Department of Mathematics

Calendar


Yesterday

Secret Seminar, Jacob Noparstak, Purdue University, UNIV 301

Friday, October 24, 2014, 11:30 - 12:30 PM EDT

Compactification of Teichm├╝ller space

Abstract: In this talk we will define three different approaches to finding compactifications of Teichm├╝ller space. First, we will look at Thurston's classical approach, then a modern approach as seen in the work of Mondello, Liu, and many others. The final approach, which is very different, is due to Penner. This is a sequel to the talk on October 10, 2014


Next Week

Geometry Seminar, Spencer Dowdall, University of Illinois at Urbana-Champaign, MATH 731

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

Fibrations and splittings of free-by-cyclic groups

Abstract: A finitely generated group that splits as a (semidirect product) free-by-cyclic group can often be expressed as such in infinitely many ways. This talk will explore the different ways a given group G splits as a free-by-cyclic group or, more generally, as an ascending HNN-extension over a finitely generated free group. It turns out that this algebraic question is closely related the the dynamical problem of finding "cross sections" of a semiflow on a certain 2-complex. After explaining this correspondence I will introduce a polynomial invariant that exactly calculates the set of cross sections and thereby identifies an interrelated family splittings of G. In fact, this family corresponds to a full connected component of the BNS-invariant of G. This is joint work with Ilya Kapovich and Christopher Leininger.

Computational & Applied Mathematics Seminar, Dr. Wujun Zhang, University of Maryland, REC 122

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

Discrete ABP Estimate and Rates of Convergence of Linear Elliptic PDEs in non-Divergence Form

Abstract: We design a finite element method (FEM) for linear elliptic equations in non-divergence form, which hinges on an integro-differential approximation of the PDE. We show the FEM satisfies the discrete maximum principle (DMP) provided that the mesh is weakly acute. Thanks to the DMP and consistency property of the FEM, we establish convergence of the numerical solution to the viscosity solution. We derive a discrete Alexandroff-Bakelman-Pucci (ABP) estimate for finite element methods. Its proof relies on a geometric interpretation of Alexandroff estimate and control of the measure of the sub-differential of piecewise linear functions in terms of jumps, and thus of the discrete PDE. The discrete ABP estimate leads to optimal rates of convergence for the finite element method under suitable regularity assumptions on the solution and coefficient matrix.

Junior Analysis Seminar, Dr. Xiang Xu, Purdue University, MATH 215

Monday, October 27, 2014, 4:30 - 5:30 PM EDT

Wasserstein Metric: a Bridge Connecting Fokker-Planck Equation and Gradient Flow

Abstract: The Fokker-Planck equation, or called forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito SDE. In our talk, we would make an informal derivation of the gradient flow structure of this equation using the celebrated Jordan-Kinderlehrer-Otto scheme, which is the minimizing movement scheme w.r.t. Wasserstein metric in the space of probability measures. This is a completely novel link between this diffusion equation and the Gibbs-Boltzmann entropy of the density, which provides a precise interpretation to the notion "diffusion arises from the tendency of the system to maximize entropy".

Basic Skills Workshop, Prof. Kiril Datchev, Purdue University, UNIV 019

Tuesday, October 28, 2014, 3:30 - 4:30 PM EDT

The Paper Writing Process

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

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

Kauffman Brackets on Surfaces

Abstract: The classical Kauffman bracket was introduced by Lou Kauffman. It is an invariant of knots in space, closely related to the famous Jones polynomial. Witten's interpretation of the Jones polynomial as a special case of a topological quantum field theory leads to a generalization of Kauffman brackets to knots drawn on a surface. I will discuss properties of these generalized Kauffman brackets. This is joint work with Helen Wong. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

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

Wednesday, October 29, 2014, 2:30 - 3:30 PM EDT

Tannakian Reconstruction and Mixed Motives

Abstract: We will present a reconstruction theorem for Hopf algebras, and get a version of Deligne's reconstruction theorem as a corollary. Time permitting, we will begin to construct the category of mixed motives.

Automorphic Forms and Representation Theory Seminar, Professor Tonghai Yang, University of Wisconsin at Madison, UNIV 103

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

A Conjecture of Colmez

ABSTRACT: In his seminal work on Mordell conjecture, Faltings introduces and studies the height of an Abelian variety. When the Abelian variety is a CM elliptic curve, its Falting's height is essentially the local derivative of the Dirichlet $L$-series associated to the imaginary quadratic field by the famous Chowla-Selberg formula. In 1990s, Colmez gave a precise conjectural formula to compute the Faltings height of a CM abelian variety of CM type $(E,\Phi)$ in terms of the log derivative of some `Artin' L-function associated to the CM type $\Phi$. He proved the conjecture when the CM number field when $E$ is abelian, refining Gross and Anderson's work on periods. Around 2007, I proved the first non-abelian case of the Colmez conjecture using a totally different method--arithmetic intersection and Borcherds product. In this talk, I will talk about its generalization to a new family of CM type, related to Shimura variety of unitary type $(n, 1)$. This is an ongoing joint work with Bruinier, Howard, Kudla, and Rapoport.

Student Commutative Algebra Seminar, Matthew Toeniskoetter, Purdue University, BRNG B202

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

Free Resolutions and Hilbert Functions, Part 9

Operator Algebras Seminar, Mr. Wei Zhang, Purdue University, MATH 731

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

Rokhlin Dimension for Actions of Redidually Finite Groups

Abstract: The talk is based on the recent paper of G. Szabo, J. Wu and J. Zacharias. In this talk, we will introduce their generalized definition of Rokhlin dimension to actions of all countable, discrete and redidually finite groups. And we will enlarge the class of C*-dynamical systems under consideration to non-unital C*-algebras, and cocycle actions instead of the ordinary actions. Their main result is: if the group in question has a box space of finite asymptotic dimension, then actions with finite Rokhlin dimension preserve the property of having finite nuclear dimension, when passing to the crossed product C*-algebra.

