# Queen's University - Department of Mathematics and Statistics

 Wednesday, February 28 Number Theory Seminar Time: 2:15 p.m. Place: Jeffery 319 Speaker: François Séguin Title: Prime divisors of sparse values of cyclotomic polynomials Abstract Attached Wednesday, February 28 Curves Seminar Time: 3:30 p.m. Place: Jeffery 319 Speaker: Mike Roth Title: Zak’s theorems on tangencies II Abstract Attached Thursday, March 1 Math Club Time: 5:30 p.m. Place: Jeffery 118 Speaker: Ivan Dimitrov Title: The Fifteen Theorem Abstract Attached Friday, March 2 Dynamics Seminar Time: 10:30 a.m. Place: Jeffery 422 Speaker: Francesco Cellarosi Title: Spectral theory of dynamical systems Abstract Attached Friday, March 2 Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 Speaker: Laura DeMarco, Northwestern University Title: Complex dynamics and arithmetic equidistribution Abstract Attached Monday, March 5 Geometry and Representation Theory Seminar Time: 4:30 p.m. Place: Jeffery 319 Speaker: Hugh Thomas, UQAM Title: The Robinson-Schensted-Knuth correspondence via quiver representations Abstract Attached

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

Wednesday, February 28, 2:15 p.m. Jeffery 319 - Number Theory Seminar

Speaker: François Séguin

Title: Prime divisors of sparse values of cyclotomic polynomials

Abstract: We will be presenting a result about the largest prime divisors of cyclotomic polynomials evaluated at a specific integer. We will also see how this ties in to problems we previously encountered.

Wednesday, February 28, 3:30 p.m. Jeffery 319 - Curves Seminar

Speaker: Mike Roth

Title: Zak’s theorems on tangencies II

Abstract: We will prove a result due to F. Zak on the secant variety to a smooth variety (under a certain codimension condition). This result proves a conjecture of Hartshorne on linear normality of subvarieties of small codimension.

Thursday, March 1, 5:30 p.m. Jeffery 118 Math Club

Speaker: Ivan Dimitrov

Title: The Fifteen Theorem

Abstract: Can you write every positive integer in the form x² +y² +z² +t² ?

How about x² + 2y² + 5z² + 5t²? Or x² + 2y² + 5z² + 5t² + 2yz + 2yt + 4zt?

There is a rather quick way to tell, which involves the number 15.(!)

. . . and what related question can possibly have answer 290?

Friday, March 2, 10:30 a.m. Jeffery 422 - Dynamics Seminar

Speaker: Francesco Cellarosi

Title: Spectral theory of dynamical systems

Abstract: I will give an introduction to the spectral theory of dynamical systems, including a spectral inequality and its application to twisted stationary sequences (generalizing von Neumann’s ergodic theorem).

Friday, March 2, 2:30 p.m. Jeffery 234 - Department Colloquium

Speaker: Laura DeMarco

Title: Complex dynamics and arithmetic equidistribution

Abstract: About 5 years ago, Matt Baker and I formulated a conjecture about the dynamics of rational maps on P^1, connecting geometry and arithmetic in the moduli space of such maps. My goal is to present recent progress on the conjecture, illustrating some of the main ideas appearing in proofs of special cases. One important special case includes a result about torsion points on elliptic curves, and I hope to discuss how this case can be related to dynamical stability and the Mandelbrot set.

Monday, March 5, 4:30 p.m. Jeffery 319 - Geometry and Representation Theory Seminar

Speaker: Hugh Thomas

Title: The Robinson-Schensted-Knuth correspondence via quiver representations

Abstract: The Robinson--Schensted--Knuth correspondence is a many-faceted jewel of algebraic combinatorics. In one variation, it provides a bijection between permutations of $n$ and pairs of standard Young tableaux with the same shape, which is a partition of $n$. In another (more general) version, it provides a bijection between fillings of a partition $\lambda$ by arbitrary non-negative integers and fillings of the same shape $\lambda$ by non-negative integers which weakly increase along rows and down columns (i.e., reverse plane partitions of shape $\lambda$). I will discuss an interpretation of RSK in terms of the representation theory of type $A$ quivers (i.e., directed graphs obtained by orienting a path graph). This allows us to generalize RSK to other Dynkin types (plus a choice of minuscule weight), and is related to periodicity results for piecewise-linear toggling. I will not assume familiarity with either RSK or with quiver representations. This is joint work with Al Garver and Becky Patrias.

### 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