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 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.

Geometry & Representation - Atabey Kaygun (Istanbul Tech University)

Monday, September 23rd, 2019

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

Speaker: Atabey Kaygun (Istanbul Technical University)

Title: Distributive Laws, Smash Biproducts and Hochschild Homology.

Abstract:  In this talk I am going to talk about distributive laws between algebras, resulting smash biproducts and their Hochschild homology. The examples include Ore extensions, Hopf smash products, quantum affine spaces and quantum complete intersection algebras. This is joint work with Serkan Sutlu.

Department Colloquium - Xudong Chen (CU Boulder)

Xudong Chen (CU Boulder)

Friday, September 20th, 2019

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

Speaker: Xudong Chen (CU Boulder)

Title: Structure Theory for Ensemble Control and Estimation of Nonholonomic Systems.

Abstract: Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of individual control systems. As a dual, ensemble estimation deals with the problem of using a finite number of measurement outputs to estimate the initial state of every individual system in the (continuum) ensemble. We introduce in the talk a novel class of ensembles of nonlinear control systems, termed distinguished ensemble systems. Every such system has two key components, namely a set of finely structured control vector fields and a set of co-structured observation functions. In the first half of the talk, we demonstrate that the structure of a distinguished ensemble system can significantly simplify the analysis of ensemble controllability and observability. Moreover, such a structure can be used as a principle for ensemble system design. In the second half of the talk, we address the issue about existence of a distinguished ensemble system for a given manifold. We will focus on the case where the underlying space of every individual system is an arbitrary semi-simple Lie group or its homogeneous space.

Professor Chen is an Assistant Professor at the University of Colorado, Boulder. Before that, he was a postdoctoral fellow in the Coordinated Science Lab at UIUC. He obtained his Ph.D. degree in Electrical Engineering from Harvard University in 2014. His research interests are in the area of control theory, stochastic processes, optimization, game theory and their applications in modeling and control of large-scale networked systems.

Dynamics, Geometry, & Groups - Ian Frankel (Queen's University)

Friday, September 20th, 2019

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: Ian Frankel (Queen's University)

Title: Local geometry of Teichmüller space: flat and quasiconformal.

Abstract: The Teichmüller distance between two homeomorphic Riemann surfaces X and Y is a number that quantifies the following question: Given a homeomorphism from X to Y, how non-conformal does the map have to be?

The optimal quasiconformal maps, i.e. those with smallest quasiconformal constant, are characterized by choices of special singular flat metrics on X and Y, and in fact fit into a large familes of maps, and the dynamics of SL(2,R) acting on this family have been the subject of many celebrated results in the past decade.

Now, suppose we are given X and Y but with singular flat metrics that are not related to the optimal map. We will describe how we can still estimate the Teichmüller distance from X to Y.

Curves Seminar—Gregory G. Smith (Queen's University)

Wednesday, September 18th, 2019

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

Speaker: Gregory G. Smith (Queen's University)

Title: Koszul complexes

Abstract: We introduce Koszul complexes and examine a couple different interpretations.  Beyond providing a concrete family of minimal free resolutions, this structure plays a significant role in analyzing the syzygies of canonical curves.