# Calendar

## Yesterday

### Ph.D. Thesis Defense, Agnid Banerjee, BRNG B212

Monday, March 10, 2014, 1:00 - 2:00 PM EDT

## Normalized p-laplacian Evolution, Boundary Behavior of Non-negative Solutions of Fully Nonlinear Parabolic Equations, Gradient Bounds for $p$-harmonic Systems with Vanishing Neumann( dirichlet) Data in a Convex Domain.

Committee: D. Danielli, Co-Chair, N. Garofalo, Co-Chair, A. Petrosyan, N K. Yip

### Geometry Seminar, Babak Modami, UIUC, MATH 731

Monday, March 10, 2014, 3:30 - 4:30 PM EDT

## Symbolic Coding of Weil-Petersson Geodesic Flow

Abstract: The Weil-Petrsson (WP) metric is an incomplete Riemannian metric on the moduli space of Riemann surfaces with sectional curvatures not bounded away from 0 and $-\infty$. These features prevent applying most of standard techniques to study the global geometry and dynamics of WP metric. I review some results about a kind of symbolic coding of the WP geodesic flow using laminations and subsurface coefficients. Further we apply some estimates on the WP metric and its derivatives in the thin part of moduli space to show that the strong asymptotics of a class of WP geodesics is determined by the associated laminations. As a result we give a symbolic condition for divergence of WP geodesics in the moduli space.

### Bridge to Research Seminar, Professor Gregery Buzzard, Purdue University, BRNG B222

Monday, March 10, 2014, 4:30 - 5:30 PM EDT

## Optimal Filters for High-speed Compressive Detection in Spectroscopy

Abstract: A key bottleneck to high-speed chemical analysis is the time required to collect and analyze chemical spectral data. One approach to overcoming this problem is based on a new type of filter, in which energy from multiple frequencies is aggregated in order to reduce noise effects and decrease the total number of measurements needed for a given purpose. In this talk I describe the mathematical formulation of this problem and describe results on the selection of optimal filters for estimation of the chemical composition of a sample when the sample is a combination of a finite set of known chemicals.

## Today

### Department of Mathematics Colloquium, Timo Seppalainen, University of Wisconsin, MATH 175

Tuesday, March 11, 2014, 4:30 - 5:30 PM EDT

## Variational Formulas for Directed Paths in a Random Medium

Abstract: This talk begins with a reminder of classic random walk and then proceeds to models of random paths currently studied in probability and statistical mechanics. In particular, we discuss directed percolation and directed polymer models. Subadditive ergodic theory gives deterministic large scale limits for these models, but properties of these limits have remained a challenge for decades. We describe some new variational formulas that characterize these limits and connections with other features of the models such as fluctuation exponents. Refreshments will be served at 4 p.m. in the Math Library Lounge.

## Tomorrow

### WAGS, Hal Schenck, University of Illinois, MATH 731

Wednesday, March 12, 2014, 3:30 - 4:30 PM EDT

## Geometry of Wachspress Surfaces

Abstract: Let P_d be a convex polygon with d vertices. The associated Wachspress surface W_d is a fundamental object in approximation theory, dened as the image of the rational map from P^2 to P^(d-1), determined by the Wachspress barycentric coordinates for Pd. We show this is a regular map on a blowup X of P^2, and if d > 4 is given by a very ample divisor on X, so has a smooth image. We determine generators for the ideal I(X), and prove that in graded lex order, the initial ideal of I(X) is given by a Stanley-Reisner ideal. As a consequence, we show that the associated surface is arithmetically Cohen-Macaulay, of Castelnuovo-Mumford regularity two, and determine all the graded Betti numbers of I(X). Joint work with Corey Irving, Santa Clara Univ.

### GMIG Seminar, Florian Faucher, Purdue University, REC 225

Wednesday, March 12, 2014, 3:30 - 4:30 PM EDT

## Multi-level, Multi-frequency Elastic full Waveform Inversion

Abstract: We study the inverse boundary value problem for the elastic wave equation and recovery of the P- and S- wavespeeds upon taking a time-Fourier transform of the data. We design a hierarchical compressed reconstruction in a multi-level scheme for the inverse problem associated with the time-harmonic elastic isotropic wave equation, at selected frequencies of the data. The compression is based on a domain partitioning of the subsurface, while the hierarchy is established through refinement. The coefficients are assumed to be piecewise constant functions following the domain partitioning. Our method is based on Haar wavelets for the compression using strategies providing a gradual increase in the number of subdomains via the analysis of the Gauss-Newton Hessian. We eventually carry out numerical experiments in two and three dimensions for the reconstruction through the update of the Lamé parameters $\lambda$ and $\mu$.

