# Calendar

## Yesterday

### Operator Algebras Seminar, Professor Thomas Sinclair, Purdue University, MATH 731

Thursday, Aug 27 2:30 pm - 3:30 pm

## W*-Rigidity for the von Neumann Algebras of Products of Hyperbolic Groups

Abstract: The "ideal" abstract for the talk is below. I will not assume any familiarity with von Neumann algebras or modern developments in their classification. We show that if $\Gamma = \Gamma_1 \times\dotsb\times \Gamma_n$ is a product of $n\geq 2$ non-elementary ICC hyperbolic groups then any discrete group $\Lambda$ which is W*-equivalent to $\Gamma$ decomposes as a k-fold direct sum exactly when $k=n$. This gives a group-level strengthening of Ozawa and Popa's unique prime decomposition theorem by removing all assumptions on the group $\Lambda$. This result in combination with Margulis' normal subgroup theorem allows us to give examples of lattices in the same Lie group which do not generate stably equivalent $II_1$ factors. (Joint work with Ionut Chifan and Rolando de Santiago)

## Next Week

### Student Colloquium, Mr. Jimmy Vogel, Purdue University, REC 225

Monday, Aug 31 2:30 pm - 3:30 pm

## A Friendly Introduction to Numerical Optimization

Abstract: In this talk, I will introduce the field of Numerical Optimization. I will begin with a discussion of feasibility, convexity, and general algorithmic strategies; all motivated by examples. I will present one of the simplest but most robust algorithms, Newton's Method, an important application of Taylor's Theorem in several variables. I will conclude by generalizing this method to so-called "Barrier Algorithms" and conclude with some of my own research wherein we can use the tools of randomized linear algebra and hierarchical matrices to build extremely fast Barrier Algorithms for a variety of optimization applications, including medical imaging and PDE solvers.

### Computational & Applied Mathematics Seminar, Professor Krzysztof J. Fidkowski, University of Michigan, REC 108

Monday, Aug 31 3:30 pm - 4:30 pm

## Output-based Adaptive Methods for Computational Fluid Dynamics

Abstract: This talk presents recent advances in output-based solution strategies for improving the accuracy and reducing the cost of steady and unsteady computational fluid dynamics (CFD) simulations. The target discretizations are of the discontinuous Galerkin (DG) finite element family, including standard DG and a hybridized version, HDG. Adaptation is output-based, driven by the solution of a discrete adjoint problem specific to a chosen scalar output. The adjoint-weighted residual yields an error estimate that corrects the output for effects of numerical error and at the same time provides an adaptive indicator for reducing the error through targeted refinement. We consider several refinement mechanisms: traditional ones such as mesh subdivision and approximation order increase, and novel ones such as node movement and optimization of the trial and test spaces. Results for the compressible Navier-Stokes simulations in two and three dimensions demonstrate the accuracy of the error estimates and the efficiency of the proposed output-based adaptation approach. We show that for these problems output error estimation and adaptation can have a significant impact on robustness and efficiency of CFD simulations.

### Geometry Seminar, Chi Li, Purdue University, MATH 731

Monday, Aug 31 3:30 pm - 4:30 pm

## On Rates and Analytic Compactifications of Asymptotically Conical Kahler Metrics

Abstract: I will show that the analytic compactification of an Asymptotically Conical (AC) manifold exists if the tangent cone at infinity is regular. In this case, I will then relate the sharp rate of the complex structure to the work of Grauert-Abate-Bracci-Toneva on how the divisor at infinity is embedded into the compactification, and also to the deformation theory of isolated cone singularities by Schlessinger-Pinkham-Wahl. In the talk I will explain what these various terminology mean. This talk is based on the paper: http://arxiv.org/abs/1405.2433.

