# Calendar

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### Bridge to Research Seminar, Dr. John Cushman, Purdue University, UNIV 203

Monday, December 1, 2014, 1:30 - 2:30 PM EST

## The Inside-Outs of Porous Media: From Cloaking Devices to Carbon Nanotube Electrodes and More

Abstract: This is a fun talk geared to peak interest in a field of study that involves most all branches of engineering, sciences and agriculture. Most everything on this planet, save the atmosphere and water bodies, is porous if viewed on the appropriate scales. That said, the “tools” developed and employed to study flows in, and deformation of, multiscale porous bodies have direct application to the study of multiscale fluid mechanics and consequently the atmosphere, oceans, lakes and rivers. In this brief talk we will summarize some of our efforts to understand flow in, and deformation of, many types of porous bodies from the nanometer to the global scale. Specific examples will include nano-tribological systems, naturally cloaked lab-scale porous bodies, swelling colloids such as clays, food stuffs and drug delivery substrates, and dispersion/diffusion in reservoirs. A brief illustration will be presented of the various mathematical tools employed in these studies. We will conclude with an introduction to some of our current problems in nanoscale electrodynamics (carbon nanotube electrodes, flow batteries and fuel cells).### Computational & Applied Mathematics Seminar, Dr. Qifeng Liao, MIT, REC 122

Monday, December 1, 2014, 3:30 - 4:30 PM EST

## Reduced Order Modeling and Domain Decomposition Methods for Uncertainty Quantification

Abstract: Traditionally, terms in PDEs such as permeabilities, viscosities or boundary conditions have been treated as known deterministic quantities. However, these quantities are not always known with certainty, and there is much interest today in treating them as random fields. In this talk, I will present a reduced basis collocation method for efficiently solving PDEs with random coefficients, which is joint work with Howard Elman of University of Maryland. I will also present a domain-decomposed uncertainty quantification approach for complex systems, which is joint work with Karen Willcox of Massachusetts Institute of Technology.### Special Colloquium, Samy Tindel, Professor, University of Lorraine, France, REC 302

Monday, December 1, 2014, 4:30 - 5:30 PM EST

## Recent Pathwise and Probabilistic Estimates for Stochastic PDEs

Abstract: We focus on two recent developments concerning stochastic partial differential equations: (i) Let us call parabolic Anderson model a stochastic heat equation whose noisy part is of the form u W, where u is the solution of the equation and W a rather general Gaussian noise. We shall review some of the situations in which the parabolic Anderson model features in a natural way. Then we will show how probabilistic methods yield fruitful information on the model, like intermittency estimates. (ii) We will summarize some of the recent techniques allowing to define solutions of stochastic PDEs in a semi-pathwise manner. These methods are all extensions of the so-called rough paths theory, the most sophisticated version being the theory of regularity structures (introduced by M. Hairer). Finally we will mention some links between the two approaches, focusing on pathwise definitions for the parabolic Anderson model and their implications in terms of regularity estimates. Some open problems will also be discussed.PROBABILISTIC UNCERTAINTY QUANTIFICATION AND EXPERIMENT DESIGN FOR NONLINEAR MODELS: APPLICATIONS IN SYSTEMS BIOLOGY Committee: Buzzard (Chair), Rundell, Feng, Lin.

### Commutative Algebra Seminar, Professor Alberto Corso, University of Kentucky, UNIV 119

Wednesday, December 3, 2014, 2:30 - 3:30 PM EST

## Associated Graded Rings via Normal Hilbert Coefficients

### Probability Seminar, David Sivakoff, Ohio State University, UNIV 103

Wednesday, December 3, 2014, 3:30 - 4:30 PM EST

## Nucleation Scaling in Jigsaw Percolation

Abstract: Jigsaw percolation is a nonlocal process that iteratively merges elements of a partition of the vertices in a deterministic puzzle graph according to the connectivity properties of a random collaboration graph. We assume the collaboration graph is an Erdos-Renyi graph with edge probability p, and investigate the probability that the puzzle graph is solved, that is, that the process eventually produces the partition {V}. In some generality, for puzzle graphs with N vertices of degrees about D, this probability is close to 1 or 0 depending on whether pD(log N) is large or small. We give more detailed results for the one dimensional ring and two dimensional torus puzzle graphs, where in many instances we can prove sharp phase transitions.### Algebraic Geometry Seminar, Prof. Sai Kee Yeung, Purdue University, MATH 731

Wednesday, December 3, 2014, 3:30 - 4:30 PM EST

## Geometry of a special surface of Euler number $3$

Abstract: The purpose of the talk is to explain a joint work with Vincent Koziarz and Donald Cartwright on the geometry of a concrete arithmetic complex two ball quotient constructed earlier by Cartwright and Steger. The Cartwright-Steger surface has the smallest possible Euler number $3$ among surfaces of general type but is a not a fake projective plane. Basic geometric properties of the surface had not been understood, such as the genus of the Albanese fibration. We would answer some questions in this direction, including the genus of the fibration. We would also use the example to study some open problems in the geometry of algebraic surfaces and complex ball quotients.### Special Colloquium, Chi Li, Post Doctoral Simons Instructor, Department of Mathematics, State University of New York (SUNY) at Stony Brook, HAAS 111

Wednesday, December 3, 2014, 4:30 - 5:30 PM EST

## On Kahler-Einstein metrics and K-stability

Abstract: The existence of Kahler-Einstein metrics on Kahler manifolds is a basic problem in complex differential geometry. This problem has connections to other fields: complex algebraic geometry, partial differential equations and several complex variables. I will discuss the existence of Kahler-Einstein metrics on Fano manifolds and its relation to K-stability. I will mainly focus on the analytic part of the theory, discuss how to solve the related complex Monge-Ampere equations and provide concrete examples. If time permits, I will also say something about the algebraic part of the theory, including the study of K-stability using Minimal Model Program (joint with Chenyang Xu) and the uniqueness of K-polystable degenerations of smooth Fano manifolds (recent joint work with Xiaowei Wang and Chenyang Xu). This talk is mostly a survey of my research results based on my research-statement: http://www.math.sunysb.edu/~chili/research-statement.pdf### Student Colloquium, Mr. Jimmy Vogel, Purdue University, UNIV 203

Wednesday, December 3, 2014, 4:30 - 5:30 PM EST

## How Eigenvalues Are Actually Computed

Abstract: Eigenvalues are a standard topic in undergraduate and graduate Linear Algebra courses, but the algorithms presented in such classes, while of great theoretical importance, are far from the ones used in most science and engineering applications. The most notable difference is that they are much slower. In this talk I introduce some of the important ideas behind fast eigenvalue solvers such as compressed storage, fast matrix-vector products, and parallelism. As an example, I discuss my recent work with my advisor Jianlin Xia, the first near-linear complexity eigenvalue solver for general symmetric rank-structured matrices. I also discuss some important applications of fast eigenvalue solvers in science and engineering. Numerical results and examples will be given to motivate theory and support claims.### Student Commutative Algebra Seminar, Christina Jamroz, Purdue University, BRNG B202

Thursday, December 4, 2014, 1:30 - 2:30 PM EST