Department of Mathematics

Calendar


Next Week

Numerical Linear Algebra Seminar, Kyle Kloster, Purdue University, UNIV 017

Monday, March 2, 2015, 2:30 - 3:30 PM EST

Matrix Calculus, and Matrix Functions

Abstract: Motivated by some uses of matrix derivatives in optimization, we will discuss the venerable product and power rules in the context of matrices. We'll also glance at how matrices interact with functions (like the inverse, log, and the exponential) and integrals.

Computational & Applied Mathematics Seminar, Professor Jingchen Liu, Columbia University, REC 108

Monday, March 2, 2015, 3:30 - 4:30 PM EST

Extreme Analysis of Gaussian Random Fields

Abstract: Gaussian random fields are employed to model spatially varying errors in various stochastic systems. In this talk, I present several recent results of the extreme analysis for such systems. In particular, the topic covers various nonlinear functionals of Gaussian random fields including the supremum norm, integrals of exponential functions, and differential equations admitting random coefficients driven by Gaussian random fields. We present the asymptotic approximations of certain tail events, their practical interpretations, and intuitions behind the technical developments. The results have applications to material science, financial risk analysis, statistical analysis of point processes, etc.

Geometry Seminar, Neha Gupta, UIUC, MATH 731

Monday, March 2, 2015, 3:30 - 4:30 PM EST

The Primitivity Index Function for a Free Group, and Untangling Closed Curves on Surfaces

Abstract: A theorem of Scott shows that any closed geodesic on a surface lifts to an embedded loop in a finite cover. Our motivation is to find a worst-case lower bound for the degree of this cover, in terms of the length of the original loop. Using probabilistic methods we establish lower bounds for certain analogous functions, like the Primitivity Index Function and the Simplicity Index Function, in a free group. These lower bounds, when applied in a suitable way to the surface case, give us some lower bounds for our motivating question. This is joint work with Ilya Kapovich.

Department of Mathematics Colloquium, Professor Guowei Wei, MSU, MATH 175

Tuesday, March 3, 2015, 4:30 - 5:30 PM EST

Mathematical Modeling and Simulation of Biomolecules

Abstract: A major feature of biological sciences in the 21st Century is their transition from phenomenological and descriptive disciplines to quantitative and predictive ones. However, the emergence of complexity in self-organizing biological systems poses fabulous challenges to their quantitative description because of the excessively high dimensionality. A crucial question is how to reduce the number of degrees of freedom, while preserving the fundamental physics in complex biological systems. We discuss a multiscale and multiphysics paradigm for biomolecular systems. We describe macromolecules, such as proteins, DNAs, ion channels, membranes, HIV viruses, etc., by a number of approaches, including macroscopic electrostatics and elasticity and/or microscopic molecular mechanics and quantum mechanics; while treating the aqueous environment as a dielectric continuum or electrolytic fluids. We use differential geometry theory of surfaces to couple various microscopic and macroscopic domains on an equal footing. Based on the variational principle, we derive the coupled Poisson-Boltzmann, Nernst-Planck, Kohn-Sham, Laplace-Beltrami, Newton, elasticity and/or Navier-Stokes equations for biomolecular structure, function, dynamics and transport. Numerical methods have been developed to solve these equations to the second order accuracy in the biomolecular context. We will also discuss geometric, topological and graph theory strategies for dealing with big data from biomolecules. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Algebraic Geometry Seminar, Profs. Robin Walters and Asilata Bapat, University of Chicago, MATH 731

Wednesday, March 4, 2015, 3:30 - 4:30 PM EST

The Bernstein-Sato polynomial of the Vandermonde determinant and the Strong Monodromy Conjecture

Abstract: The Bernstein-Sato polynomial, or b-function, is an important invariant in singularity theory, which is difficult to compute in general. We describe a few different results towards computing the b-function of the Vandermonde determinant \xi . In 1989, Eric Opdam computed the b-function of a related polynomial, and we use his result to produce a lower bound for the b-function of \xi . We use this lower bound to prove a conjecture of Budur, Mustaţă, and Teitler for the case of finite Coxeter hyperplane arrangements, proving the Strong Monodromy Conjecture in this case.In our second result, we use duality of some D-modules to show that the roots of this b-function of $\xi$ are symmetric about -1. Finally, we use results about jumping coefficients together with Kashiwara's proof that the roots of a b-function are rational in order to prove an upper bound for the b-function of $\xi$ and give a conjectured formula.