### Function Theory Seminar, Eugenia Malinnikova (NTNU, Trondheim, Norway, visiting Purdue)

Tuesday, Sep 1 3:00 pm - 4:00 pm

## On Ratios of Harmonic Functions

Abstract: We consider pairs of harmonic functions in the unit ball of R^n with the same zero set Z and prove that the ratio is a well-defined real-analytic function that satisfies the maximum principle, the Harnack inequality and a certain gradient estimate. The constants in these inequalities depend only on the zero set Z, moreover, in dimension two the dependence is only on the length of the zero set. This is a joint work with A. Logunov.

### Commutative Algebra Seminar, Professor David Eisenbud, MSRI and UC Berkeley, MATH 215

Tuesday, Sep 1 3:00 pm - 4:00 pm

## NOTE: UNUSUAL DAY AND TIME

### Probability Seminar, Nate Eldredge, University of Northern Colorado, REC 302

Tuesday, Sep 1 3:30 pm - 4:30 pm

## Strong Hypercontractivity for Hypoelliptic Heat Kernels on Lie Groups

Abstract: The transition semigroup $T_t$ of the Ornstein-Uhlenbeck process on $\mathbb{R}^n$ has a famous regularizing property called hypercontractivity: if $\mu$ is standard Gaussian measure, $f \in L^p(\mu)$, and $q > p$, then for large enough $t$, we have $T_t f \in L^q(\mu)$. This property is known to be closely related to the logarithmic Sobolev inequality. Strong hypercontractivity is a phenomenon that arises if we work in the complex world: if you replace $\mathbb{R}^n$ by $\mathbb{C}^n$ and consider $f$ which is holomorphic, then $T_t f \in L^q(\mu)$ for smaller $t$. In other words, in this setting the regularizing happens faster''. In this talk, I will explain the relationship between these concepts, and then discuss recent work in which we carry it over to a setting where $\mathbb{C}^n$ is replaced by a complex nilpotent Lie group, and Gaussian measure is replaced by a so-called hypoelliptic heat kernel. (You do not need to know anything about Lie groups for this talk.) This is joint work with Bruce Driver, Leonard Gross, and Laurent Saloff-Coste.

### Department of Mathematics Colloquium, Professor Michael Christ, University of California, Berkeley, MATH 175

Tuesday, Sep 1 4:30 pm - 5:30 pm

## The Fine Structure of the Fourier Transform, Seen Through the Lense of Additive Combinatorics

Abstract: One of the most fundamental facts concerning the Fourier transform is the Hausdorff-Young inequality, which states that for any locally compact Abelian group, the Fourier transform maps $L^p$ boundedly to $L^q$ for certain exponents. For Euclidean space, the optimal constant in this inequality for general exponents was found only in the mid-70s, by Beckner in a celebrated work. Lieb later determined that all extremizers are Gaussian functions. This is a uniqueness theorem; these Gaussians form the orbit of a single function under the group of natural symmetries of the inequality. A stabler form of uniqueness has recently been established: Any function that nearly achieves the optimal constant in the inequality must be close in norm to a Gaussian, with a quantitative bound for the distance. This can be equivalently viewed as a refinement of the inequality. A foundational ingredient is a precompactness theorem, which guarantees that extremizers exist, and that functions or sets that nearly extremize the inequalities must be close to exact extremizers, without yielding any quantitative bound. At the heart of its proof lie principles of additive combinatorics. These complement structural properties of the Fourier transform. In this talk I will state recent results in Fourier analysis, introduce tools and concepts from combinatorics and analysis used in the proofs, and give some indication of how these fit together.

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### Informal Algebraic Geometry Seminar (IAGS), Donu Arapura, Purdue University, MATH 731

Wednesday, Sep 2 10:30 am - 11:30 am

## Vanishing Cycles

Abstract: I'll give a somewhat more precise description of the formalism in both the classical and etale settings, following SGA7.

