# Math Calendar

### Upcoming Events

## The Saturation Number of Pineapples

Alex Cameron, Vanderbilt University

Location: Stevenson 1432

Given a fixed graph F, a graph G is said to be F-saturated if it contains no copy of F and the addition of any edge creates a copy of F. The minimum number of edges that an F-saturated graph on n vertices can have is the saturation number of F. We determine the saturation numbers for a class of graphs called “pineapples” formed by taking a complete graph on t vertices and adding s pendant edges to one of its vertices. This is joint work with Gregory J. Puleo (Auburn).

## Property (T), Affine Actions and (Reduced) Cohomology

Jesse Peterson, Vanderbilt University

Location: Stevenson 1320

We will present several equivalent conditions for property (T) in terms of affine actions and (reduced) cohomology. This follows the work of Delorme, Guichardet, Shalom, and Ozawa. (This is Lecture 5 in a semester-long series on SL(3,Z) and Property (T).)

## Computation v. Simulation or: How I learned to Stop Worrying and Love the RNG

Jon Ashbrock, Vanderbilt University

Location: Stevenson 1206

Computation of probabilities and averages is one of the most common tasks asked of applied mathematicians in industry. While most problems of this type are tractable via pen-and-paper calculation, I claim this is not the best approach. With the use of your favorite RNG and a little bit of coding knowledge, you can estimate the probability in a much faster method. Tonight, we’ll demonstrate this technique in two ways: showing you how to have the most fun playing roulette and by providing an introduction to Monte-Carlo integration.

## Turbulence Suppression in Navier-Stokes Fluids of Dimension d=3, by Means of Stabilizing, Finite Dimensional, Tangential, Boundary Feedback Controls

Roberto Triggiani, The University of Memphis

Location: Stevenson 5211

The problem of turbulence suppression (technically, uniform stabilization) in a Navier-Stokes fluid originated in a 2004-Indiana paper, where the stabilizing, finite dimensional, feedback control acts on an arbitrarily small subdomain of the bounded domain occupied by the fluid. This was soon followed by studies aimed at obtaining the stabilizing feedback control to act tangentially on a small portion of the boundary (non-invasive control, implemented by jets of air). Results obtained so far left open the question as to whether such stabilizing control can be taken to be finite dimensional also in dimension d=3 in full generality. This talk will give an affirmative answer. To this end, it was necessary to recast prior studies in an altogether different functional setting, where additional technical and conceptual challenges arise, particularly since the control acts on the boundary in a feedback form (the way a thermostat works). The role and impact of unique continuation theorems of over-determined Oseen eigen-problems will be discussed [The “bad guy” is the pressure!]. This is joint work with I.Lasiecka and our PhD student Buddhika Priyasad.

Tea at 3:33 pm in SC 1425. (Contact Person: Gieri Simonett)

## How Much More Could We Explain with Genetics?: Medical Data Mining & the Undiagnosed Patient

Lisa Bastarache, Vanderbilt Dept. of Biomedical Informatics

Location: Garland Hall 101

## Evolutions Arising in Flow-Structure Interactions

Irena Lasiecka, University of Memphis

Location: Stevenson 1307

Fluid-structure interactions and flow-structure interactions are ubiquitous in nature. Problems such as attenuation of turbulence or flutter in an oscillating structure are prime examples of relevant applications. Mathematically, the models are represented by nonlinear Partial Dierential Equations (Navier Stokes-Euler equations and nonlinear elasticity) which display a strong boundary-type coupling at the interface between the two media. Moreover, in most models, the dynamical character of the two PDEs evolving on their corresponding domains is different and the overall system may display a parabolic/hyperbolic or hyperbolic/hyperbolic coupling, separated by the interface. This provides for a rich mathematical structure opening the door to several unresolved problems in the area of nonlinear PDE’s, dynamical systems and related harmonic analysis and geometry. Of particular interest are models with mixed boundary conditions [such as Kutta Joukovsky boundary conditions] which lead to a plethora of open problems in elliptic theory with related Hilbert-Riesz transform theory. This talk aims at providing a brief overview of recent developments in the area along with a presentation of some recent advances addressing the issues of mixed boundary conditions arising in modeling of panels fluttering in a non-viscous environment.

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Ben Hayes, University of Virginia

Location: Stevenson 1432

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Zack Tripp, Vanderbilt University

Location: Stevenson 1206

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Arie Levit, Yale University

Location: Stevenson Center 1308

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Kate Ponto, University of Kentucky

Location: Stevenson 1310

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Adam Prenosil, Vanderbilt University

Location: Steveson 1206

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Steven Lalley, University of Chicago

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Mark Sapir)

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Sayan Das, University of Iowa

Location: Stevenson 1432

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Jürgen Saal, Heinrich-Heine-Universität Düsseldorf

Location: Stevenson 1307

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Alejandro Adem, University of British Columbia

Location: Stevenson 5211

Tea at 3:33 pm in SC 1425. (Contact Person: Anna Marie Bohmann)

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Huy Nguyen, Brown University

Location: Stevenson 1307

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Ionut Chifan, University of Iowa

Location: Stevenson 1432

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Mihaela Ignatova, Temple University

Location: Stevenson 1307

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Sergei Tabachnikov, Pennsylvania State University

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Mark Sapir)

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Jeremy LeCrone, University of Richmond

Location: Stevenson 1307

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Lara Ismert, University of Nebraska, Lincoln

Location: Stevenson 1432

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Yuanzhen Shao, Georgia Southern University

Location: Stevenson 1307

## Shanks Workshop on Homotopy Theory 2019, April 13-14

Locations: Stevenson Center 1 (Math Building)

For more information, visit the workshop website.

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Vladimir Sverak, University of Minnesota

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Gieri SImonett)

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Lauren Ruth, Vanderbilt University

Location: Stevenson 1432

## On the Linear Forced Euler and Navier-Stokes Equations: Damping and Modified Scattering

Christian Zillinger, University of Southern California

Location: Stevenson 1307

We study the long-time asymptotic behavior of the linearized Euler and nonlinear Navier-Stokes equations close to Couette flow. As a main result we show that suitable forcing breaks asymptotic stability results at the level of the vorticity, but that solutions never the less exhibit convergence of the velocity field. Thus, here linear inviscid damping persists despite instability of the vorticity equations.

## Spring 2019 Semester

Location: Vanderbilt University

Undergraduate classes end on April 22, 2019. For more information, Visit the Office of the University Registrar online.

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Gerard Misiolek, University of Notre Dame

Location: Stevenson 1307

## NCGOA Spring Institute 2019 and 34th Annual Shanks Lecture, May 3-9

Location: Stevenson Center 4309

The topic of the Seventeenth Annual Spring Institute on Noncommutative Geometry and Operator Algebras is “Algebra and Geometry Quantized and Quantified.” The conference will focus on common themes and recent developments in topology, quantum algebra, topological condensed matter physics, subfactor theory, and quantum information theory. NCGOA 2019 will be held in conjunction with the 34th Shanks Lecture, delivered by Fields Medalist Michael Freedman (Microsoft Research). More information is available on the conference website.

## Approximation Theory 16, May 19-22, 2019

Location: Vanderbilt University

This meeting will be the sixteenth in a series of international conferences on Approximation Theory held every three years at various locations in the U.S. For more information, please visit the conference website.