Spectral and Scattering Theory Seminar, Plamen Stefanov, Purdue University, REC 226

Wednesday, March 4, 2015, 3:30 - 4:30 PM EST

The Geodesic X-ray Tansform with Conjugate Points

Commutative Algebra Seminar, Matthew Toeniskoetter, Purdue University, MATH 215

Wednesday, March 4, 2015, 4:30 - 5:30 PM EST

Ideal Theory of Infinite Directed Unions of Local Quadratic Transforms

Abstract: We examine ideal-theoretic properties of the directed union S of an infinite sequence of local quadratic transforms of a regular local ring. We associate a boundary valuation ring V to the sequence and examine its relation to S and to the complete integral closure of S. We define an associated invariant tau and describe how tau determines the structure of V and S, namely the rank of V, whether S is archimedean, and whether S is completely integrally closed.

Arithmetic and Topology Seminar, Artur Jackson, Purdue University, REC 108

Wednesday, March 4, 2015, 4:30 - 6:30 PM EST

Arakelov in Higher Dimensions - Intro: Descent and Durov's Category

Abstract: I will cover (without proof) aspects of étale descent of bundle data on schemes. We will see how compact subgroups of GL(n,Q_p) naturally arise as descent data and relate this reason why Hermitian metrics on Arakelov line bundles should be seen as the natural analogue of gluing data `at infinity'.

Probability Seminar, Ju-Yi Yen, University of Cincinnati, REC 308

Thursday, March 5, 2015, 3:30 - 4:30 PM EST

TBA

PDE Seminar, Xin Yang Lu, BRNG B261

Thursday, March 5, 2015, 3:30 - 4:30 PM EST

Grain Boundary Characteristic Distribution

Abstract: Many useful materials are composed of myriads of monocrystalline grain cells separated by grain boundaries. One model for evolution of such systems, proposed by Mullins in the 1950s, is the curvature driven evolution, which is highly non-local in nature. Predicting the evolution of such systems is desirable. The theory of Grain Boundary Characteristic Distribution (GBCD) was proposed by Kinderlehrer et al. as predictive theory for grain network evolutions. The GBCD is a relative distribution of certain quantities, generally difficult to identify, whose evolution follows a predictable pattern. The mathematical formulation of the theory of GBCD heavily relies on optimal transport theory. In this talk we present a rigorous derivation of the GBCD theory in 2D.

Topology Seminar, Cary Malkiewich, UIUC, UNIV 319

Thursday, March 5, 2015, 4:00 - 5:00 PM EST

Coassembly in Algebraic K-theory

Abstract: The coassembly map allows us to approximate any contravariant homotopy-invariant functor by an excisive functor, i.e. one that behaves like a cohomology theory. We'll apply this construction to Waldhausen's algebraic K-theory of spaces, and its corresponding THH functor. The results are somewhat surprising: a certain dual form of the A-theory Novikov conjecture is false, but when the space in question is the classifying space BG of a finite p-group, coassembly on THH is split surjective after p-completion. Even better, we can show that thecoassembly map links up with the more familiar assembly map to produce the equivariant norm. As a result, we get some splitting theorems after K(n)-localization, and a surprising connection between the Whitehead group and Tate cohomology.

Secret Seminar, Artur Jackson, Purdue University, MATH 731

Friday, March 6, 2015, 11:30 - 1:30 PM EST

Topological Methods in Algebra and Arithmetic

Abstract: This will be the first of n talks on the usage of simplicial methods and homotopy theory in completely `non-topological' situations. I will touch lightly on homotopy categories, model categories and simplicial sets for some background. Concrete applications will arise in survey fashion via Galois/étale descent, cotangent complex, and étale homotopy groups.

CCAM Lunch Seminar, Professor R. Edwin García, Purdue University, REC 226

Friday, March 6, 2015, 11:30 - 12:30 PM EST

Modeling and Simulation of Porous Lithium-Ion Batteries

Abstract: In modern high energy density lithium-ion battery electrodes, the underlying topology controls the macroscopic charge, total delivered energy, and instantaneous power of the cell, particularly at high electronic current and power densities. In this presentation, we report on progress towards the development of a combined numerical+analytical framework to describe the effect of spatial distributions and morphologies of battery particle materials on the processing-induced macroscopic and position dependent performance. The state-of-the-art, theoretical and numerical limits of the field are described. Here, by proposing variational principles and spatially resolving the electrochemical fields, the effect of particle size polydispersity on the voltage behavior is analyzed. We detail such effects in structures of controlled processing and materials parameters on the macroscopic response for existing and emerging energy storage devices. The framework presented herein enables to establish relations that combine geometrical parameters such as tortuosity and reactivity of the individual (starting) components.

