Date |
Speaker |
Title & Abstract |
Host |
April 2 |
Prof. Leonard Gross
(Cornell Univ.) |
Title.
Spaces of geometric flows in quantum field theory
Abstract. No matter what discoveries are made at the Large Hadron Collider in Switzerland when it begins operating next year, its a sure thing that gauge fields (i.e., connections on vector bundles) will continue to play the central role in elementary particle theory that they have for the past 40 years. The quantization of a pure gauge field amounts, informally, to the construction of a suitable measure on the configuration space of the gauge field, (i.e., the moduli space: connection forms modulo gauge transformations.) This is an infinite dimensional manifold which must be chosen large enough, in some distribution sense, to support this measure. In this talk I am going to show how one can hope to realize such nonlinear distribution spaces as spaces of geometric flows. Specifically, I will describe the state of the art for the Yang-Mills heat equation on a three manifold with boundary. |
Bruce Driver |
April 9 |
Prof. Eric Cances
(Ecole des Ponts ParisTech) |
Title.
Some mathematical aspects of Density Functional Theory
Abstract. Electronic structure calculations are commonly used to understand and predict the electronic, magnetic and optic properties of molecular systems and materials. They are also at the basis of ab initio molecular dynamics, the most reliable technique to investigate the atomic scale behavior of materials undergoing chemical reactions (oxidation, crack propagation, ...). In the first part of my talk, I will briefly review the foundations of the density functional theory for electronic structure calculations. In the second part, I will present some recent achievements in the field, as well as open problems. I will focus in particular on the mathematical modelling of defects in crystalline materials. |
Bo Li |
April 16 | |||
April 23
Special event |
Dr. Richard Libby
(Barcley Global Investors) |
Title. Metamathematical Finance: How Logical Paradox Helped Decipher the Credit Crisis | Sam Buss & Jeff Remmel |
April 30 | |||
May 7 |
Prof. Dan Jeske
(UC Riverside) |
Title.
Statistical Inference Procedures for Clock Synchronization
Abstract. A well known method of estimating the oset between two clocks in a data communication network involves exchanging timing messages between the clocks. Dierent distributions of the transmission delays in the two directions associated with the exchanged messages cause the estimator to be biased. Bootstrap bias- correction improves the estimator with respect to mean squared error. Studies on network trac show that no single distribution adequately characterizes delays, and thus robustness of an estimator to dierent distribution assumptions is a critical property for an estimator to have. For common distribution assumptions for the transmission delays, the bias-corrected estimator has smaller mean squared error than the uncorrected estimator. Recent studies of Internet trac show that delay distributions can be heavy-tailed. Evaluation of bootstrap bias corrected estimators in the context of heavy tailed network delays leads to some surprising results. Condence interval procedures for clock oset and a brief discussion of estimating the dierence in rates between two clocks will also be given. |
Lily Xu |
May 14 |
Prof. Lizhen Ji
(Univ. Michigan) |
Title.
Coarse Schottky problem and equivariant cell decomposition of Teichmuller space
Abstract. In this talk, I will explain some similar results and interaction between locally symmetric spaces and moduli spaces of Riemann surfaces. For example, let M_g be the moduli space of Riemann of genus g, and A_g be the moduli space of principally polarized abelian varieties of dimension g, i.e., the quotient of the Siegel upper space by Sp(2g, Z). Then there is a Jacobian map J: M_g \to A_g, by associating to each Riemann surface its Jacobian. The celebrated Schottky problem is to characterize the image J(M_g). Buser and Sarnak viwed A_g as a complete metric space and showed that J(M_g) lies in a very small neighborhood of the boundary of A_g as g goes to infinity. Motivated by this, Farb formulated the coarse Schottky problem: determine the image of J(M_g) in the asymptotic cone (or tangent space at infinity) C_\infty(A_g) of A_g, as defined by Gromov in large scale geometry. In a joint work with Enrico Leuzinger, we showed that J(M_g) is c-dense in A_g for some constant c=c(g) and hence its image in the asymptotic cone C_\infty(A_g) is equal to the whole cone. Another example is that the symmetric space SL(n, R)/SO(n) admits several important equivariant cell decompositions with respect to the arithmetic group SL(n, Z) and hence a cell decomposition of the locally symmetric space SL(n, Z)\SL(n, R)/SO(n). One such decomposition comes from the Minkowski reduction of quadratic forms (or marked lattices). We generalize the Minkowski reduction to marked hyperbolic Riemann surfaces and obtain a solution to a folklore problem: an intrinsic equivariant cell decomposition of the Teichmuller space T_g with respect to the mapping class groups Mod_g, which induces a cell decomposition of the moduli space M_g. If time permits, I will also discuss other results on similarities between the two classes of spaces and groups. |
Lei Ni |
May 21 | |||
May 28 | |||
June 4 |
Date |
Speaker |
Title & Abstract |
Host |
Jan. 8 |
Prof. Enno Lenzmann
(MIT) |
Title.
