# Calendar

## Yesterday

## Drift estimation for differential equations driven by fractional Brownian motions

Abstract: We focus in this talk on statistical problems for noisy differential equations driven by an additive fractional Brownian motion, either in a 1-d or general d-dimensional context. I will first review the standard procedures in order to estimate the Hurst parameter, the diffusion coefficient and finally the drift coefficient of the equation. Then I will give an account on two new results in this direction:A new class of estimators in ergodic situations, when the dependence of the drift with respect to the parameter in not linear.

The LAN property for ergodic equations, which yields a lower bound for the convergence of estimators.

These results are based on some ongoing works with Eulalia Nualart (Barcelona) and Fabien Panloup (Toulouse).

## Today

### Informal Algebraic Geometry Seminar (IAGS), Hongshan Li, Purdue University, MATH 731

Wednesday, Oct 7 10:30 am - 11:30 am

## The Lefschetz Hyperplane Theorem and Lefschetz Pencils

### Commutative Algebra Seminar, Dr. Jonathan Montano, University of Kansas, MATH 731

Wednesday, Oct 7 1:30 pm - 2:30 pm

## Levels of Perfect Complexes

Abstract: Let R be a commutative ring. A complex of R-modules F is perfect if it is quasi-isomorphic to a bounded complex of finitely generated projective modules, or equivalently, if it belongs to the smallest thick subcategory of D(R) that contains R. The latter implies that every perfect complex can be built from R using a finite sequence of mapping cones, shifts, and direct summands. The level of F, denoted by l(F), measures the number of steps it takes to build F. In this talk, we will present a lower bound for l(F) in terms of the gaps in the homology of F. This result allows us to give estimates for levels of Koszul complexes and of complexes whose homology has finite length. This is joint work with Hannah Altmann, Eloisa Grifo, Srikanth Iyengar, William Sanders, and Thanh Vu.### Algebraic Geometry Seminar, Tatsunari Watanabe, Purdue University, MATH 731

Wednesday, Oct 7 3:30 pm - 4:30 pm

## Rational Points of Generic Curves in Positive Characteristic

Abstract: For the second talk, I’ll continue from where my first talk ended.### Jean Rubin Memorial Lecture, Professor Anna Gilbert, University of Michigan, LWSN 1142

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

## Recent Developments in the Sparse Fourier Transform

Abstract: The Discrete Fourier Transform (DFT) is a fundamental component of numerous computational techniques in signal processing and scientific computing. The most popular means of computing the DFT is the Fast Fourier Transform (FFT). However, with the emergence of big data problems, in which the size of the processed data sets can easily exceed terabytes, the “Fast” in Fast Fourier Transform is often no longer fast enough. In addition, in many big data applications it is hard to acquire a sufficient amount of data in order to compute the desired Fourier transform in the first place. The Sparse Fourier Transform (SFT) addresses the big data setting by computing a compressed Fourier transform using only a subset of the input data, in time sub-linear in the data set size. The goal of this talk is to survey these recent developments, to explain the basic techniques with examples and applications in big data, to demonstrate trade-offs in empirical performance of the algorithms, and to discuss the connection between the SFT and other techniques for massive data analysis such as streaming algorithms and compressive sensing.Bio: Anna Gilbert received an S.B. degree from the University of Chicago and a Ph.D. from Princeton University, both in mathematics. In 1997, she was a postdoctoral fellow at Yale University and AT&T Labs-Research. From 1998 to 2004, she was a member of technical staff at AT&T Labs-Research in Florham Park, NJ. Since then she has been with the Department of Mathematics at the University of Michigan, where she is now the Herman H. Goldstine Collegiate Professor. She has received several awards, including a Sloan Research Fellowship (2006), an NSF CAREER award (2006), the National Academy of Sciences Award for Initiatives in Research (2008), the Association of Computing Machinery (ACM) Douglas Engelbart Best Paper award (2008), the EURASIP Signal Processing Best Paper award (2010), a National Academy of Sciences Kavli Fellow (2012), and the SIAM Ralph E. Kleinman Prize (2013).

Her research interests include analysis, probability, networking, and algorithms. She is especially interested in randomized algorithms with applications to harmonic analysis, signal and image processing, networking, and massive datasets.