Basic Notions Seminar, Christopher Leininger, BRNG 1245

Friday, March 6, 2015, 3:30 - 4:30 PM EST

Surface Homeomorphisms

Abstract: Surfaces are central objects in many important areas of mathematics. In this talk, I will discuss homeomorphisms of surfaces. As always, there will be FREE PIZZA at the seminar.


Two Weeks

Computational & Applied Mathematics Seminar, Professor Yue Yu, Lehigh University, REC 108

Monday, March 9, 2015, 3:30 - 4:30 PM EDT

Stabilized Numerical Methods for Fluid-Structure Interactions: Analysis and Simulations

Abstract: There are two approaches in formulating the discrete systems in simulating multiphysics prob-lems: (1) the monolithic approach, where the unknowns of each domain are lumped together into one large linear system; (2) the partitioned approach, where each domain with different physics is treated separately hence requiring proper interface transmission conditions. The former is efficient for small problems but does not scale up to realistic sizes, whereas the latter suffers from numerical stability issues. Here we consider the partitioned approach and we develop new stabilized algorithms for fluid-structure interaction (FSI) problems. In particular, in FSI problems (e.g. blood flow in arterial networks) where the mass ratio between the structure and the fluid is relatively small, the partitioned approach gives rise to the so-called added-mass effect which renders the simulation unstable. I will present two new numerical methods to handle this added-mass effect: (1) by introducing fictitious pressure (acceleration) terms in the fluid (structure) equations to balance the added-mass effect, which stabilizes the coupled formulation and reduces drastically the number of subiterations in each time step; (2) by relaxing the exact no-slip boundary condition and introducing proper penalty terms on the fluid-structure interface, which enables the possibility of stable explicit coupling procedure. For both methods we obtained the optimal parameters via theoretical analysis, and numerically verified that stability can be achieved irrespective of the fluid-structure mass ratio. Based on these new methods, three-dimensional large scale simulations were obtained for patient-specific cerebral aneurysms and for long flexible risers used in offshore industry.

Department of Mathematics Colloquium, Daniel Allcock, University of Texas, MATH 175

Tuesday, March 10, 2015, 4:30 - 5:30 PM EDT

TBA

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

Probability Seminar, Malva Asaad, University of Connecticut, REC 308

Thursday, March 12, 2015, 3:30 - 4:30 PM EDT

TBA

Special Mathematics Colloquium, Francis Su, MAA, LWSN 1142

Thursday, March 12, 2015, 4:30 - 5:30 PM EDT


March

Computational & Applied Mathematics Seminar, Professor John Lowengrub, University of California at Irvine, REC 108

Monday, March 23, 2015, 3:30 - 4:30 PM EDT

TBA

Department of Mathematics Colloquium, Prof. Grzegorz Banaszak, Adam Mickiewicz University, Poznan, MATH 175

Tuesday, March 24, 2015, 4:30 - 5:30 PM EDT

An Analogue of Weil's Program for the Riemann Zeta Function and Dirichlet L-functions

Abstract: In the 1940s A. Weil used the intersection theory on surfaces to prove the Riemann hypothesis for curves over finite fields. In our work we introduce axioms of (what we call) abstract intersection theory for an operator $A : H \rightarrow H$ in the Hilbert space $H$. These axioms are analogous to the properties of the Frobenius morphism used in Weil's theory. In our work we investigate a special class of operators $A$ with spectrum, which is only the point spectrum, located in the critical strip $0 < Re s < 1$. We say that $A$ satisfies the Riemann Hypothesis if its spectrum is on the critical line $Re s = 1/2$. We constructed two special models of the abstract intersection theory: the GNS (Gelfand-Naimark-Segal) model and the standard model. We proved that the axioms of the standard model for $A$ are satisfied if and only if the Riemann hypothesis for $A$ is true and the semi-simplicity property for $A$ holds. Similar results can be proven for the GNS model. These results can be applied to the investigation of nontrivial zeros of the Riemann zeta function and Dirichlet L-functions. Namely for every Dirichlet character, using the method of automorphic scattering, Yoichi Uetake constructed an operator $A$ with spectrum equal to the set of nontrivial zeros (counting with multiplicities) of the corresponding Dirichlet L-function. In particular, for the trivial character, this construction concerns the Riemann zeta function. As a consequence we can show that a Dirichlet $L$-function (including the Riemann zeta-function) satisfies the Riemann hypothesis and its all nontrivial zeros are simple if and only if the axioms of the corresponding standard or GNS model are satisfied. This is joint work with Yoichi Uetake. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, Rodrigo Bañuelos, Purdue University, REC 308