Nonlinear Evolution Equations and Gravitational Collapse
Abstract. In this talk, I will discuss a novel class of nonlinear dispersive equations, which describe the dynamical evolution of self-gravitating relativistic matter. In fact, the analysis of these model equations will give a mathematical vindication of Chan- drasekhars acclaimed physical theory of gravitational collapse. In particular, I will present results concerning the well-posedness of the initial-value problem, the singularity formation of solutions (blowup), as well as solitary wave solutions and their stability. Time permitting, I will also discuss some recent and ongoing work. This is partly joint work with Jurg Frohlich (ETH Zurich), Joachim Krieger (UPenn), Pierre Raphael (Toulouse) and Rupert Frank (Princeton). |
Peter Ebenfelt |
Jan. 15 |
Prof. Gil Ariel
(Univ. of Texas, Austin) |
Title.
Modeling and computation with multiple time scales
Abstract. Many interesting examples of dynamical systems involve several well separated time scales. In many applications, for example in molecular dynamics simulations, one is only interested in the slow aspects of dynamics, or on the long-time behavior of the solutions. However, when the different scales are coupled, small or fast perturbations can build up to an observable effect that cannot be neglected. In this talk I will discuss several types of models and address some of the analytic and computational difficulties common to many systems evolving on multiple time scales. We give a complete characterization of the slow aspects of the dynamics and devise efficient computational algorithms that take advantage of the scale separation. It is shown that the computational cost is practically independent of the spectral gap. Among the systems studied are highly oscillatory ODEs and a benchmark model of elastic spheres with disparate masses. |
Li-Tien Cheng
and Bo Li |
11:00 am-12:00 noon,
Jan. 16. AP&M 6402 (Special time) |
Prof. Ronny Hadani
(Univ. of Chicago) |
Title.
Group representation patterns in digital signal processing I
Abstract. In my colloquium talk, I will explain how various fundamental structures from group representation theory appear naturally in the context of discrete harmonic analysis and can be applied to solve concrete problems from digital signal processing. I will begin by describing our solution to the problem of finding a canonical orthonormal basis of eigenfunctions of the discrete Fourier transform (DFT). Then I will explain how to generalize the construction to obtain a larger collection of functions that we call "The oscillator dictionary". Functions in the oscillator dictionary admit many interesting properties, in particular, I will explain two of these properties which arise in the context of problems of current interest in communication theory. This is joint work with Shamgar Gurevich (Berkeley) and Nir Sochen (Tel Aviv). There is a sequel to my colloquium talk, which will be slightly more specialized and will take place during the algebraic geometry seminar. Here, my main objective is to introduce the geometric Weil representation which is an algebra-geometric ($ \ell $-adic Weil sheaf) counterpart of the Weil representation. Then, I will explain how the geometric Weil representation is used to prove to main result stated in my colloquium talk. In the course, I will explain Grothendieck's geometrization procedure by which sets are replaced by algebraic varieties and functions by sheaf theoretic objects. |
Wee Teck Gan |
Jan. 22 |
Prof. J. Milne Anderson
(Univ. College, London Univ.) |
Title. The Logrithmic Derivative of a Polynomial
Abstract. If Q_N(z) is a polynomial of degree N and P > 0, then estimates for the size of the set where the logrithmic derivative Q'(z)/Q(z) has modulus greater than P are given in terms of P and N. These estimates are shown to be essentially the best possible. This is joint work with V. Ya. Eiderman. |
James Bunch |
Tuesday, Jan. 27
(special day) |
Prof. Todd Kemp
(MIT) |
Title: Resolvents of $R$-Diagonal Operators | Bruce Driver |
Jan. 29 |
Prof. Sergiu Klainerman
(Princeton Univ.) |
Title.