Refreshments in LWSN 1142 at 4:00 pm

## Functorial Field Theories from Factorization Algebras

Abstract: There are various, quite different mathematical approaches to quantum field theories, among them functorial field theories in the sense of Atiyah and Segal and the factorization algebras of quantum observables constructed by Costello and Gwilliam. In the talk I will describe a construction that produces a twisted functorial field theory from a factorization algebra, thus relating these two approaches. This is joint work with Bill Dwyer and Peter Teichner.## Tomorrow

## Ergodic Equivalence Relations and Von Neumann Algebras

Abstract: I'll discuss equivalence relations coming from group actions and the connection to the group-measure space construction of von Neumann algebras.### Numerical Linear Algebra Seminar, Kyle Kloster, Purdue University, HAAS 111

Thursday, Oct 8 1:00 pm - 2:00 pm

## The Fiedler and PageRank vectors, Part 2

Abstract: The Fiedler and PageRank vectors offer loads of information about a graph's structure. We will sketch a proof that the Fiedler vector can give a near-optimal cut in a graph, then explore how locally-biased versions of these vectors can identify clusters in graphs, and end by modeling the convergence of these vectors with their "solution paths", which yield insights into each individual node's place in the greater scheme of things.## Regularity of the Free Boundary for a ParabolicProblem with variable coefficients

Abstract: In this talk I will discuss my work on the regularity of the free boundary for a Bernoulli type parabolic problem. The prescribed free boundary condition is a jump in the spacial gradient across the free boundary. This takes the form $(u_\nu^+)^2-(u_\nu^-)^2 =1$. Problems of this type can arise from a singular perturbation problem modeling combustion.In particular I will show that Lipschitz free boundaries are $C^{1,\alpha}$ in space and $C^{1,\beta}$ in time and that solutions are Lipschtiz across the free boundary, which is optimal regularity for this problem.

### Bridge to Research Seminar, Dr. Carl Cowen, Purdue University, REC 112

Thursday, Oct 8 4:30 pm - 5:30 pm

## Invariant Subspaces and Complex Analysis

Abstract: Many subjects in mathematics can be studied from several different, but mathematically equivalent, perspectives. While the choice of perspectives may be thought to be arbitrary, in my point of view, in practice, very often a perspective enabling the best intuition is most productive! Pay attention to your intuition!! For me, connections to complex analysis offer the best intuition for approaches to research in operator theory.The goal of this talk is to discuss the question of invariant subspaces for operators on Hilbert spaces and show how there is a strong connection between operator theory and complex analysis. Examples of operators related to analytic functions will be given and a connection between operator theoretic questions and function theoretic questions will be explained.

## Next Week

### Algebraic Geometry Seminar, Alex Dimca, University of Nice, MATH 731

Wednesday, Oct 14 3:30 pm - 4:30 pm

## Free Curves in P^{2} and free surfaces in P^{3}

Abstract: After defining a free projective hypersurface in the complex projective space P^{n}, we discuss some geometric properties of these objects for n=2 and n=3. They are related in a rather mysterious way to the rational cuspidal curves for n=2, while for n=3 they give rise to many new examples of homaloidal hypersurfaces i.e. hypersurfaces for which the gradient map is a birational automorphism of P

^{n}.

## Equivariant Invariants of External and Symmetric Products of Quasi-Projective Varieties

Abstract: I will start by revisiting formulae for the generating series of genera of symmetric products (with suitable coefficients), which hold for complex quasi-projective varieties with any kind of singularities, and which include many of the classical results in the literature as special cases. Important specializations of these results include generating series for extensions of Hodge numbers and Hirzebruch genus to the singular setting and, in particular, generating series for intersection cohomology Hodge numbers and Goresky-MacPherson intersection cohomology signatures of symmetric products of complex projective varieties. In the second part of the talk, I will describe a generating series formula for equivariant invariants of external products, which includes all of the above-mentioned results as special cases. This is joint work with Joerg Schuermann.### Spectral and Scattering Theory Seminar, Professor Jeffrey Galkowski, Stanford University, BRNG 1238

