Seminars and Colloquiums
for the week of February 4, 2019
Ryan Unger, University of Tennessee
Jie Xiong, Southern University of Science & Technology, PRC
Ken Stephenson, University of Tennessee
Steve Wise, University of Tennessee
Daniel Sussman, Boston University
David Cruz-Uribe, University of Alabama
Paul Hurtado, University of Nevada, Reno
Laura Miller, University of North Carolina at Chapel Hill
TEA TIME - cancelled for this week
3:00 PM – 3:30 PM
Monday, Tuesday & Wednesday
Room: Ayres 401
GEOMETRIC ANALYSIS READING SEMINAR
TITLE: Introduction to Ricci flow and 3-manifolds
SPEAKER: Ryan Unger, University of Tennessee
TIME: 3:35 PM-5:30 PM
ROOM: Ayres 113
Perelman proved the Poincare and geometrization conjectures in 2003 using Ricci flow with surgery. In this talk I will give a broad overview of how Ricci flow (with and without surgery) can be used to understand the topology of 3-manifolds.
TITLE: Stackelberg game with partial information
SPEAKER: Jie Xiong, Southern University of Science & Technology, PRC
TIME: 2:10 PM-3:25 PM
ROOM: Ayres 114
This talk is concerned with a leader-follower stochastic differential game with asymmetric information, where the information available to the follower is based on some sub-$\sigma$-algebra of that available to the leader. Such kind of game problems has wide applications in finance, economics and management engineering such as newsvendor problems, cooperative advertising and pricing problems. Stochastic maximum principles and verification theorems with partial information will be presented. As an application, a linear-quadratic leader-follower stochastic differential game with asymmetric information is studied. It is shown that the open-loop Stackelberg equilibrium admits a state feedback representation if some system of Riccati equations is solvable. This talk is based on a joint work with Shi and Wang.
TITLE: Projective Structures and the Schwarzian Derivative
SPEAKER: Ken Stephenson, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 113
I will introduce the Schwarzian derivative of an analytic function and some of its basic properties --- in particular, its invariance under Mobius transformations. This property makes the Schwarzian particularly useful in the study of projective structures on Riemann surfaces. I will concentrate on those I've discussed previously, namely, affine structures on 1-tori. These have been discretized via circle packing, raising the issue of how one might discretize the Schwarzian. We will discuss a notion proposed by my former student Gerald Orick and see if it leads somewhere.
COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
TITLE: Convergence Analyses of some Nonlinear Multi-Level Algorithms for Non-Quadratic Convex Optimization Problems via Space Decomposition and Subspace Correction, Part I
SPEAKER: Steve Wise, University of Tennessee
TIME: 3:35 PM-4:25 PM
ROOM: Ayres 113
Nonlinear multi-level methods, such as the full approximation storage (FAS) multigrid scheme, are widely used solvers for nonlinear problems. In this paper, a new framework to analyze FAS-type methods for convex optimization problems is developed. FAS can be recast as an inexact version of a nonlinear multigrid method based on space decomposition and subspace correction, namely the successive subspace optimization (SSO) method of Jinchao XU and coauthors. The theory is quite general and is an abstraction of both SSO and the preconditioned steepest descent (PSD) method. In our algorithm, we show that the local problem in each subspace can be simplified to be linear and one gradient decent iteration is enough to ensure linear convergence of the FAS scheme. In Part I, I will introduce the terminology and primary assumptions, and we will give an improved convergence result for SSO in a Hilbert space setting. Then we will motivate and define the generalized FAS algorithm. This work is joint with Long Chen and Xiaozhe Hu.
MATHEMATICAL DATA SCIENCE SEMINAR
TITLE: Multiple Network Inference: From Joint Embeddings to Graph Matching
SPEAKER: Daniel Sussman, Boston University
TIME: 12:30 PM-2:00 PM
ROOM: Ayres 405
Statistical theory, computational methods, and empirical evidence abound for the study of individual networks. However, extending these ideas to the multiple-network framework remains a relatively under-explored area. Individuals today interact with each other through numerous modalities including online social networks, telecommunications, face-to-face interactions, financial transactions, and the sharing and distribution of goods and services. Individually these networks may hide important activities that are only revealed when the networks are studied jointly. In this talk, we'll explore statistical and computational methods to study multiple networks, including a tool to borrow strength across networks via joint embeddings and a tool to confront the challenges of entity resolution across networks via graph matching.
DIFFERENTIAL EQUATIONS SEMINAR
TITLE: Matrix Ap weights, degenerate Sobolev spaces, and mappings of finite distortion
SPEAKER: David Cruz-Uribe, University of Alabama
TIME: 2:10 PM-3:25 PM
ROOM: Ayres 114
(pdf of abstract)
MATH BIOLOGY SEMINAR
SPEAKER: Paul Hurtado, University of Nevada, Reno
TIME: 11:15 AM-12:05 PM
ROOM: Ayres 401
We have been discussing the paper by Drs. Paul Hurtado and Adam Kirosingh titled "Generalizations of the ‘Linear Chain Trick’: Incorporating more flexible dwell time distributions into mean field ODE models." During this week's seminar, we host a visit by co-author Paul Hurtado from the University of Nevada, Reno to discuss this work in person. Following a brief introduction of the main ideas of the work by Dr. Hurtado, graduate students Danielle Burton and Athma Senthilnathan will moderate the discussion with the group. If you are interested in being added the Math Biology Seminar 'BaseCamp' site to receive notices and seminar materials directly, please contact Judy Day at firstname.lastname@example.org.
TITLE: The dispersal of aerial plankton: Spider ballooning and flapping with bristled wings
SPEAKER: Laura Miller, University of North Carolina at Chapel Hill
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
A vast body of research has described the complexity of flight in insects ranging from the fruit fly, Drosophila melanogaster, to the hawk moth, Manduca sexta. Over this range of scales, flight aerodynamics as well as the relative lift and drag forces generated are surprisingly similar. The smallest flying insects (Re~10) have received far less attention, although previous work has shown that flight kinematics and aerodynamics can be significantly different. At a similar scale, spiders use a type of aerial dispersal called “ballooning” to move from one location to another. In order to balloon, a spider releases a silk dragline from its spinnerets and when the movement of air relative to the dragline generates enough force, the spider takes flight.
In this presentation, we have used a multi-pronged approach that consists of measurements of flight kinematics, quantification of wing morphology and dragline properties, measurements of flow velocities and forces using physical models, and direct numerical simulations to compute flow and lift and drag forces. For tiny insects, the lift to drag ratio during hovering flight decreases significantly as the Re decreases below 10. The clap and fling mechanism of lift generation does augment lift forces ~30%, however, peak drag can increase almost an order of magnitude due to viscous effects from wing-wing interaction. Bristles can reduce these peak forces, and may aid in passive flight behavior. In spiders, the dynamics of ballooning is significantly influenced by the spider mass and the length of the dragline. Dragline properties such as the bending modulus also play important roles. While the spider-dragline is in flight, the instability of the atmosphere and stratification layers may allow the spider to remain airborne for long periods of time.
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
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