## Thursday

### Automorphic Forms Seminar, Dr. Yueke Hu, University of Wisconsin-Madison, REC 302

Thursday, March 13, 2014, 1:30 - 2:30 PM EDT

Local Integral of Triple Product L-function and Subconvexity Bound Abstract: Venkatesh proposed a strategy to prove the subconvexity bound in the level aspect for triple product L-function. With the integral representation of triple product L-function, if one can get an upper bound for the global integral and a lower bound for the local integrals, then one can get an upper bound for the L-function, which turns out to be a subconvexity bound. Such a subconvexity bound was obtained essentially for representations of square free level. I will talk about how to generalize this result to the case with higher ramifications as well as joint ramifications.

### Probability Seminar, Hosam Mahmoud, George Washington University, REC 226

Thursday, March 13, 2014, 3:30 - 4:30 PM EDT

## Analysis of Quickselect under Yaroslavskiy's Dual-Pivoting Algorithm

There is excitement within the algorithms community about a new partitioning method introduced by Yaroslavskiy. This algorithm renders Quicksort slightly faster than the case when it runs under classic partitioning methods. We show that this improved performance in Quicksort is NOT sustained in Quickselect, a variant of Quicksort for finding order statistics. Distributions of several cost measures (when suitably scaled) are given as the fixed-point solution of distributional equations defining contraction in the Zolotarev metric space. These limiting distributions are of perpetuities (a sum of products of independent mixed continuous random variables).

### PDE Seminar, Prof. Fernando Charro, University of Texas at Austin, REC 316

Thursday, March 13, 2014, 3:30 - 4:30 PM EDT

## A Fractional Analogue of the Monge-Ampere Operator

Abstract: In this talk we consider a fractional analogue of the Monge-Ampere operator. Our operator is a concave envelope of fractional linear operators of the form $\inf_{A\in \mathcal{A}}L_Au,$ where the set of operators corresponds to all affine transformations of determinant one of a given multiple of the fractional Laplacian. We set up a relatively simple framework of global solutions prescribing data at infinity and global barriers. In our key estimate, we show that the operator that realizes the infimum remains strictly elliptic, which allows to deduce an Evans-Krylov regularity result and therefore that solutions are classical.

### Learning Seminar on Perfectoid Space, Prof. Andrei Jorza, University of Notre Dame,, MATH 731

Thursday, March 13, 2014, 3:30 - 4:30 PM EDT

## Rigid Geometry (I)

Abstract: Scholze uses the language of perfectoid spaces to prove a comparison theorem for rigid analytic spaces in the spirit of the Hodge decomposition for de Rham cohomology of compact Kaehler manifolds. We'll explore rigid analytic spaces and their formal models through examples.

### Commutative Algebra Seminar, Dr. Paolo Mantero, University of California, Riverside, UNIV 301

Thursday, March 13, 2014, 4:30 - 5:30 PM EDT

## On two conjectures by Harbourne-Huneke and Chudnovsky

Abstract: A long-standing conjecture by Chudnovsky predicts the existence of a specific lower bound c(X) for the degree of any hypersurface in P^N passing through a fixed set X of points with multiplicity m. The lower bound c(X) is defined in terms of N and the initial degree of the ideal defining X. Harbourne and Huneke in 2011 showed that this conjecture would follow from a new conjecture that they propose (which would give refined comparison information between symbolic and ordinary powers of the ideal defining X). In this talk we will discuss these two conjectures and prove some results, for instance, when X is a set of general points.

## Two Weeks

### Department of Mathematics Colloquium, Craig Evans, Berkeley, MATH 175

Tuesday, March 25, 2014, 4:30 - 5:30 PM EDT

TBA Refreshments will be served at 4 p.m. in the Math Library Lounge.

### Learning Seminar on Perfectoid Space, Prof. Andrei Jorza, University of Notre Dame,, MATH 731

Thursday, March 27, 2014, 3:30 - 4:30 PM EDT

## Rigid Geometry (II)

Abstract: Perfectoid spaces are objects in Huber's category of adic spaces, which are the "most canonical" types of rigid geometric objects. We'll look at how adic and Berkovich spaces differ from rigid spaces and what makes adic spaces suitable, mainly through examples.