Thursday, Oct 15 2:30 pm - 3:30 pm

## A Quantum Sabine Law for Resonances in Transmission Problems

Abstract: We prove a quantum Sabine law for the location of resonances in transmission problems. In this talk, our main applications are to scattering by strictly convex, smooth, transparent obstacles and highly frequency dependent delta potentials. In each case, we give a sharp characterization of the resonance free regions in terms of dynamical quantities. In particular, we relate the imaginary part of resonances to the chord lengths and reflectivity coefficients for the ray dynamics and hence give a quantum version of the Sabine law from acoustics.### PDE Seminar, Professor Gierei Simonett, Vanderbilt University, REC 121

Thursday, Oct 15 3:30 pm - 4:30 pm

## Moving Surfaces in Phase Transitions>

Abstract: Moving surfaces are ubiquitous in many areas of mathematics and the applied sciences. In this talk I will first introduce some well-known geometric evolution equations, and then proceed to a thermodynamically consistent Stefan problem with surface tension which models a system that can undergo phase transitions. The model is derived from fundamental principles in physics and thermodynamics. Existence of solutions and stability properties of equilibria will be investigated. It will pointed out that all equilibria are located at the critical points of an entropy functional, and it will be shown that multiple-equilibria comprise unstable configurations. Additional examples with fluid flows and phase transitions will be introduced.### Mathematics/Statistics NSF GRFP Seminar, Edray Goins and Mark Ward, Purdue University, REC 121

Thursday, Oct 15 5:00 pm - 6:00 pm

## NSF GRFP Writing Studio

ABSTRACT: The National Science Foundation (NSF) Graduate Research Fellowship Program (GRFP) is perhaps this most prestigious graduate fellowship for those of us in the mathematical sciences. Edray Goins (Associate Professor of Mathematics) and Mark Ward (Associate Professor of Statistics, Associate Director of Actuarial Science, and Undergraduate Chair) will run two seminars to maximize your chances of being awarded this fellowship!In this the second of two seminars, we will host a writing studio. We will discuss examples research statements with an emphasis on the concepts of ``intellectual merit'' and ``broader impact''. We'll discuss the ``do's and don'ts'' of applying for the fellowship; and best practices for maximizing your chances of being awarded the fellowship. If you have a partially completed fellowship which you wish to be read and critiqued, feel free to bring your documents!

At the seminars, we will have several Purdue staff and students in Mathematics and Statistics who have served on NSF GRFP panels and/or been awarded the fellowships over the years. And Dinner will be served at both sessions!

## Two Weeks

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

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

## Communication-Avoiding Algorithms for Linear Algebra and Beyond

Abstract: Algorithms have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving very general loop nests and array accesses, in a way that could be incorporated into compilers.Refreshments will be served at 3:00 pm outside of LWSN 1142.

### Probability Seminar, Jiro Akahori, Ritsumeikan University, REC 302

Tuesday, Oct 20 3:30 pm - 4:30 pm

## TBA

## Three Weeks

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

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

## Optimal Control Theory and its Application in a Malaria Model

Abstract: Malaria is the most prevalent tropical parasitic disease in the world, killing 500,000 people in 2013, mostly kids under age five. The commonly used control strategies include insecticide-treated bed-nets and indoor/outdoor residual chemical sprays. In July 2015, the first licensed malaria vaccine, RTS,S was approved by European regulators, which adds an option for battling the disease. However, the vaccine has shown only partial protection during Phase III human trials, 50 percent effective for kids and 25 percent effective for infants.In this talk, we will propose two age-structured mathematical models studying the effectiveness of the vaccine. We also form an optimal control problem to maximize the benefit of applying this vaccine. The optimal control problem is solved by a so-called forward-backward-sweep method (FBSM). We will also discuss some computational issues with the numerical method.

## TBA

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

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

## From Classical to Quantum and Back

Abstract: Microlocal analysis exploits mathematical manifestations of the classical/quantum (particle/wave) correspondence and has been a very successful tool in spectral theory and partial differential equations. We can say that these two fields lie on the "quantum/wave side".Recently, microlocal methods have been applied to the study of classical dynamical problems, in particular of chaotic (Anosov) flows. I will explain how it works in the context of Ruelle resonances, decay of correlations meromorphy of dynamical zeta functions and applications to inverse problems.

The talk, based on the works of several mathematicians, including Datchev, Dyatlov, Faure, Guillarmou, Giulietti, Liverani, Nonnenmacher, Sjöstrand, Paternain, Pollicott, Salo, Tsujii, Uhlmann and the speaker, will be non-technical and is intended as an introduction to both microlocal analysis and to chaotic dynamics.

