Department of Mathematics

Calendar


Yesterday

Function Theory Seminar, Alexander Aptekarev, Inst. Applied Math., Moscow, and IUPUI, MATH 731

Tuesday, September 30, 2014, 3:00 - 4:00 PM EDT

Structure of multi-valued analytic functions and Hermite-Pade Approximants

Abstract: Let a germ of an analytic function be given, which has an analytic continuation along any path in the complex plane minus a finite set where the function has branch points. We discuss constructive procedures, which allow to determine "extremal" domains of holomorphy or even several sheets of the Riemann surface for this function.

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.


Today

Topology Seminar, Carolyn Yarnall, Wabash College, BRNG B206

Wednesday, October 1, 2014, 1:30 - 2:30 PM EDT

Equivariant Stable Homtopy Theory and the Slice Filtration

Abstract: In equivariant stable homotopy theory, the objects we are primarily concerned with are G-spectra. The homotopy “groups” of such spectra actually have more structure; they are Mackey functors. After recalling the definition of a Mackey functor, I will discuss how to compute the Mackey-functor valued homotopy of G-spectra and work a few examples. I will then discuss the slice filtration, a filtration of equivariant spectra that was essential to the solution to the Kervaire invariant-one problem. Time permitting, I will present a few recent results concerning this filtration.

Commutative Algebra Seminar, Dr. Linquan Ma, Purdue University, UNIV 119

Wednesday, October 1, 2014, 2:30 - 3:30 PM EDT

On Lech's Conjecture

Mixed Tate Motives Seminar, Artur Jackson, Purdue University, UNIV 301

Wednesday, October 1, 2014, 2:30 - 3:30 PM EDT

Catégories Tannakiennes

Abstract: In this talk we will present the background material needed for defining motivic fundamental groups. This requires the language of Tannakian categories. The Tannakian philosophy says that reasonably nice tensor categories ``are'' categories of representations of some algebraic group. Moreover, one can reconstruct this group. This talk will make precise these statements and provide some illuminating examples from representation theory and geometry.

Algebraic Geometry Seminar, Chin-Jui Lai, Purdue University, MATH 731

Wednesday, October 1, 2014, 3:30 - 4:30 PM EDT

Exceptional Collection on Fake Projective Planes

Abstract: In this talk, I present the joint work with S.K. Yeung on a geometric approach to the existence of a sequence of special type exceptional collection on fake projective planes. This answers partially a question of Galkin, Katzarkov, Mellit, and Shinder, [GKMS]. We will also discuss some motivations and related problems about phantoms and mini folds.


Tomorrow

Student Commutative Algebra Seminar, Christina Jamroz, Purdue University, BRNG B202

Thursday, October 2, 2014, 1:30 - 2:30 PM EDT

Free Resolutions and Hilbert Functions, Part 5

Number Theory Seminar, Mr. Alex Barrios, Purdue University, MATH 731

Thursday, October 2, 2014, 3:30 - 4:30 PM EDT

Hilbert and Ring Class Fields: From Quadratic Forms to Ideals in Number Fields

Abstract: We discuss Section 5 of David Cox's book ``Primes of the Form $x^2 + n y^2$''.

PDE Seminar, Professor Francesco Maggi, University of Texas at Austin, REC 317

Thursday, October 2, 2014, 3:30 - 4:30 PM EDT

A General Compactness Theorem for Plateau's Problem

Abstract: Plateau's problem (minimizing area among surfaces spanning a given boundary curve) is one of the most basic questions in the Calculus of Variations. To give a precise mathematical formulation of this problem one needs to specify notions of surface, area and boundary, and the properties of solutions depend crucially on these choices. For example, by solving Plateau's problem (on surfaces in R3) in the framework of the theory of currents one finds solutions which are always smooth away from their boundary, in contrast to what is occasionally observed on real soap films spanning specific boundary curves. Various alternative formulations have been proposed in the years, starting with the pioneering work by Reifenberg, and ending up with more recent contributions by David, De Pauw, Harrison and Pugh, and others. We provide here a compactness principle which is applicable to different formulations of Plateau's problem in codimension one and which is exclusively based on the theory of Radon measures and elementary comparison arguments. Exploiting some additional techniques in geometric measure theory, we can use this principle to give a different proof of a theorem by Harrison and Pugh and to answer a question raised by Guy David about "sliding minimizers". This is a joint work with Camillo De Lellis and Francesco Ghiraldin (U. Zurich).