### Probability Seminar, TBA, REC 226

Thursday, March 27, 2014, 3:30 - 4:30 PM EDT

TBA

## Three Weeks

### Ph.D. Thesis Defense, Urs Fuchs, BRNG 1255

Thursday, April 3, 2014, 3:30 - 4:30 PM EDT

## Pseudoholomorphic curves in symplectic and contact geometry and their application in dynamics

Committee: P. Albers (Co-Chair), L. Lempert (Co-Chair), S. Bell, S.K. Yeung

### Probability Seminar, TBA, REC 226

Thursday, April 3, 2014, 3:30 - 4:30 PM EDT

TBA

### Computational and Applied Mathematics Seminar, Professor Hongyu Liu, Univ. of North Carolina at Charlotte, REC 316

Friday, April 4, 2014, 3:30 - 4:30 PM EDT

## Recovery by a Single Far-Field Measurement

Abstract: In this talk, I will describe the recent theoretical and computational progress on recovering electromagnetic scatterers by using a single far-field measurement. We establish the uniqueness in determining PEC obstacles of general polyhedral type. We also develop several direct imaging schemes, which work in an extremely general setting, assuming the uniqueness holds true.

## April

### Department of Mathematics Colloquium, Arlie Petters, Duke, MATH 175

Tuesday, April 8, 2014, 4:30 - 5:30 PM EDT

TBA Refreshments will be served at 4 p.m. in the Math Library Lounge.

### Ph.D. Thesis Defense, Dan Tran, BRNG B261

Thursday, April 10, 2014, 3:30 - 4:30 PM EDT

## Direct Images as Hilbert Fields and Their Curvatures

Committee: L. Lempert (Chair), D. Catlin, S.K. Yeung, S. Bell

### Probability Seminar, TBA, REC 226

Thursday, April 10, 2014, 3:30 - 4:30 PM EDT

TBA

### Ph.D. Thesis Defense, Koushik Ramachandran, REC 303

Friday, April 11, 2014, 1:15 - 2:15 PM EDT

## Asymptotic behavior of positive harmonic functions in certain unbounded domains

Committee: A. Eremenko (Co-chair), S. Mayboroda (Co-chair), R. Banuelos, D. Drasin, B. Davis

### Computational and Applied Mathematics Seminar, Professor Robert Krasny, University of Michigan, REC 316

Friday, April 11, 2014, 3:30 - 4:30 PM EDT

## A Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver for Solvated Proteins

Abstract: We present a treecode-accelerated boundary integral (TABI) solver for electrostatics of solvated proteins described by the linear Poisson-Boltzmann equation. The method uses a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated by MSMS and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES and the matrix-vector product is carried out by a Cartesian treecode which reduces the cost from $O(N^2)$ to $O(N\log N)$, where $N$ is the number of faces in the triangulation. The code is applied to two test cases, the Kirkwood sphere and a medium sized protein. We compare TABI results with those obtained using the grid-based APBS code, in terms of error, CPU run time, and memory usage, and we also present parallel TABI simulations. The TABI solver exhibits good serial and parallel performance combined with relatively simple implementation, efficient memory usage, and geometric adaptability. This is joint work with Weihua Geng (Southern Methodist University).

### Department of Mathematics Colloquium, David Isaacson, RPI, MATH 175

Tuesday, April 15, 2014, 4:30 - 5:30 PM EDT

## Problems in Electrical Impedance Tomography

Abstract: Several mathematical problems that arise in the design , construction, and testing of electrical impedance tomography, EIT, systems will be discussed. These systems apply patterns of currents to electrodes on a bodies surface and measure the voltages that result. From this electrical data images of the conductivity inside the body are reconstructed and displayed. Since lungs filled with air and hearts emptied of blood have lower conductivities that lungs depleted of air and hearts filled with blood , both heart and lung functions can be monitored by EIT systems. Since the dispersion relations of breast cancers may be different from noncancerous tissues EIT may be used to try to improve the diagnosis of breast cancer. From a mathematical point of view the reconstruction of internal conductivity from surface measurements of the current to voltage map is an inverse boundary value problem for a low frequency approximation to Maxwell's equations. It will be explained how the analysis of this inverse problem led to the design of adaptive current tomography systems at RPI. Images and movies made by RPI's ACT systems showing ventilation and perfusion , as well as breast cancers will be shown. Refreshments will be served at 4 p.m. in the Math Library Lounge.

