## Skip Garibaldi delivers Norbert Wiener Lectures at Tufts University

### 2014 04 23 - [algebraic-groups] [lotteries] [lecture-series] [tufts] Skip Garibaldi gave the Wiener
Lectures in the Tufts University Math
Department in
April 2014.

**Some people have all the luck** (public lecture)

**Abstract:** Winning a prize of at least $600 in the lottery is a
remarkable thing - for a scratcher ticket the odds are worse than
1-in-1200 and 1-in-9000 is a more typical figure. Some people have
won many of these large prizes, and clearly they are very lucky or
they buy a ton of lottery tickets. When we investigated records of
all claimed lottery prizes, we discovered that some people had won
hundreds of these prizes! Such people seem to be not just lucky, but
suspiciously lucky. I will explain what we thought they might have
been up to, what mathematics says about it, and what further
investigations revealed. This talk is about joint work with Lawrence
Mower, an investigative reporter for the Palm Beach Post, and Philip
B. Stark, professor and chair of the UC Berkeley Department of
Statistics.

**Topological and generic methods in algebra** (math major lecture)

**Abstract:** In calculus we take limits and think about graphs all
the time, and it would be nice to be able to use the same sorts of
techniques in courses like abstract linear algebra and abstract
algebra, even when you aren’t working with real or complex
numbers. I’ll explain how these techniques can be used and give some
examples of their application.

**Simple algebraic groups and polynomial
invariants** (colloquium lecture)

**Abstract:** The classical “linear preserver problem” asks: Given a
polynomial in finitely many variables, what is the group of linear
transformations that preserve it? This problem has been solved for
many interesting polynomials, usually by means that are special to the
particular polynomial under consideration. We turn this problem on
its head by starting with a polynomial that is preserved by a simple
algebraic group and observe that the full preserver can be described
by a general theorem. The results are new even in the case where the
field is the complex numbers, and as an application we shed some light
on a 125+ year old problem. This is joint work with Bob Guralnick.

Skip Garibaldi gave the Wiener Lectures in the Tufts University Math Department in April 2014.

**Some people have all the luck**(public lecture)

**Abstract:** Winning a prize of at least $600 in the lottery is a
remarkable thing - for a scratcher ticket the odds are worse than
1-in-1200 and 1-in-9000 is a more typical figure. Some people have
won many of these large prizes, and clearly they are very lucky or
they buy a ton of lottery tickets. When we investigated records of
all claimed lottery prizes, we discovered that some people had won
hundreds of these prizes! Such people seem to be not just lucky, but
suspiciously lucky. I will explain what we thought they might have
been up to, what mathematics says about it, and what further
investigations revealed. This talk is about joint work with Lawrence
Mower, an investigative reporter for the Palm Beach Post, and Philip
B. Stark, professor and chair of the UC Berkeley Department of
Statistics.

**Topological and generic methods in algebra**(math major lecture)

**Abstract:** In calculus we take limits and think about graphs all
the time, and it would be nice to be able to use the same sorts of
techniques in courses like abstract linear algebra and abstract
algebra, even when you aren’t working with real or complex
numbers. I’ll explain how these techniques can be used and give some
examples of their application.

**Simple algebraic groups and polynomial invariants**(colloquium lecture)

**Abstract:** The classical “linear preserver problem” asks: Given a
polynomial in finitely many variables, what is the group of linear
transformations that preserve it? This problem has been solved for
many interesting polynomials, usually by means that are special to the
particular polynomial under consideration. We turn this problem on
its head by starting with a polynomial that is preserved by a simple
algebraic group and observe that the full preserver can be described
by a general theorem. The results are new even in the case where the
field is the complex numbers, and as an application we shed some light
on a 125+ year old problem. This is joint work with Bob Guralnick.