Thursday, March 26, 2015, 3:30 - 4:30 PM EDT

TBA

CCAM Lunch Seminar, Alex Konomi, University of Cincinnati, REC 226

Friday, March 27, 2015, 11:30 - 12:30 PM EDT

Bayesian Treed Multivariate Gaussian Process

Abstract: Computer experiments are widely used in scientific research to study and predict the behavior of complex systems, which often have responses consisting of a set of nonstationary outputs. The computational cost of simulations at high resolution often is expensive and impractical for parametric studies at different input values. In this presentation, I will present the Bayesian treed multivariate Gaussian process, a recent extension of the Bayesian treed Gaussian process to model the cross-covariance function and the nonstationarity of the multivariate output. We facilitate the computational complexity of the Markov chain Monte Carlo sampler by choosing two different covariance functions and prior distributions.

Computational & Applied Mathematics Seminar, Professor Oliver Goubet, University of Picardie Jules Verne, REC 108

Monday, March 30, 2015, 3:30 - 4:30 PM EDT

TBA

Department of Mathematics Colloquium, Prof. Robert Hardt, Rice University, MATH 175

Tuesday, March 31, 2015, 4:30 - 5:30 PM EDT

TBA

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


April

Ph.D. Thesis Defense, Luis Acuna Valverde, BRNG 1254

Thursday, April 2, 2015, 1:30 - 3:00 PM EDT

HEAT KERNELS, SCHRODINGER OPERATORS AND SMALL TIME ASYMPTOTICS Committee: Banuelos (Chair), Sa Barreto, B.Davis, Baudoin

Probability Seminar, Shuwen Lou, University of Illinois at Chicago, REC 308

Thursday, April 2, 2015, 3:30 - 4:30 PM EDT

TBA

Computational & Applied Mathematics Seminar, Professor Zhiliang Xu, University of Notre Dame, REC 108

Monday, April 6, 2015, 3:30 - 4:30 PM EDT

TBA

Department of Mathematics Colloquium, Andrew Pollington, NSF, MATH 175

Tuesday, April 7, 2015, 4:30 - 5:30 PM EDT

TBA

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

Probability Seminar, Rohini Kumar, Wayne State University, REC 308

Thursday, April 9, 2015, 3:30 - 4:30 PM EDT

TBA

Ph.D. Thesis Defense, Andrew Homan, REC 309

Friday, April 10, 2015, 3:00 - 4:30 PM EDT

Applications of Microlocal Analysis to Some Hyperbolic Inverse Problems Committee: Stefanov (Chair), Sa Barreto, Datchev, and Li

Ph.D. Thesis Defense, Christina Alvey, BRNG B206

Monday, April 13, 2015, 9:30 - 11:00 AM EDT

Investigating Synergy: Mathematical Models for the Coupled Dynamics of HIV and HSV-2 and Other Endemic Diseases Committee: Feng (Chair), Buzzard, Yip, and John Glasser.

Computational & Applied Mathematics Seminar, Dr. John Glasser, CDC, REC 108

Monday, April 13, 2015, 3:30 - 4:30 PM EDT

TBA

Department of Mathematics Colloquium, Feng Luo, Rutgers, MATH 175

Tuesday, April 14, 2015, 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, Professor Pengtao Yue, Virginia Tech, REC 108

Monday, April 20, 2015, 3:30 - 4:30 PM EDT

TBA

Department of Mathematics Colloquium, Dihua Jiang, University of Minnesota, MATH 175

Tuesday, April 21, 2015, 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. Andrew Hill, Emory University, CDC, REC 108

Friday, April 24, 2015, 1:30 - 2:30 PM EDT

TBA

Computational & Applied Mathematics Seminar, Professor Jianfeng Lu, Duke University, REC 108

Monday, April 27, 2015, 3:30 - 4:30 PM EDT

TBA


May

Computational & Applied Mathematics Seminar, Professor Bingyu Zhang, University of Cincinnati, REC 108

Monday, May 4, 2015, 3:30 - 4:30 PM EDT

TBA


September

Graduate Student Invited Colloquium, Bernd Sturmfels, University of California, MATH 175

Tuesday, September 22, 2015, 4:30 - 5:30 PM EDT