# Queen's University - Department of Mathematics and Statistics

 Tuesday, February 14 Seminar in Free Probability and Random Matrices Time: 2:30 p.m. Place: Jeffery 222 Speaker: Mario Diaz, Queen’s University Title: The linearization technique. Part I: Motivation and linearization of polynomials Abstract Attached Tuesday, February 14 Dynamics Seminar Time: 3:30 p.m. Place: Jeffery 422 Speaker: Maria Avdeeva, Queen’s University Title: Statistical properties of discontinuous sawtooth map Abstract Attached Wednesday, February 15 Curves Seminar Time: 3:30 p.m. Place: Jeffery 422 Speaker: Mike Roth Title: Quotients of affine varieties by reductive groups: Examples Abstract Attached Thursday, February 16 Math Club Time: 5:30 p.m. Place: Jeffery 118 Speaker: Francesco Cellarosi Title: Infinitely iterated exponentials Abstract Attached Friday, February 17 Number Theory Seminar Time: 10:30 a.m. Place: Jeffery 422 Speaker: Arunabha Biswas Title: Erdős discrepancy problem and Tao’s work Abstract Attached Friday, February 17 Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 Math & Stat 3 minute thesis competition Monday, February 20 Family Day University offices will be closed.

Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.

Tuesday, February 14, 2:30 p.m. Jeffery 222

Seminar in Free Probability and Random Matrices

Speaker: Mario Diaz

Title: The linearization technique. Part I: Motivation and linearization of polynomials

Abstract: In this talk we will show that every complex polynomial in non-commutative variables can be linearized into a polynomial with matricial coefficients. This linearization technique, also knows as 'descriptor realizations' in the control theory community, has important consequences in the realm of free probability theory.

Seminar website: http://www.mast.queensu.ca/~mingo/seminar/

Tuesday, February 14, 3:30 p.m. Jeffery 422 - Dynamics Seminar

Speaker: Maria Avdeeva

Title: Statistical properties of discontinuous sawtooth map

Abstract: The discontinuous sawtooth map is a measure-preserving automorphism of the torus with a

discontinuity line. We will provide a short survey of the properties of this map and outline a proof of its ergodicity. The proof relies on the Hopf argument for systems with singularities (originally due to Sinai) and generalizations are known; we will limit ourselves to a particular result by S. Vaienti.

Wednesday, February 15, 3:30 p.m. Jeffery 422 - Curves Seminar

Speaker: Mike Roth

Title: Quotients of affine varieties by reductive groups: Examples

Abstract: We will study some examples of group quotients, to see the theorems we have proved in action.

Thursday, February 16, 5:30 p.m. Jeffery 118 Math Club

Speaker: Francesco Cellarosi

Title: Infinitely iterated exponentials

Abstract: Can you find rational solutions to the equation $x^y=y^x$, besides $2^4=4^2$? What does this equation have to do with the bizarre function $$f(x)=x^{x^{x^{x^{...}}}}\HUGE ?$$
We will answer these questions explore some fundamental properties of this function. For instance,
we will compute $$\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{...}}}}$$ and 'prove' along the way that $2=4$.

Friday, February 17, 10:30 a.m. Jeffery 422 - Number Theory Seminar

Speaker: Arunabha Biswas

Title: Erdős discrepancy problem and Tao’s work

Abstract: In 1930s, Erdős speculated that every sequence of {-1,+1} assigned to natural numbers must have large "imbalances" among multiples of some integer. More than eight decades later, Tao confirmed this speculation is correct. In this talk I shall tell a few stories about this magnificent problem.

### Contact Info

 Department of Math & Stats Jeffery Hall, 48 University Ave. Kingston, ON Canada, K7L 3N6 Phone: (613) 533-2390 Fax: (613) 533-2964 mathstat@mast.queensu.ca Office Hours: 8:30am-12:00pm & 1:00pm-4:30pm