00-16:00

Speaker: Prof. Ron Adin
Title: Coxeter groups
Coxeter Groups, named after a mathematician who lived up to the age of 96, form a very important family of groups. They have applications in geometry, algebra and combinatorics, with strong connections to such diverse notions as reflections, platonic solids, and Lie algebras. Some of these groups are fundamental to the drawings of M. C. Escher.

DATE: 24/10/2010, 15:00-16:00

Speaker: Prof. Louis Rowen
Title: Introduction to Lie Algebras
Lie Algebras are the most important non-associative alebraic structure. The speaker will tell you what they are, give various examples, and indicate the basics of their structure theory.

DATE: 17/10/2010, 15:00-16:00

Speaker: Prof. Uzi Vishne
Title: Growth in groups
When you first encounter a finite group, you will ask for its order. However for infinite groups this strategy is of no value: basically all interesting infinite groups are either countable or of the cardinality of the continuum. In this talk, I will explain how we measure the rate at which an infinite group becomes infinite, and present various aspects of this multifaceted approach.

Academic year   2006-07


Meetings will be held on Mondays, 14:00-15:30, or Thursdays, 12:00-13:30, in the coffee room (third floor).
(The seminar counts as `research activity', and so we ignore the strike).

DATE: 9/7/2007, Monday, 14:00

Speaker: Prof. L. Rowen
Title: Polynomial identities

DATE: 2/7/2007, Monday, 14:00

Speaker: Dr. Meirav Amram
Title: The braid group

DATE: 25/6/2007, Monday, 14:00

Speaker: Dr. Uzi Vishne
Title: Gelfand-Kirillov dimension

DATE: 18/6/2007, Monday, 14:00

Speaker: Dr. Uzi Vishne
Title: Tensor products

I will review constructions, properties and examples of tensor products.

DATE: 11/6/2007, Monday, 14:00

Speaker: Prof. Ron Adin
Title: How many faces can a polytope have?

DATE: 4/6/2007, Monday, 14:00

Speaker: Dr. Shmuel Dahari
Title: Bernoulli numbers

The plan is to connect Bernoulli numbers to sums of powers, Riemann zeta function, and the Fermat's last theorem

DATE: 27/5/2007, Monday, 14:00.

Speaker: Dr. Uzi Vishne
Title: Cohomology of groups

I will present a detailed construction of the first cohomology groups H^i(G,-), and will explain what features of the given group G do they measure.

DATE: 17/5/2007

Speaker: Prof. Tanya Bandman
Title: Genus

DATE: 10/5/2007

Speaker: Prof. Malka Schaps
Title: Basic notions behind the news: Calculating the representations of E8

Basic Notions: Computation over finite fields, Representation of a group, and Exceptional and non-exceptional algebraic groups

DATE: 3/5/2007

Speaker: Dr. Andre Reznikov
Title: p-adic numbers

DATE: 26/4/2007

Speaker: Dr. Tahl Novik
Title: Knots

DATE: 19/4/2007

Speaker: Prof. Misha Katz
Title: E_7 and Gromov's systolic inequality

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Last updated: 6 Oct 2010