Seminars and Colloquiums
for the week of April 16, 2018
Kyle Austin, Weizmann Institute of Science, Tel Aviv, Israel
Yaozhong Hu, University of Alberta
Ryan Unger, University of Tennessee
Cassie Micucci, University of Tennessee
Ling Xiao, University of Connecticut
Daniel Anderson, George Mason University
Monday, April 16
TOPOLOGY/ GEOMETRY SEMINAR
Title: Coordinates in Operator Algebras
Speaker: Kyle Austin, Weizmann Institute of Science, Tel Aviv, Israel
Time: 2:30 PM-3:20 PM
Room: Ayres 112
I will discuss how ideas in geometric topology can be interpreted as coordinatization of spaces and I will use this viewpoint to discuss the Gelfand duality theorem which says that locally compact Hausdorff spaces are the coordinates for commutative C*-algebras and visa versa. My first order of business will be to explain how to extend Gelfand duality by considering partial maps of spaces. From there I will discuss how groups and groupoids both behave as coordinates for more complex C*-algebras. I will discuss my current project with Atish Mitra on a vast extension of Gelfand duality between locally compact Hausdorff groupoids and a slight generalization of Cartan pairs. There will be no prerequisites for C*-algebras needed. My aim in this talk is just to give the big ideas to the things I do and the overall philosophy of coordinatization.
Tuesday, April 17
Title: Necessary and sufficient conditions to solve a heat equation with general Additive Gaussian noise
Speaker: Yaozhong Hu, University of Alberta
Time: 2:10 PM-3:20 PM
Room: Ayres 114
In this talk I will present a recent result on stochastic heat equation with general additive Gaussian noise.
The aim is to derive some necessary and sufficient conditions on the structure of Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two different methods, respectively based on variance computations and on path-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution. Then we show that this condition is also sufficient to obtain existence and uniqueness in the multiplicative case.
GENERAL RELATIVITY SEMINAR
Title: Dimension reduction and minimal surface singularities
Speaker: Ryan Unger, University of Tennessee
Time: 5:00 PM-6:00 PM
Room: Ayres 113
We will present Federer's dimension reduction argument and indicate how this can be used to control the dimension of the singular set of a minimizing current. This is important for the regularity theory of minimal surfaces and Schoen and Yau's minimal slicings.
Wednesday, April 18
COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
Title: Geometry Helps to Compare Persistence Diagrams
Speaker: Cassie Micucci, University of Tennessee
Time: 3:35 PM-4:35 PM
Room: Ayres 112
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft–Karp algorithm for bottleneck matching (based on previous work by Efrat el al.), and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.
Thursday, April 19
GEOMETRIC ANALYSIS SEMINAR
Title: Complete translating solitons to the mean curvature flow in $R^3$ with nonnegative mean curvature.
Speaker: Ling Xiao, University of Connecticut
Time: 3:00 PM-4:00 PM (note change)
Room: Ayres 404 (note change)
We prove that any complete immersed two-sided mean convex translating soliton $\Sigma\subset R^3$ for the mean curvature flow is convex. As a corollary it follows that an entire mean convex graphical translating soliton in $R^3$ is the axisymmetric “bowl soliton”. We also show that if the mean curvature of $\Sigma$ tends to zero at infinity, then $\Sigma$ can be represented as an entire graph and so is the “bowl soliton”. Finally we classify all locally strictly convex graphical translating solitons defined over strip regions. This is a joint work with Joel Spruck.
Friday, April 20
Title: Convective instabilities in alloy solidification.
Speaker: Daniel Anderson, George Mason University
Time: 3:35 PM-4:35 PM
Room: Ayres 405
Solidification of binary and multicomponent alloys occurs in many industrial and geophysical systems. Often in these systems instabilities of the solid/liquid interface lead to dendritic regions that separate completely solid regions from the liquid region. These so-called mushy layers, which are reactive (evolving) porous media, have important consequences for heat and solute transfer between the solid and liquid regions. In this talk we outline mathematical models and their connection to laboratory experiments that help understand the physical processes occurring in these systems. Through linear stability analyses and numerical calculations, convective instabilities that occur in solidifying ternary alloys will be compared to related processes such as double-diffusive convection in non-reactive porous layers. Novel fluid dynamical phenomena that occur in mushy layers will be discussed.
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu
3_12_18 (spring break)