### Probability Seminar, TBA, REC 226

Thursday, April 17, 2014, 3:30 - 4:30 PM EDT

TBA

### CCAM Lunch Seminar, Professor Aditya Viswanathan, Michigan State University, BRNG 1222

Friday, April 18, 2014, 11:30 - 12:30 PM EDT

## TBA

### Computational & Applied Mathematics Seminar, Professor Fabio Milner, Arizona State University, REC 316

Friday, April 18, 2014, 3:30 - 4:30 PM EDT

TBA

### Ph.D. Thesis Defense, Lichen Ni, BRNG B212

Monday, April 21, 2014, 2:00 - 3:00 PM EDT

## C^1-continuous Spectral Elements

Committee: S. Dong (Chair), J. Xia, J. Shen, P. Li

### Ph.D. Thesis Defense, Shuhao Cao, BRNG 1254

Monday, April 21, 2014, 4:00 - 5:00 PM EDT

## The a posteriori error estimation in finite element method for the H(curl) problems

Committee: Z. Cai (Chair), J. Xia, J. Shen, P. Li

### Ph.D. Thesis Defense, Jing Wang, BRNG B212

Wednesday, April 23, 2014, 1:00 - 2:00 PM EDT

## C^1-continuous Spectral ElementsSub-Riemannian Heat Kernels on Model Spaces and Curvature-dimension Inequalities on Contact Manifolds

Committee: F. Baudoin (Chair), R. Banuelos, D. Danielli, N. Garofalo

### Probability Seminar, TBA, REC 226

Thursday, April 24, 2014, 3:30 - 4:30 PM EDT

TBA

### Computational & Applied Mathematics Colloquium, Professor Leszek Demkowicz,The University of Texas at Austin, REC 316

Friday, April 25, 2014, 3:30 - 4:30 PM EDT

## Discontinuous Petrov Galerkin (DPG) Method with Optimal Test Functions Fundamentals

Abstract: The coming June will mark the fifth anniversary of the first two papers in which Jay Gopalakrishnan and I proposed a novel Finite Element (FE) technology based on what we called the ultra-weak variational formulation'' and the idea of computing (approximately) optimal test functions on the fly [1,2]. We called it the Discontinuous Petrov Galerkin Method''. Shortly afterward we learned that we owned neither the concept of the ultra-weak formulation nor the name of the DPG method, both introduced in a series of papers by colleagues from Milano: C. L. Bottasso, S. Micheletti, P. Causin and R. Sacco, several years earlier. The name ultra-weak'' was stolen from O. Cessenat and B. Despres. But the idea of computing optimal test functions was new... From the very beginning we were aware of the fact that the Petrov-Galerkin formulation is equivalent to a Minimum Residual Method (generalized Least Squares) in which the (minimized) residual is measured in a dual norm, the idea pursued much earlier by colleagues from Texas A&M: J. Bramble, R. Lazarov and J. Pasciak. Jay and I were lucky; a few months after putting [1,2] on line, Wolfgang Dahmen and Chris Schwab presented essentially the same approach pointing to a connection with mixed methods and the fact that the use of discontinuous test functions is not necessary. The lecture will focus on fundamentals of the DPG method. We will discuss the equivalence of several formulations: Petrov-Galerkin method with optimal test functions, minimum residual formulation and a mixed formulation. We will summarize well-posedness results for formulations with broken test functions: the ultra-weak formulation based on first order systems and the formulation derived from standard second order equations. Standard model problems: Poisson, linear elasticity, Stokes, linear acoustics and Maxwell equations, will be used to illustrate the methodology with h-, p-, and hp-convergence tests. The DPG method comes with a posteriori-error evaluator (not estimator...) built in which provides a natural framework for adaptivity. Take home message: The DPG method guarantees stability for any well-posed linear problem. [1] L. Demkowicz and J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. PartI: The transport equation,'' CMAME: 199, 23-24, 1558-1572, 2010. [2] L. Demkowicz and J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. Part II: Optimal test functions,'' Num. Meth. Part. D.E.:27, 70-105, 2011.
Refreshments will be served in the Math Library Lounge at 3:00 PM.

## May

### Computational and Applied Mathematics Seminar, Professor Shari Moskow, Drexel University, REC 316

Friday, May 2, 2014, 3:30 - 4:30 PM EDT