Probability Seminar, Jonathon Peterson, Purdue University, UNIV 103

Thursday, October 2, 2014, 3:30 - 4:30 PM EDT

Recurrence, Transience, and Ballisticity for One-Dimensional Excited Random Walks with Bounded Jumps

Abstract: Excited random walks (also called cookie random walks) are a model for a self-interacting random motion where the transition probabilities are a function of the local time of the random walk. Much is known about one-dimensional excited random walks including a criterion for recurrence/transience and a criterion for ballisticity of the walk. For the model that is usually studied, the random walk always moves in steps of size one. In this talk we generalize the model of excited random walks to include bounded jumps. There are some natural generalizations of the results from the nearest neighbor case, but the proofs of some of the facts (such as the criterion for ballisticity) completely break down when the walk has bounded jumps. Nevertheless, in certain cases we are able to use completely different methods to prove the natural conjectures for recurrence/transience and ballisticity. This is joint work with Burgess Davis.

Mathematics Club, Professor Greg N. Frederickson, Purdue University, REC 108

Thursday, October 2, 2014, 6:00 - 7:00 PM EDT

Beyond Swinging: Hinged Dissections that Twist or Fold

ABSTRACT: A geometric dissection is a cutting of a geometric figure into pieces that can be rearranged to form another figure. Some dissections can be connected with hinges so that the pieces form one figure when swung one way on the hinges, and form the other figure when swung another way. In addition to using "swing hinges", which allow rotation in the plane, we can use "twist hinges", which allow one piece to be flipped over relative to another piece via rotation by 180 degrees through a third dimension. Furthermore, we can use "fold hinges", which allow rotation along a shared edge, a motion that is akin to folding. This talk will introduce a variety of twist-hinged and fold-hinged dissections of regular polygons and stars, and other figures such as polyominoes. The emphasis will be on both appreciating and understanding these fascinating mathematical recreations. I will employ algorithmic and tessellation-based techniques, as well as symmetry and other geometric properties, to design the dissections. The goal will be to minimize the number of pieces, subject to the dissection being suitably hinged. Animations and video will be used to demonstrate the hinged dissections, in addition to actual physical models.


Friday

Secret Seminar, Professor Ben McReynolds, Purdue University, UNIV 301

Friday, October 3, 2014, 11:30 - 1:30 PM EDT

Profinite Topology and Separability Continued

Abstract: This will be a continuation of the previous week's lecture.


Next Week

Bridge to Research Seminar, Professor Steven Dong, Purdue University, UNIV 203

Monday, October 6, 2014, 1:30 - 2:30 PM EDT

Bouncing Water Drops and Floating Paper Clips: Mathematics, Numerics, and Simulations

Abstract: What do these phenomena have in common? Both phenomena involve two different fluids (air and water), the fluid interface, and some hydrophobic solid-wall surface. They both result from the interactions among the gravity, the surface tension, and the wall hydrophobicity. These problems belong to a wider class of flow problems involving two or more fluid phases, surface wettability, and moving contact lines. In this talk, I will provide a gentle introduction to the simulation methods our group is developing on how to numerically simulate two-phase flows and how to deal with surface wettability and a host of other issues. These techniques have been used for simulating the above problems, as well as a wide class of other interesting physical processes and phenomena. We will look into the physical and mathematical principles underlying the methods. I will also discuss the numerical and computational challenges involved therein, and the potential opportunities for aspiring graduate students.

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.

Basic Skills Workshop, Prof. Carl Cowen, Purdue University, UNIV 019

Tuesday, October 7, 2014, 3:30 - 4:30 PM EDT

How to Get an Academic Job

Abstract: Besides taking the qualifying exams, there is little more stressful in the process of getting a PhD in mathematics than "Getting a Job!!" at the end of the PhD!! This presentation will consist of the advice and observations of the speaker, concerning the process of getting a job, and especially about getting an academic job. While these suggestions are NOT universally agreed upon, they reflect observations gleaned from both hiring post-docs and faculty in this Department and also from students' recent experience in getting positions. We will touch all aspects of the process from the start of planning the spring 16 or 18 months before the August you hope to be in a new position through the usual course of events after the January meetings in the year you will finish and get the position. Since your advisor will be the best source of information on how to get a post-doc position in your research area, the emphasis in this discussion will be on other kinds of positions.