### Algebraic Geometry Seminar, Chris Skalit, University of Illinois, Chicago, MATH 731

Wednesday, Sep 2 3:30 pm - 4:30 pm

## Intersection Multiplicity and Transversality in Unramified Regular Local Rings

Abstract: Suppose that $X/k$ is a smooth variety and that $Y$ and $Z$ are complimentary-dimensional subvarieties meeting at a single point $P$. Classical work of Serre shows that the intersection multiplicity of $Y$ and $Z$ has an explicit lower bound given in terms of the individual subvarieties' Hilbert-Samuel multiplicities at $P$. Furthermore, a theorem of Fulton-Lazarsfeld asserts that this minimum is achieved precisely when the tangent cones of $Y$ and $Z$ at $P$ intersect trivially. In this talk, we shall discuss how to extend these results in an unramified, mixed-characteristic setting - say, for example, when we replace our ground field by a number ring $O_K$.

### Topology Seminar, Arnold Yim, Purdue University, REC 108

Wednesday, Sep 2 4:30 pm - 5:30 pm

## Homological Properties of Determinantal Arrangements

### Secret Seminar, BRNG 1254

Thursday, Sep 3 12:00 pm - 1:00 pm

## Organizational Meeting

### Operator Algebras Seminar, Professor Thomas Sinclair, Purdue University, MATH 731

Thursday, Sep 3 2:30 pm - 3:30 pm

## W*-Rigidity for the von Neumann Algebras of Products of Hyperbolic Groups, Part II

Abstract: The "ideal" abstract for the talk is below. I will not assume any familiarity with von Neumann algebras or modern developments in their classification. We show that if $\Gamma = \Gamma_1 \times\dotsb\times \Gamma_n$ is a product of $n\geq 2$ non-elementary ICC hyperbolic groups then any discrete group $\Lambda$ which is W*-equivalent to $\Gamma$ decomposes as a k-fold direct sum exactly when $k=n$. This gives a group-level strengthening of Ozawa and Popa's unique prime decomposition theorem by removing all assumptions on the group $\Lambda$. This result in combination with Margulis' normal subgroup theorem allows us to give examples of lattices in the same Lie group which do not generate stably equivalent $II_1$ factors. (Joint work with Ionut Chifan and Rolando de Santiago)

### Probability Seminar, Mathew Junge, University of Washington, REC 302

Thursday, Sep 3 3:30 pm - 4:30 pm

## The Frog Model on Trees

Abstract: On a d-ary tree place some number (random or otherwise) of sleeping frogs at each site, as well as one awake frog at the root. Awake frogs perform simple random walk and wake any "sleepers" they encounter. A longstanding open problem: Does every frog wake up? It turns out this depends on d and the amount of frogs. The proof uses two different recursions and two different versions of stochastic domination. Joint with Christopher Hoffman and Tobias Johnson.

### Bridge to Research Seminar, Dr. Laszlo Lempert, Purdue University, REC 112

Thursday, Sep 3 4:30 pm - 5:30 pm

## A Taste of Complex Analysis

Abstract: After introducing the notion of holomorphic functions of one or several variables, I will discuss a problem of interpolation, and how it led to the idea of analytic cohomology.

## Two Weeks

### UNIVERSITY HOLIDAY (LABOR DAY), CLASSES ARE NOT IN SESSION

Monday, Sep 7 8:00 am - 5:00 pm

### Department of Mathematics Colloquium, Professor Nets Katz, CALTECH, MATH 175

Tuesday, Sep 8 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### CCAM Lunch Seminar, Jimmy Vogel, Purdue University

Friday, Sep 11 11:30 am - 12:30 pm

## Superfast Divide-and-Conquer Eigensolvers

Abstract: We present nearly O(n) complexity divide-and-conquer methods for finding all the eigenvalues and eigenvectors of a class of symmetric matrices, as well as the perturbation analysis. The matrices have certain rank structures, as often encountered in practical applications such as Toeplitz matrices and some discretized problems. We show how to quickly and stably perform the major operations. Eigenvalue approximation accuracies, clustered eigenvalues, and generalizations to SVDs are studied. As applications, we show how these algorithms can be used to solve certain classes of elliptic PDEs and nonlinear optimization problems in near-linear time. This is joint work with Jianlin Xia.

