# Calendar

## Yesterday

### Representation Theory Seminar, Dr. Mohammad Hadi Hedayatzadeh, Purdue University, UNIV 103

Thursday, September 18, 2014, 1:30 - 2:30 PM EDT

## Exterior Powers of Lubin-Tate groups: Part 1 of 2

ABSTRACT: This introductory talk will be a preparation for the second talk and is aimed at the non-experts. Depending on time, we will cover a subset of the following: finite flat group schemes, Cartier duality, étale and infinitesimal group schemes, Frobenius and Verschiebung, Dieudonné theory, p-divisible groups. We will try to give basic definitions and main results.### Student Commutative Algebra Seminar, Alessandra Costantini, Purdue University, BRNG B202

Thursday, September 18, 2014, 1:30 - 2:30 PM EDT

## Free Resolutions and Hilbert Functions, Part 3

### Number Theory Seminar, Professor Edray Goins, Purdue University, MATH 731

Thursday, September 18, 2014, 3:30 - 4:30 PM EDT

## An Introduction to Composition of Quadratic Forms and Quadratic Reciprocity

ABSTRACT: To motivate the semester's learning seminar, we discuss Section 1 of David Cox's book ``Primes of the Form $x^2 + n y^2$''.### Mathematics Club, Professor Edray Goins, Purdue University, REC 108

Thursday, September 18, 2014, 6:00 - 7:00 PM EDT

## A Survey of Diophantine Equations

ABSTRACT: There are many beautiful identities involving positive integers. For example, Pythagoras knew $3^2 + 4^2 = 5^2$ while Plato knew $3^3 + 4^3 + 5^3 = 6^3$. Euler discovered $59^4 + 158^4 = 133^4 + 134^4$, and even a famous story involving G.~H.~Hardy and Srinivasa Ramanujan involves $1^3 + 12^3 = 9^3 + 10^3$. But how does one find such identities? Around the third century, the Greek mathematician Diophantus of Alexandria introduced a systematic study of integer solutions to polynomial equations. In this talk, we'll focus on various types of so-called Diophantine Equations, discussing such topics as Pythagorean Triples, Pell's Equations, Elliptic Curves, and Fermat's Last Theorem.## Today

### CCAM Lunch Seminar, Professor Jingwei Hu, Purdue University, REC 121

Friday, September 19, 2014, 11:30 - 12:30 PM EDT

## Fast algorithms for the Boltzmann collision operator

Abstract: The Boltzmann equation is the fundamental equation in kinetic theory. It describes the non-equilibrium dynamics of a large number of classical/quantum particles. The most prominent feature of this equation is a high-dimensional integral operator modeling particle collisions, whose nonlinear and nonlocal structure poses a great challenge for numerical simulation. I will introduce a fast algorithm for computing the Boltzmann collision operator. It is a Fourier-spectral method based on a separated expansion of the collision kernel. I will start with the simpler classical case and then generalize to the quantum case so that the presentation is accessible to beginning graduate students. If time permits, I will talk about possible improvements and applications.### Basic Notions Seminar, Britain Cox, Purdue University, BRNG B222

Friday, September 19, 2014, 3:30 - 4:30 PM EDT

## Trapdoors, Locked Boxes and Magic Caves

Abstract: Until modern cryptography, pure mathematics was a veritable Eden, absent of application. Now, we have a cute fig leaf with which to defend ourselves against skeptical engineers. In this talk, we will discuss how seemingly whimsical exercises actually underpin much of modern life. We will also discuss some basic philosophy of cryptography, whose extraordinary flexibility allows for interchanging very different mathematical disciplines. True to our ancestral traditions, we will spend little time on applications.## Next Week

### Bridge to Research Seminar, Dr. Plamen Stefanov, Purdue University, UNIV 203

Monday, September 22, 2014, 1:30 - 2:30 PM EDT

## Inside Out – what is an inverse problem and what are inverse problems good for?

Abstract: The talk will give a brief introduction to Inverse Problems. We will motivate the interest to them by problems arising in Medical Imaging, Quantum Mechanics and Geophysics on one hand, and in Geometry and Integral Geometry, on the other. The talk will be very non-technical but being a math talk, it will include at least one proof.### Geometry Seminar, Mark F. Hagen, RTG Postdoctoral Assistant Professor, University of Michigan, MATH 731

Monday, September 22, 2014, 3:30 - 4:30 PM EDT

## Cubulating hyperbolic free-by-Z groups

Abstract: Let $G$ be a word-hyperbolic group admitting an epimorphism to $Z$ with finitely-generated free kernel. Then $G$ acts freely and cocompactly on a CAT(0) cube complex. This has numerous nice consequences, notably $Z$-linearity of $G$. I'll say some words about applications and about the strategy of the proof. This is joint work with Dani Wise.### Student Commutative Algebra Seminar, Alessio Sammartano, Purdue University, BRNG B202

