Seminars and Colloquiums
for the week of September 5, 2016
Yu-Ting Chen, UTK, Tuesday
Faruk Yilmaz, UTK, Wednesday
Steve Wise, UTK, Wednesday
Nam Le, Indiana University, Thursday
Max Schuchard, UTK, Thursday
Dustin Cartwright, UTK, Friday
3:00 pm – 3:30 pm
Tuesday, & Wednesday
Room: Ayres 401
Hosted By: Mustafa Elmas
Tuesday, September 6th
TITLE: KPZ equation, II
SPEAKER: Yu-Ting Chen, UTK
TIME: 2:10pm – 3:25pm
ROOM: Ayres 114
Continuation of the introductory discussion of the KPZ equation.
The Kardar-Parisi-Zhang stochastic PDE is expected to describe universally the fluctuations of weakly asymmetric interface growth. Its ill-posedness challenges the classical Ito theory for stochastic integration, and continues to inspire the development of new techniques for stochastic analysis.
This talk is an introductory discussion of the KPZ stochastic PDE. I will start with the physical background of the Kardar-Parisi-Zhang equation and discuss some recent progress in stochastic analysis in this field.
Wednesday, September 7th
TITLE: "Approximation of Invariant Subspaces in some Dirichlet-type spaces", part III
SPEAKER: Faruk Yilmaz, UTK
TIME: 2:30pm – 3:20pm
In this talk, I will define D_alpha} spaces and give some known properties of these spaces. In particular I will focus on D_2. When the convergence of a sequence of subspaces is mentioned, this is actually a statement about the convergence of the corresponding sequence of projections. In 1972, Korenblum gave the complete characterization of the invariant subspaces of the multiplication operator on D_2. I will prove a theorem about approximation of invariant subspaces of D_2 in terms of finite co-dimensional ones.
COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR
Title: Preconditioned Steepest Descent Methods for some Nonlinear Elliptic Equations Involving p-Laplacian Terms
Speaker: Steve Wise, UTK
Time: 3:35pm – 4:35pm
Room: Ayres 113
I will describe preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration.
This is joint work with W. Feng, A. Salgado, and C. Wang.
Thursday, September 8th
DIFFERENTIAL EQUATIONS SEMINAR
Title: Global smoothness of the Monge-Ampere eigenfunctions
Speaker: Nam Le, Indiana University
Time: 2:00pm – 3:00pm
Room: Ayres 112
The question of global higher derivative estimates up to the boundary of the eigenfunctions of the Monge-Ampere operator is a well-known open problem. In this talk, I will discuss the proof of global smoothness of the eigenfunctions of the Monge-Ampere operator on smooth, bounded and uniformly convex domains in all dimensions. A key ingredient in our analysis is boundary Schauder estimates for certain degenerate Monge-Ampere equations. This is joint work with Ovidio Savin.
Title: Decentralization and Pseudonymity in Bitcoin
Speaker: Max Schuchard, Electrical Engineering and Computer Science UTK
Room: Ayres 405
Bitcoin is a cryptocurrency launched started seven years ago with the goal of providing a decentralized and pseudonymous way for individuals to transfer currency digitally. In this talk I will discuss how well Bitcoin has managed to maintain those goals. I will share some of my research examining how adversaries can, through careful observation and statistical analysis, link transaction pseudonyms with real world identities. We will also briefly examine how Bitcoin's proof of work scheme functions, look at why it fails to democratize mining, and examine alternative proof of work schemes which might provide better decentralization. The talk will cover all necessary background information, and no prior knowledge of Bitcoin or cryptocurrencies is required.
Friday, September 9th
TITLE: Topology of nonarchimedean varieties
SPEAKER: Dustin Cartwright, UTK
ROOM: Ayres 405
A projective variety is the zero set in projective space of a collection of homogeneous polynomials. While the topology of complex varieties has been well-studied from a variety of perspectives, analogous questions are open if the complex numbers are replaced by a non-Archimedean field, meaning a field with an absolute value that satisfies the ultrametric property. I will discuss some results on the topology of non-Archimedean fields, starting with outlining what the relevant topology is.