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

Read More Here

Number Theory Seminar

Monday, January 22nd, 2024

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

Speaker: Nic Fellini (Queen's University)

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.

Math Club

Thursday, January 25th, 2024

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

Speaker: M. Ram Murty (Queen’s University)

Title: The century of elliptic curves

Abstract: Twentieth century number theory was definitely THE century of elliptic curves. Beginning with the celebrated theorem of Mordell in 1922 on the finite generation of of the group of rational points of an elliptic curve over Q, the arithmetic theory of elliptic curves had an exponential growth culminating in the solutions of Fermat's Last Theorem, Ramanujan conjectures, Mordell's conjecture and the Sato-Tate conjecture, to name a few. We will give a retrospective survey of these developments and indicate possible future directions of the theory, especially with regard to the (still open) ABC conjecture.

Dynamics, Geometry and Groups Seminar

Friday, January 26th, 2024

Time: 11:30 a.m.  Place: Jeffery Hall, Room 101

Speaker: Abdul Zalloum (University of Toronto)

Title: Effective rank-rigidity and uniform exponential growth.

Abstract: Let G be a finitely generated group which contains a free subgroup. Gromov asked whether there is an integer m such that for any finite generating set S for G, one can find a pair of elements g,h in G whose length is bounded above by m and which generate a free subgroup. I will discuss some results in that direction.

Curves Seminar

Thursday, January 18th, 2024

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

Speaker: Deepanshu Prasad

Title: Cartan Matrices and Cluster Algebras of Finite Type

Abstract: We'll talk about Cartan matrices and the associated Coxeter-Dynkin diagrams. We'll see how they can be used to classify seed patterns (or the associated cluster algebra) of finite type.

PDEs & Applications Seminar

Tuesday, September 19th, 2023

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Christopher Kennedy (Queen’s)

Title: A Bochner Formula on Path Space for the Ricci Flow

Abstract: Aaron Naber (Northwestern) and Robert Haslhofer (Toronto) have characterized solutions of the Einstein equation in terms of both sharp gradient estimates for Brownian motion and a Bochner formula on elliptic path space. They also successfully characterized solutions of the Ricci flow in terms of an infinite-dimensional gradient estimate on parabolic path space of space-time. In this talk, we shall generalize the classical Bochner formula for the heat flow on evolving manifolds to an infinite dimensional Bochner formula for martingales, thus proving the parabolic counterpart of their results in the elliptic setting as well as characterizing solutions of the Ricci flow in terms of Bochner inequalities on parabolic path space. Time-permitting, we shall also discuss gradient and Hessian estimates for martingales on parabolic path space as well as a condensed proof of previous characterizations of the Ricci flow.

PDEs & Applications Seminar

Tuesday, September 26th, 2023

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Anirban Dutta (Queen’s)

Title: Continuous dependence of solutions to evolution equations in the setting of maximal L^p regularity

Abstract: In this talk, I will introduce the notions of sectorial operator and operator satisfying the property of maximal L^p regularity. These notions play a fundamental role for the well-posedness of linear and quasilinear evolution equations. We will discuss under which conditions both notions are equivalent. After this, I will present a result on the continuous dependence of solutions to nonlinear evolution equations upon data, parameters and forcing in the same set up. An application will be presented.