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

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

Topology of Commuting Matrices

Abstract: In this talk we will describe basic topological properties of the space of commuting unitary matrices. In particular we will show that they can be assembled to form a space which classifies commutativity for vector bundles and which has very interesting homotopy-theoretic properties. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, UNIV 103

Thursday, October 9, 2014, 3:30 - 4:30 PM EDT

Outstanding Alumnus Seminar, Professor Jiongmin Yong, University of Central Florida, LWSN 1142

Thursday, October 9, 2014, 4:30 - 5:30 PM EDT

Time-Inconsistent Problems in Optimal Control Theory

Abstract: It will be very ideal if once an optimal policy/strategy is made today, it will stay optimal forever. However, rational people know that this is hardly possible, namely, a best-looking decision for today usually will not be best for tomorrow. This is called the time-inconsistency. The main reasons are due to the so-called time-preferences and risk-preferences of the decision makers. In this talk, I will survey some history of time-inconsistent problems, and some recent works on time-consistent equilibrium strategies, by means of dynamic programming, differential games and Hamilton-Jacobi equations. Refreshments will be served at 4:00 p.m. in LWSN 1142.

CCAM Lunch Seminar, Professor Xiangxiong Zhang, Purdue University, REC 121

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

TBA

Secret Seminar, Mr. Jacob Noparstak, Purdue University, UNIV 301

Friday, October 10, 2014, 11:30 - 1:30 PM EDT

Introduction to Teichmüller Space

Abstract: I will introduce the notion of the Teichmüller spaces of both hyperbolic surfaces and hyperbolic surfaces with boundary. I will also prove some basic but very important results on these Teichmuller spaces. This talk will be designed for people with a basic understanding of manifolds and surfaces; any other needed notions are introduced.


Two Weeks

Computational & Applied Mathematics, Professor Ivan I Smalyukh, University of Colorado at Boulder, REC 121

Wednesday, October 15, 2014, 3:30 - 4:30 PM EDT

Probability Seminar, UNIV 103

Thursday, October 16, 2014, 3:30 - 4:30 PM EDT


Three Weeks

Computational & Applied Mathematics Colloquium, Professor Qiang Du, Columbia University, REC 122

Monday, October 20, 2014, 3:30 - 4:30 PM EDT

TBA
Refreshments will be served in the Math library lounge from 3 to 3:30 p.m.

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.

Probability Seminar, UNIV 103

Thursday, October 23, 2014, 3:30 - 4:30 PM EDT


October

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.

Number Theory Seminar, Mr. Jeremy Fuller, Purdue University, MATH 731

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

Genus Theory for Quadratic Forms Revisited: The Genus Field

ABSTRACT: We discuss Section 6 of David Cox's book ``Primes of the Form $x^2 + n y^2$''.

Probability Seminar, UNIV 103

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

CCAM Lunch Seminar, Professor Zhilan Feng , Purdue University, REC 121

Friday, October 31, 2014, 11:30 - 12:30 PM EDT

TBA


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

Computational & Applied Mathematics Seminar, Professor Yuanwei Qi, University of Central Florida, REC 122

Monday, November 10, 2014, 3:30 - 4:30 PM EST

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

Department of Mathematics Colloquium, Boris Tsygan, Northwestern University, MATH 175

Tuesday, November 18, 2014, 4:30 - 5:30 PM EST

TBA

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

Probability Seminar, UNIV 103

Thursday, November 20, 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

Computational & Applied Mathematics Seminar, Professor Xu Yang, UC at Santa Barbara, REC 122

Monday, November 24, 2014, 3:30 - 4:30 PM EST

TBA


December

Computational & Applied Mathematics Seminar, Dr. Qifeng Liao, MIT, REC 122

Monday, December 1, 2014, 3:30 - 4:30 PM EST

Reduced Order Modeling and Domain Decomposition Methods for Uncertainty Quantification

Abstract: Traditionally, terms in PDEs such as permeabilities, viscosities or boundary conditions have been treated as known deterministic quantities. However, these quantities are not always known with certainty, and there is much interest today in treating them as random fields. In this talk, I will present a reduced basis collocation method for efficiently solving PDEs with random coefficients, which is joint work with Howard Elman of University of Maryland. I will also present a domain-decomposed uncertainty quantification approach for complex systems, which is joint work with Karen Willcox of Massachusetts Institute of Technology.

Probability Seminar, UNIV 103

Thursday, December 4, 2014, 3:30 - 4:30 PM EST

CCAM Lunch Seminar, Professor Changyou Wang, Purdue University, REC 121

Friday, December 5, 2014, 11:30 - 12:30 PM EST

TBA

Probability Seminar, UNIV 103

Thursday, December 11, 2014, 3:30 - 4:30 PM EST


2015

Computational & Applied Mathematics Seminar, Professor Alina Chertock, North Carolina State University, REC 122

Monday, January 26, 2015, 3:30 - 4:30 AM EST

TBA