PDE Seminar, Professor Yannick Sire, Aix-Marseille University, REC 317

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

Bounds on Eigenvalues for the Laplace-Beltrami Operator

Abstract: An important question in spectral analysis is to get bounds on (say) the first eigenvalue of the laplace operator in terms of changes of the metric. The purpose of this talk is to develop a complete theory in the case of surfaces. As a consequence of our strategy of proof, we settle a conjecture by Yau et al.

Probability Seminar, Luis Acuna, Purdue University, UNIV 103

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

A Decomposition for Additive Functionals of Levy Processes

Abstract: Motivated by the recent results of Nualart and Xu concerning limits laws for occupation times of one dimensional symmetric stable processes, we prove a decomposition for functionals of one dimensional symmetric Levy processes under certain conditions on the characteristic exponent and compute the moments of the decomposition.

Joint Algebraic Geometry/Number Theory Seminar, Professor Mihai Fulger, Princeton University, MATH 731

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

Positivity for Higher (co)dimensional Numerical Cycle Classes

Abstract: It is classical to study the geometry of a projective variety through positive cones of numerical classes of divisors or curves. The Mori cone in particular plays an important role in the classification of projective algebric varieties. A number of pathological examples have shifted attention from the higher (co)dimensional case. They show that the analogous definitions do not lead to the same positivity properties. To correct the negative outlook, I look at stronger positivity conditions. A sample result is that the pseudoeffective cone of numerical k-dimensional cycle classes is pointed for all k. The proof works in all characteristics, and without restrictions on singularities. This is in joint work with Brian Lehmann.

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

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

Emerging Disease Dynamics in A Model Coupling Within-Host and Between-Host Systems

Abstract: Epidemiological models and immunological models have been studied largely independently. However, the two processes (within- and between-host interactions) occur jointly and models that couple the two processes may generate new biological insights. Particularly, the threshold conditions for disease control provided by the coupled model can be dramatically different from those generated by the epidemiological or immunological models separately. The mathematical model we considered links an SI epidemiological model and an immunological model for pathogen-cell dynamics. When the two sub-systems are considered in isolation, the dynamics are standard and simple. That is, either the infection-free equilibrium is stable or a unique positive equilibrium is stable depending on the relevant reproduction number being less or greater than 1. However, when the two sub-systems are dynamically coupled, the full system exhibits more complex dynamics including backward bifurcations; that is, multiple positive equilibria exist with one of which being stable even if the reproduction number is less than 1. The biological implications of such bifurcations are illustrated using an example concerning the spread and control of toxoplasmosis.

Secret Seminar, Jason Lucas, Purdue University, UNIV 301

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

Homotopy Invariant Algebraic Structures

Abstract: Associativity does not behave well in respect to homotopy. By this we mean that a space homotopy equivalent to a given topological space with an associative multiplication need not have strict associative multiplication that is recognized by that equivalence. It would seem that two important areas of topology, homotopy theory and theory of algebraic structures, stand apart from each other. Operads provide us with tools for bridging this gap. In this talk we will give the definition of an operad, discuss the key notion of an algebra over an operad, and explain the way in which an operad can impart a space with a homotopy invariant algebraic structure.


Two Weeks

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

A Few Thoughts on Time Integration

Abstract: In this talk, I will discuss our recent work on developing accurate and efficient time integration schemes for differential equation initial value problems. Covered topics include the mathematical foundations for a class of "optimal" time discretization schemes, iterative methods for solving the resulting algebraic equations, different preconditioning techniques to improve the efficiency, and the coupling of these time integration schemes with the spatial fast integral equations solvers we have been developing for the past ten years. The developed techniques have been applied to study the dynamics of bio- and physical systems.

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.

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

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

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, 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


Three Weeks

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

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

Existence and Non-Existence of Traveling Waves in Isothermal Chemical Reaction Systems

Abstract: Traveling waves arises in many important physics and biology models. They play an important role in explaining many interesting biological phenomena. In this talk I shall present some recent results on the existence and non-existence of traveling waves for a class of chemical reaction systems.

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


November

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, Anirban DasGupta, Purdue University, UNIV 103

Thursday, November 20, 2014, 3:30 - 4:30 PM EST

Asymptotic Expansions Related to Ramanujam's First Letter to Hardy, the Rubin Conjecture, and their Poisson-Gamma Consequences

Computational & Applied Mathematics Seminar, Professor Christopher Kribs, University of Texas at Arlington, REC 103

Thursday, November 20, 2014, 3:30 - 4:30 PM EST

TBA

Ph.D. Thesis Defense, Xiaoxiao Chen, BRNG 1206

Friday, November 21, 2014, 10:00 - 11:30 AM EST

Epistemic Uncertainty Quantification in Scientific Committee: Xiu (Co-Chair), Dong (Co-Chair), Buzzard, Li

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

Frozen Gaussian approximation and its applications

Abstract: We propose the frozen Gaussian approximation for the computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool based on the asymptotic analysis on phase plane. Compared to geometric optics, it provides a valid solution around caustics. Compared to the Gaussian beam method, it overcomes the drawback of beam spreading. We will present numerical examples as well as preliminary application in seismology to show the performance of this method.

Computational & Applied Mathematics Seminar, Professor Jinglai Li, Shanghai Jiaotong University, REC 122

Monday, November 24, 2014, 4:30 - 5:30 PM EST

TBA


December

Monday, December 1, 2014, 3:30 - 5:00 PM EST

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