Department of Mathematics

Calendar


Yesterday

Topology Seminar, Ben Knudsen, Northwestern University, BRNG B206

Wednesday, October 29, 2014, 1:30 - 2:30 PM EDT

Rational homology of configuration spaces via factorization homology

Abstract: The study of configuration spaces is particularly tractable over a field of characteristic zero, and there has been great success over the years in producing chain complexes simple enough for explicit computations, formulas for Betti numbers, and descriptive results such as homological stability. I will discuss recent work identifying the homology of the configuration spaces of an arbitrary manifold M with the homology of a certain Lie algebra constructed from the compactly supported cohomology of M. The aforementioned results follow immediately from this identification, albeit with hypotheses removed; in particular, one obtains a new, elementary proof of homological stability for configuration spaces. Time allowing, I will also touch on work in progress concerning cup products for configuration spaces.

Commutative Algebra Seminar, Mr. Naoki Taniguchi, Meiji University, UNIV 119

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

Sequentially Cohen-Macaulay Rees Modules

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.


Today

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.

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.


Tomorrow

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.


Next Week

Bridge to Research Seminar, Dr. Jingwei Hu, Purdue University, UNIV 203

Monday, November 3, 2014, 1:30 - 2:30 PM EST

Asymptotic-preserving Schemes for the Semiconductor Boltzmann Equation with Two-scale Collisions

Abstract: Kinetic equations usually contain small parameters such as the mean free path/time that lead to various asymptotic regimes. To deal with such multiscale phenomena, the classical numerical methods are prohibitively expensive. The asymptotic-preserving (AP) schemes are designed to preserve the asymptotic limit at the discrete level without resolving the small scales, hence are particularly efficient in transition regime. In this talk, I will use the semiconductor Boltzmann equation as a concrete example to illustrate how the AP schemes can be constructed for problems with two-scale stiff collisions.

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.

Geometry Seminar, Brian Benson, Kansas State University, MATH 731

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

Cheeger's Constant and Buser's Inequality for Higher Eigenvalues

Abstract: Buser's Inequality gives an upper bound on the first non-zero eigenvalue of the Laplacian of a closed, connected Riemannian n-manifold M in terms its Cheeger constant, denoted h(M), a quantity related to the isoperimetric problem. In his study of hyperbolic manifolds, Agol considered quantitative improvements of Buser's inequality. I will first introduce and give an overview of these ideas. I will then show how to extend these results to all higher eigenvalues. Specifically, this result is a comparison between the eigenvalues of M and the eigenvalues of an ODE eigenvalue problem (specifically, a Sturm-Liouville problem) which depends on n, the Ricci curvature of M, and h(M), the same data used in Buser's inequality. I will then compare the asymptotic growth rate of this upper bound with the growth of the higher eigenvalues established by the work of Gromov and Berard, Besson, and Gallot when the volume of M is given instead of h(M).

Department of Mathematics Colloquium, Jean Bellissard, Georgia Institute of Technology, MATH 175

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

The Topology of Tiling Spaces

Abstract: A review of few examples of tilings and their potential relevance for material science is proposed first. Then, a mathematical description is proposed using Delone sets and specializing to tilings of finite local complexity (FLC). The concept of Hull is introduced together with its topology and the corresponding C*-algebra. This leads to the so-called "Gap Labeling Theorem". The calculation of topological invariants of the Hull uses various cohomologies. Some explicit results will be provided at the end of the talk. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Topology Seminar, Rune Haugseng, Max Planck Institute, Bonn, BRNG B206

Wednesday, November 5, 2014, 1:30 - 2:30 PM EST

The higher Morita Category of $E_n$-algebras

Abstract: I will discuss a construction of a higher category of E_n-algebras and iterated bimodules, generalizing the classical bicategory of algebras and bimodules. This leads to generalizations of the Picard and Brauer groups, which have been studied in stable homotopy theory as interesting invariants of ring spectra, and should also lead to an "algebraic" construction of factorization homology as an extended topological quantum field theory.

