Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Curves Seminar - Mike Roth (Queen's University)

Wednesday, October 9th, 2019

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Classical results on canonical embeddings.

Abstract: We will discuss the canonical map in the case of hyperelliptic curves, the geometric interpretation of the Riemann-Roch theorem via the canonical map, the Hilbert polynomial and Hilbert function of canonically embedded curves, and start looking at examples of resolutions of canonical embeddings in small genus.

Geometry & Representation - John Michael Machacek (York University)

Monday, October 7th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: John Michael Machacek (York University)

Title: Mutation combinatorics and upper cluster algebras.

Abstract:  Any cluster algebra is contained in an intersection of Laurent polynomial rings known as its upper cluster algebra. There are known cases where this containment is equality as well as cases of strict containment. We will discuss combinatorial approaches to determining if this containment is strict or not. Notions used will include reddening sequences and locally acyclic cluster algebras.

Department Colloquium - Diane Maclagan (Warwick)

Diane Maclagan (Warwick)

Friday, October 4th, 2019

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

Speaker: Diane Maclagan (Warwick)

Title: Geometry of the moduli space of genus zero curves.

Abstract: The moduli space $\overline{M}_{0,n}$ of stable genus zero curves with $n$ marked points is a beautiful space that has been intensively studied by algebraic geometers and topologists for over half a century. It arises from a simple geometric question ("How can we arrange $n$ points on a sphere?"), but is the first nontrivial case of several interesting families of varieties (higher genus curves, stable maps, ...) and phenomena. Despite the long history there are still many mysteries about this variety. I will introduce this moduli space, and discuss some combinatorial approaches to understanding it.

Diane Maclagan (Warwick) is a Professor of Mathematics at the University of Warwick. She received her PhD from UC Berkeley, and moved to Warwick from Rutgers, following postdocs at IAS and Stanford. Her research is in Combinatorial Algebraic Geometry, with a particular focus on Tropical Geometry.

Curves Seminar - Mike Roth (Queen's University)

Wednesday, October 2nd, 2019

Time: 4:30-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Canonically embedded curves II.

Abstract: We will show that the canonical map is always an embedding for non-hyperelliptic curves, understand the canonical map in the hyperelliptic case, and discuss the ‘geometric interpretation’ of the Riemann-Roch theorem, via the canonical embedding.

Note that the seminar is starting later than its usual time, and will only go for an hour this week.

Department Colloquium - Kathryn Mann (Cornell University)

Kathryn Mann (Cornell University)

Friday, September 27th, 2019

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

Speaker: Kathryn Mann (Cornell University)

Title: Structure theorems for actions of homeomorphism groups.

Abstract: The groups $\mathrm{Homeo}(M)$ and $\mathrm{Diff}(M)$ of homeomorphisms or diffeomorphisms of a manifold $M$ have many striking parallels with finite dimensional Lie groups. In this talk, I'll describe some of these, and explain new work, joint with Lei Chen, that gives an orbit classification theorem and a structure theorem for actions of homeomorphism and diffeomorphism groups on other spaces, analogous to some classical results for actions of locally compact Lie groups. As applications, we answer many concrete questions towards classifying all actions of $\mathrm{Diff}(M)$ on other manifolds (many of which are nontrivial, for instance $\mathrm{Diff}(M)$ acts naturally on the unit tangent bundle of $M$...) and resolve several threads in a research program initiated by Ghys. I'll aim to give both a broad overview and several toy applications in the talk.

Professor Kathryn Mann received her PhD from the University of Chicago in 2014, she then held post-doctoral positions at MSRI, UC Berkeley and the Institut de mathématiques de Jussieu before becoming a Manning Assistant Professor of Mathematics at Brown University. In 2019, she joined Cornell University. Among her accolades is an Alfred P. Sloan Foundation Fellowship (2019), an NSF Career Award (2019), the AWM-Birman Research Prize in Topology and Geometry (2019), the Kamil Duszenko Award (2019) and the Mary Ellen Rudin young researcher award (2017).

Curves Seminar - Mike Roth (Queen's University)

Wednesday, September 25th, 2019

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Canonically embedded curves.

Abstract: Green’s conjecture concerns ‘canonical curves’ — curves embedded in projective space by their canonical bundle. We will review the basic language of line bundles, divisors, and the Riemann-Roch theorem for curves, and show that, for non-hyperelliptic curves, the canonical bundle of a curve of genus $g\geq 2$ is ‘very ample’, i..e, gives an embedding of the curve in projective space.

Number Theory Seminar - Brad Rodgers (Queen's University)

Tuesday, September 24th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Brad Rodgers (Queen's University)

Title: Moments and pseudomoments of the Riemann zeta-function.

Abstract: In this talk I will discuss moments of the Riemann zeta-function and "pseudomoments", in which the zeta-function is replaced by a finite Dirichlet polynomial. I hope to explain the connection to random multiplicative functions and if there is sufficient time discuss a conjecture of Helson (recently proved by Harper) along with a weighted version previously proved by Bondarenko, Heap, and Seip.

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