## Three Weeks

### Student Colloquium, Mr. Eddie Price, Purdue University, REC 225

Monday, Sep 14 2:30 pm - 3:30 pm

## The Ordinal Numbers and Transfinite Induction

### Computational & Applied Mathematics Seminar, Professor Chun Liu, Penn State University , REC 108

Monday, Sep 14 3:30 pm - 4:30 pm

### Department of Mathematics Colloquium, Professor Joachim Zacharias, University of Glasgow, MATH 175

Tuesday, Sep 15 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

## September

### Computational & Applied Mathematics Seminar, Professor Yingjie Liu, Georgia Tech, REC 108

Monday, Sep 21 3:30 pm - 4:30 pm

## TBA

### Graduate Student Invited Colloquium, Bernd Sturmfels, University of California, MATH 175

Tuesday, Sep 22 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### Outstanding Alumnus Special Colloquium, BRNG 2290

Thursday, Sep 24 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### Geometry Seminar, Michelle Chu, UT Austin, MATH 731

Monday, Sep 28 3:30 pm - 4:30 pm

## TBA

### Computational & Applied Mathematics Seminar, Dr. Xiaohui Wu, Exxon Mobile, REC 108

Monday, Sep 28 3:30 pm - 4:30 pm

TBA

### Department of Mathematics Colloquium, Professor Wilhelm Winter, University of Muenster, MATH 175

Tuesday, Sep 29 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

## October

### Geometry Seminar, Dave Futer, Temple University

Friday, Oct 2 3:30 pm - 4:30 pm

## TBA

### PhD Defense, Drew Swartz, UNIV 301

Monday, Oct 5 9:00 am - 11:00 am

Analysis of Models for Curvature Driven Motion of Interfaces Committee: Yip (Chair), Phillips, Petrosyan, and M. Koslowski.

### Computational & Applied Mathematics Seminar, Professor Constantine Megaridis, University of Illinois Chicago, REC 108

Monday, Oct 5 3:30 pm - 4:30 pm

TBA

### Jean Rubin Memorial Lecture, Professor Anna Gilbert, University of Michigan, LWSN 1142

Wednesday, Oct 7 4:30 pm - 5:30 pm

## TBA

Refreshments in LWSN 1142 at 4:00 pm

### CCAM Distinguished Lecture, Professor James Demmel, University of California, Berkeley, LWSN 1142

Monday, Oct 19 3:30 pm - 4:30 pm

### Geometry Seminar, Tarik Aougab, Brown University, MATH 731

Monday, Oct 19 3:30 pm - 4:30 pm

## TBA

### CCAM Seminar Joint with CS Colloquium, Professor Ruijun Zhao, Minnesota State University, Mankato, LWSN 3102AB

Monday, Oct 26 3:30 pm - 4:30 pm

## TBA

### Department of Mathematics Colloquium, Professor Maciej Zworski, University of California, Berkeley, MATH 175

Tuesday, Oct 27 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

## November

### CCAM Distinguished Lecture, Professor George Karniadakis, Brown University, LWSN 1142

Monday, Nov 2 3:30 pm - 4:30 pm

TBA

### Computational & Applied Mathematics Seminar, Professor Henning Struchstrup, University of Victoria, REC 108

Monday, Nov 9 3:30 pm - 4:30 pm

## TBA

This seminar will be co-host by Jingwei Hu and Alina Alexeenko, a joint-seminar of Math and AAE.

### Computational & Applied Mathematics Seminar, Professor David Kopriva, Florida State University, REC 108

Monday, Nov 16 3:30 pm - 4:30 pm

## December

### Computational & Applied Mathematics Seminar, Professor Lin Lin, UC Berkeley, REC 108

Monday, Dec 7 3:30 pm - 4:30 pm

## 2016

### Computational & Applied Mathematics Colloquium, Professor Andrew Noymer, UC Irvine, REC 108

Wednesday, Mar 9 3:30 pm - 4:30 pm

TBA