Thursday, September 25, 2014, 1:30 - 2:30 PM EDT

## Free Resolutions and Hilbert Functions, Part 4

### Representation Theory Seminar, Dr. Mohammad Hadi Hedayatzadeh, Purdue University, UNIV 103

Thursday, September 25, 2014, 1:30 - 2:30 PM EDT

## Exterior Powers of Lubin-Tate Groups: Part 2 of 2

ABSTRACT: After defining exterior powers of $\pi$-divisible modules, we prove that the exterior powers of $\pi$-divisible modules of dimension at most one over any base scheme exist and their construction commute with arbitrary base change.### PDE Seminar, Professor Xiang Xu, Purdue University, REC 317

Thursday, September 25, 2014, 3:30 - 4:30 PM EDT

## Cubic instability in a dynamic Q-tensor model for nematic liquid crystals

Abstract: We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal configurations described using the $Q$-tensor settings. This energy functional involves a cubic term and is unbounded from below. We study dynamical effects produced by the presence of this cubic term by considering the corresponding $L^2$ gradient flow. We work in $2D$ and higher dimensions separately, and try to understand relations between the physicality of the initial data and the global well-posedness of the system.### CCAM Lunch Seminar, Professor Steven Dong, Purdue University, REC 121

Friday, September 26, 2014, 11:30 - 12:30 PM EDT

TBA

## Two Weeks

### Jean Rubin Memorial Lecture, Margaret Cheney, Colorado State University, MATH 175

Tuesday, September 30, 2014, 4:30 - 5:30 PM EDT

## Introduction to Synthetic-Aperture Radar Imaging

Abstract: Radar imaging is a technology that has been developed, very successfully, within the engineering community during the last 50 years. Radar systems on satellites now make beautiful images of regions of our earth and of other planets such as Venus. One of the key components of this impressive technology is mathematics, and many of the open problems are mathematical ones. This lecture will explain, from first principles, some of the basics of radar and the mathematics involved in producing high-resolution radar images. Refreshments will be served in the Math Library Lounge at 4:00 p.m.## Three Weeks

### Computational & Applied Mathematics Colloquium, Professor Mark Ainsworth, Brown University, REC 122

Monday, October 6, 2014, 3:30 - 4:30 PM EDT

## Dispersive Behaviour of High Order Finite Element Schemes for the One-Way Wave Equation

Abstract: We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparison is made with the spectral element method and the discontinuous Galerkin method with centred fluxes. It is shown that all schemes admit a spurious mode. The spectral element method is always inferior to the finite element and discontinuous Galerkin schemes; a somewhat surprising result in view of the fact that, in the case of the second order wave equation, the spectral element method propagates waves with an accuracy superior to that of the finite element scheme. The comparative behaviour of the finite element and discontinuous Galerkin scheme is also somewhat surprising: the accuracy of the finite element method is superior to that of the discontinuous Galerkin method in the case of elements of odd order by two orders of accuracy, but worse, again by two orders of accuracy, in the case of elements of even order.Refreshments will be served in the Math library lounge from 3 to 3:30 p.m.

### Department of Mathematics Colloquium, Alejandro Adem, University of British Columbia, MATH 175

Tuesday, October 7, 2014, 4:30 - 5:30 PM EDT

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### CCAM Lunch Seminar, Professor Xiangxiong Zhang, Purdue University, REC 121

Friday, October 10, 2014, 11:30 - 12:30 PM EDT

TBA

## October

### Department of Mathematics Colloquium, Jonathan Rosenberg, University of Maryland, MATH 175

Tuesday, October 21, 2014, 4:30 - 5:30 PM EDT

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Computational & Applied Mathematics Seminar, Dr. Wujun Zhang, University of Maryland, REC 122

Monday, October 27, 2014, 3:30 - 4:30 PM EDT

TBA

### Department of Mathematics Colloquium, Francis Bonahon, University of Southern California, MATH 175

Tuesday, October 28, 2014, 4:30 - 5:30 PM EDT

## TBA

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

### Computational & Applied Mathematics Seminar, Professor Jingfang Huang, University of North Carolina, Chapel Hill, REC 122

Monday, November 3, 2014, 3:30 - 4:30 PM EST

TBA

### Department of Mathematics Colloquium, Jean Bellissard, Georgia Tech, MATH 175

Tuesday, November 4, 2014, 4:30 - 5:30 PM EST

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Probability Seminar, Camelia Pop, University of Pennsylvania, UNIV 103

Thursday, November 6, 2014, 3:30 - 4:30 PM EST

### CCAM Lunch Seminar, Professor Guang Lin, Purdue University, REC 121

Friday, November 7, 2014, 11:30 - 12:30 PM EST

TBA

### Department of Mathematics Colloquium, Justin Moore, Cornell, MATH 175

Tuesday, November 11, 2014, 4:30 - 5:30 PM EST

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Probability Seminar, Daniel Kelleher, Purdue University, UNIV 103

Thursday, November 13, 2014, 3:30 - 4:30 PM EST

### CCAM Lunch Seminar, Mr. Drew Swartz, Purdue University, REC 121

Friday, November 21, 2014, 11:30 - 12:30 PM EST

TBA