Algebraic Geometry Seminar, Prof. Pinaki Mondal, Weizmann Institute of Science, MATH 731

Wednesday, November 5, 2014, 3:30 - 4:30 PM EST

Newton-type diagrams for singular flags and counting number of solutions of polynomials

Abstract: The Newton diagram of a polynomial or analytic function is a powerful tool for studying its behaviour near a point. We introduce a "global version" of Newton diagram of a polynomial at a subvariety in order to study behaviour of the polynomial near generic points of the subvariety. We apply this notion to the "affine Bezout-problem" of counting number of isolated solutions (in $C^n$) of a system of n polynomials and show that it is possible to arrive at the exact count by a recursive formula which involves at each step mixed volume of the faces of these Newton-type diagrams with respect to various (possibly singular) "flags of subvarieties". This in particular is a natural extension of the Bernstein-Kushnirenko-Khovanskii approach to the affine Bezout-problem.

Student Commutative Algebra Seminar, Gabriel Sosa, Purdue University, BRNG B202

Thursday, November 6, 2014, 1:30 - 2:30 PM EST

Free Resolutions and Hilbert Functions, Part 10

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


Two 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, Prof. Justin Moore, Cornell, MATH 175

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

Piecewise Projective Homeomorphisms and Amenability

Abstract: It is now well known that a nonabelian free group is not amenable - it does not admit a finitely additive translation invariant measure. A. Ol'shanskii was the first to show in 1980 that there are other obstructions to amenability. The first `easy' examples of such groups however, were only described recently by N. Monod and consist of certain piecewise fractional linear transformations of the real line. We will explore a finitely presented subgroup of Monod's group. This is joint work with Yash Lodha. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Student Commutative Algebra Seminar, Jonathan MontaƱo, Purdue University, BRNG B202

Thursday, November 13, 2014, 1:30 - 2:30 PM EST

Free Resolutions and Hilbert Functions, Part 11

Probability Seminar, Daniel Kelleher, Purdue University, UNIV 103

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


Three Weeks

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.

Function Theory Seminar, Prof. Andrei Martinez, University of Almeira, Spain, REC 121

Wednesday, November 19, 2014, 3:00 - 4:00 PM EST

Random Matrix Models, Non-intersecting random paths, and the Riemann-Hilbert Analysis

Abstract: Random matrix theory (RMT) is a very active area of research and a great source of exciting and challenging problems for specialists in many branches of analysis, spectral theory, probability and mathematical physics. The analysis of the eigenvalue distribution of many random matrix ensembles leads naturally to the concepts of determinantal point processes and to their particular case, biorthogonal ensembles, when the main object to study, the correlation kernel, can be written explicitly in terms of two sequences of mutually orthogonal functions. Another source of determinantal point processes is a class of stochastic models of particles following non-intersecting paths. In fact, the connection of these models with the RMT is very tight: the eigenvalues of the so-called Gaussian Unitary Ensemble (GUE) and the distribution of random particles performing a Brownian motion, departing and ending at the origin under condition that their paths never collide are, roughly speaking, statistically identical. A great challenge is the description of the detailed asymptotics of these processes when the size of the matrices (or the number of particles) grows infinitely large. This is needed, for instance, for verification of different forms of "universality" in the behavior of these models. One of the rapidly developing tools, based on the matrix Riemann-Hilbert characterization of the correlation kernel, is the associated non-commutative steepest descent analysis of Deift and Zhou. Without going into technical details, some ideas behind this technique will be illustrated in the case of a model of squared Bessel nonintersecting paths.

Ph.D. Thesis Defense, Katia Vogt Geisse, CL50 129

Thursday, November 20, 2014, 1:30 - 4:00 PM EST

Structured deterministic models applied to malaria and other endemic diseases Committee: Feng (Chair), Buzzard, Yip, Kribs

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


November

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

Ph.D. Thesis Defense, Vu Dinh, BRNG B247

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

PROBABILISTIC UNCERTAINTY QUANTIFICATION AND EXPERIMENT DESIGN FOR NONLINEAR MODELS: APPLICATIONS IN SYSTEMS BIOLOGY Committee: Buzzard (Chair), Rundell, Feng, Lin.

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