## 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

## Multi-fidelity Information Fusion Algorithms for High Dimensional Systems and Massive Data-sets

Abstract: We develop a framework for multi-fidelity information fusion and predictive inference in high dimensional input spaces and in the presence of massive data-sets. Hence, we tackle simultaneously the "big- N" problem for big data and the curse-of-dimensionality in multivariate parametric problems. The proposed methodology establishes a new paradigm for constructing response surfaces of high dimensional stochastic dynamical systems, simultaneously accounting for multi-fidelity in physical models as well as multi-fidelity in probability space. Scaling to high dimensions is achieved by data-driven dimensionality reduction techniques based on hierarchical functional decompositions and a graph-theoretic approach for encoding custom auto-correlation structure in Gaussian process priors. Multi-fidelity information fusion is facilitated through stochastic auto-regressive schemes and frequency-domain machine learning algorithms that scale linearly with the data. Taking together these new developments lead to linear complexity algorithms as demonstrated in benchmark problems involving deterministic and stochastic fields in up to 100,0000 input dimensions and 100,000 training points on a standard desktop computer.Refreshments will be served at 3:00 pm outside of LWSN 1142.

### Probability Seminar, Daniel Krenn, Alpen-Adria Universität Klagenfurt, REC 302

Tuesday, Nov 3 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

## Macroscopic Models for Rarefied Flows: Thermal Stress vs. Thermal Transpiration

Abstract: Rarefied gas flows show interesting effects that are not encountered in classical hydrodynamics, such as: thermal stresses, where flow is driven by temperature gradients; transpiration flow, which is driven by temperature gradients in the wall-boundaries; non-Fourier heat flux, which is induced by anisotropic stresses; Knudsen layers in front of the wall, due to strong non-equilibrium induced by particle wall interactions; and more. Any model that aims at describing rarefied gas flows should be able to describe these effects in good approximation.In the last decade, we have derived and developed the Regularized 13 Moment Equations (R13) which have been shown to describe rarefied flows for moderate Knudsen numbers in excellent detail, and at much lower computational cost than microscopic methods. The equations include all hydrodynamics, but add the description of the above mentioned rarefaction effects. Moreover, the R13 equations avoid problems like instabilities and discontinuous shocks that hamper earlier competing approaches.

The talk will introduce the ideas behind the R13 equations, and then highlight their capabilities by examination of a particular flow problem concerning the competition of thermal stress and thermal transpiration.

For this, we consider the R13 equations with modified boundary conditions which allow to tune the strength and direction of the thermal transpiration force. Microscopic and macroscopic transport equations for rarefied gases are solved to study the intricate, and unexpected, flow patterns, and identify the main thermodynamic forces. Simplified macroscopic models, such as jump-and slip hydrodynamics, or the equations for slow non-isothermal flow (SNIF) can only describe aspects of the microscopic flow, while the R13 equations provide a detailed approximation. It turns out that the patterns arise from a competition between thermal transpiration force at the boundary, and thermal stresses in the bulk.

(based on joint work with Manuel Torrilhon, Alireza Mohammadzadeh and Anirudh Singh Rana)

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

## TBA

### CCAM Lunch Seminar, Xiaofeng Yang, University of South Carolina, REC 225

Friday, Nov 13 11:30 am - 12:30 pm

## TBA

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

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

## TBA

### Probability Seminar, Yarong Feng, George Washington University, REC 302

Tuesday, Nov 17 3:30 pm - 4:30 pm

## TBA

### Computational & Applied Mathematics Seminar, Professor Mimmo Iannelli, University of Trento, Italy, REC 108

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

## TBA

## December

### Probability Seminar, Michael Perlmutter, Purdue University, REC 302

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

## TBA

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

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

## 2016

### Department of Mathematics Colloquium, Professor Alex Furman, University of Illinois at Chicago, MATH 175

Tuesday, Feb 2 4:30 pm - 5:30 pm

## TBA

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

### Computational & Applied Mathematics Seminar, Barry Lee, Southern Methodist University, REC 108

Monday, Feb 22 3:30 pm - 4:30 pm

## TBA

### Computational & Applied Mathematics Seminar, Professor Tao Lin, Virginia Tech, REC 108

Monday, Feb 29 3:30 pm - 4:30 pm

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