¾ÅÐãÖ±²¥

Math Club

Thursday, February 8th, 2024

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: Thomas Barthelmé (Queen’s University)

Title: Bifoliations of the plane to prelaminations of the circle and back again

Abstract: Think of the plane as an (infinite) plate. Then a foliation of the plane is like (infinite) spaghettis on your plate but arranged so that every point of the plate is covered by one and only one spaghetto.This is joint work with Kathyrn Mann and Christian Bonatti.

An old (1940s) result of Kaplan, improved by Mather (1982), is that given your plate of spaghettis, you can make a border of your plate so that each spaghetto is attached at exactly two points of the border of the plate.This is joint work with Kathyrn Mann and Christian Bonatti.

Now a bifoliation of the plane is a plate with two types of spaghetti (some reds and some greens) such that through every point of the plate passes two spaghetti (one red and one green) and such that all the red spaghettis are transverse (ie crosses) the green spaghettis. Similarly, one can add a border to the plate so that each spaghetto ends at exactly two distinct points of the boundary (in that generality, this result is due to Bonatti, in 2023). This set of ends is an example of a prelamination of the circle.This is joint work with Kathyrn Mann and Christian Bonatti.

After describing more precisely the results above, and how one can obtain them, I'll discuss the opposite direction: Given a set of pairs of points on the border of the plate, what are sufficient conditions so that these are the ends of a platter of green/red spaghettis?This is joint work with Kathyrn Mann and Christian Bonatti.

This is joint work with Kathyrn Mann and Christian Bonatti.

PDEs & Applications Seminar

Tuesday, February 6th, 2024

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319 (Via Zoom)

Speaker: Jameson Graber (Baylor University)

Title: The Master Equation in Mean Field Game Theory

Abstract: Mean field game theory was developed to analyze Nash games with large numbers of players in the continuum limit. The master equation, which can be seen as the limit of an N-player Nash system of PDEs, is a nonlinear PDE equation over time, space, and measure variables that formally gives the Nash equilibrium for a given population distribution. In this talk, I will emphasize the fact that the master equation can be seen as a nonlinear transport equation. In particular, the Nash equilibrium is unique if and only if the characteristics do not cross, and when they do cross, we are faced with the question of making a rational selection among multiple equilibria. I will provide some examples to show how subtle this problem is, and in particular, I will show that the usual theory of entropy solutions is in general not sufficient for the purposes of equilibrium selection.

Math & Stats Department Colloquium

Friday, February 2nd, 2023

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Regina Rotman (UofT)

Title: Length of a shortest closed geodesic on a closed Riemannian 3-manifold with positive scalar curvature

Abstract: Let $M$ be a closed Riemannian manifold with the scalar curvature bounded below by some positive constant $\kappa$. We will prove that there exists a closed non-trivial geodesic on $M$ of length at most $\frac{c}{\sqrt{\kappa}}$. (Joint with Y. Liokumovich, D. Maximo.)

Bio: Prof. Regina Rotman obtained her Ph.D. from Stony Brook University in 1998 and is now a Professor of Mathematics at the University of Toronto. Her research interests include geometric inequalities, periodic geodesics and minimal surfaces on compact and non-compact manifolds, geodesic nets, and width of homotopies.

Curves Seminar

Thursday, February 1st, 2024

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Calvin Fletcher

Title: Seed patterns of type D_m

Abstract: In this talk we will demonstrate that seed patterns of type D_m are of finite type. To this end, we will introduce a new combinatorial construction: tagged arcs on a punctured disc. This construction will allow us to use the "full Z-rank" argument to generalize a particular case to the more general case. Finally, we will return to some examples from the opening weeks of this seminar to see this result in practice.

Math Club

Thursday, February 1st, 2024

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: David Wehlau (Queen’s University and Royal Military College)

Title: Pascal's Hexagrammum Mysticum: Solving a 400-Year-Old Geometry Problem

Abstract: In 1639, the 16 year old Blaise Pascal proved his Hexagrammum Mysticum Theorem which provides a straightedge construction to test whether 6 points in the plane lie on a conic. This naturally led to the question of whether there is a straightedge construction which tests whether there is a cubic curve through 10 given points in the plane. I will discuss my joint solution with former ¾ÅÐãÖ±²¥ mathematics undergraduate Dr. Will Traves (US Naval Academy) to this problem explaining some of the history.

PDEs & Applications Seminar

Tuesday, January 30th, 2024

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319 (Via Zoom)

Speaker: Mark Veraar (Delft University of Technology)

Title: Stochastic partial differential equations in critical spaces

Abstract: In this talk I will give an overview of several recent developments on quasi- and semi-linear stochastic PDEs in critical spaces. I will present a new method to prove local and global well-posedness results, and new bootstrap method to show higher order regularity of the solution. In the talk several applications to reaction diffusion equations will be discussed in details. In particular, the new setting allows to prove global well-posedness for several systems which do not satisfy classical coercivity estimates. The talk is based on joint work with Antonio Agresti.

Curves Seminar

Thursday, January 25th, 2024

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Julia McClellan

Title: Seed Patterns of Type Am

Abstract: In this talk we will focus on seed patterns of type Am. Our main goal will be to prove that such seed patterns are of finite type. Consequently, we can say exactly how many cluster variables and seeds such patterns have.

Math & Stats Department Colloquium

Friday, January 26th, 2023

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Steven Boyer (UQAM)

Title: The ADE Link Conjecture

Abstract: The Dynkin diagrams of types A, D and E form a meta-pattern in mathematics in that they structure a number of seemingly unrelated classification problems. In this talk we will survey the current state of knowledge concerning the ADE Link Conjecture, a modest addition to this list which relates the topology of links in the 3-sphere arising from algebraic curves in C2 to ordered groups, taut foliations and Floer homology. This is joint work with Michel Boileau, Cameron Gordon, and Ying Hu.

Bio: Steven Boyer is a Professor of Mathematics at the Universit´e du Qu´ebec `a Montr´eal. He obtained his Ph.D. from Cornell University in 1983. After two years as an NSERC postdoctoral fellow at the University of Cambridge, he worked at the University of Toronto before moving to UQ`AM in 1987. He has held many visiting positions in France, Switzerland and the United Kingdom, and has served on the editorial boards of the Canadian Journal of Mathematics, the Canadian Mathematics Bulletin, and the Annales Math´ematiques Blaise Pascal. Currently he is a member of the editorial boards of Algebraic and Geometric Topology and the Annales des sciences math´ematiques du Qu´ebec. He is also the director of CIRGET in Montr´eal. His research area is the topology and geometry of low-dimensional manifolds.

Distinguished lecture with Xiao-Li Meng

Thursday, March 21st, 2024

Time: 5:30 p.m.  Place: Jeffery Hall, Room 127

Speaker: Xiao-Li Meng (Harvard University)

Title: Being, Training, and Employing Data Scientists: Wisdoms and Warnings from Harvard Data Science Review

Number Theory Seminar

Monday, January 22nd, 2024

Time: 3:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Nic Fellini (¾ÅÐãÖ±²¥)

Title: Reflections on the congruence relations of Ankeny, Artin, and Chowla

Abstract: In 1951, Ankeny, Artin, and Chowla released a short note containing four congruence relations involving the arithmetic invariants of \Q(\sqrt{d}) for d\equiv 1 \bmod{4}. The following year, Ankeny, Artin, and Chowla proved three of the four congruences from their earlier note using p-adic methods. Using p-adic L-functions we will give a cohesive explanation of these congruences as well as a new proof of the originally omitted congruence.