Why Black Holes are exciting mathematical objects
Abstract. I will talk about some of the main open problems in the theory of Black Holes. I will talk in particular on recent results concerning uniqueness and stability. |
Hans Lindblad |
Feb. 5 |
Prof. Jozsef Balogh
(UIUC) |
Title: Recent Progress in Bootstrap Percolation | Fan Chung Graham |
Feb. 12 |
Kiran Kedlaya
(MIT) |
Title: Formal classification of flat connections | Cristian Popescu |
Feb. 19 |
Prof. Michael P. Friedlander
(Univ. of British Columbia) |
Title: Algorithms for large-scale sparse reconstruction
Abstract. Many signal-processing applications seek to approximate a signal as a superposition of only a few elementary atoms drawn from a large collection. This is known as sparse reconstruction. The theory of compressed sensing allows us to pose sparse reconstruction problems as structured convex optimization problems. I will discuss the role of duality in revealing some unexpected and useful properties of these problems, and will show how they lead to practical, large-scale algorithms. I will also describe some applications of the resulting algorithms. |
Philip Gill |
Feb. 26 |
Prof. Burkhard Wilking
(Univ. Muenster) |
Title.
Ricci flow in high dimensions
Abstract. We consider a very simple curvature condition: Given constant $c$ and a dimension $n$ we say that a manifold $(M,g)$ satisfies the condition (c,n) if the scalar curvature is bounded below by c times the norm of the Weyl curvature. We show that in each large even dimensions there is precisely one constant $c^2=2(n-1)(n-2)$ such that this condition is invariant under the Ricci flow. The condition behaves very similar to scalar curvature under conformal transformations and we indicate how this can be utilized to get a large source of examples. Finally we speculate what kind singularities should develop under the Ricci flow. |
Lei Ni |
Friday, Feb. 27
4:00 pm. AP&M 6402 |
Prof. Rene Schoof
(Univ. di Roma "Tor Vergata") |
Title. The analogy between number fields and algebraic curves: Arakelov meets Tate | Cristian Popescu |
March 5
Charles Lee Powell Distinguished Lecture. |
Professor Claudio Procesi | Title. The Spirit of Algebra |
Efim Zelmanov
and Lance Small |
March 12 | |||
March 19 |
Prof. Paul Tseng
(Univ. Washington) |
Title.
On SDP and ESDP Relaxation for Sensor Network Localization
Abstract. Recently Wang, Zheng, Boyd, and Ye proposed a further convex relaxation of the SDP relaxation for the sensor network localization problem, which they called edge-based SDP (ESDP). The ESDP is easier to solve than the SDP and, in simulation, yields solution about as accurate as the SDP relaxation. We show that, when the distance measurements are exact, we can determine which sensors are correctly positioned in the ESDP solution by checking if their individual traces are zero. On the other hand, we show that, when the distance measurements are inexact, this check is unreliable for both ESDP and SDP solutions. We then propose a robust version of ESDP relaxation for which small individual trace is a reliable check of sensor position accuracy. Moreover, the position error for such a sensor is in the order of the square root of its trace. Lastly, we propose a coordinate gradient descent method, using log-barrier penalty, to solve ESDP. This method is more efficient than interior-point method for solving SDP or ESDP and is implementable in a distributed manner. (This is joint work with Ting Kei Pong.) |
Jiawang Nie and
Bill Henton |
Date |
Speaker |
Title & Abstract |
Host |
Oct. 2 |
Prof. Shandy Hauk
(Univ. of Northern Colorado) Biography. Shandy Hauk, Associate Professor of Mathematics, University of Northern Colorado. Graduated cum laude with a B.A. in theater and film and completed a PhD in dynamical systems/PDEs at the University of California, Irvine; had a two-year NSF post-doc in collegiate mathematics education at Arizona State University, and is currently PI for the FIPSE-funded project, Video Cases for Novice College Mathematics Instructor Development. |
Title.
Developping Video Cases of College Math Instruction
Abstract. A national cooperative of universities is developing a collection of videos about college math instruction as a resource for helping novice instructors to build their teaching skills. Currently midway through the 3-year project, initial draft video and text materials are ready for review. The purpose of the presentation is to share some of these materials, discuss their potential uses, and gather comments on how to shape and re-develop them. Attendance by all department members, from those very experienced in teaching mathematics to those with a few days experience to those with intentions to teach in the future, is heartily encouraged. Video clips come from advanced as well as introductory undergraduate mathematics teaching and learning situations. |
John Eggers |
Oct. 9 | |||
Oct. 16 | |||
Oct. 23 | |||
Oct. 30 |
Prof. Jichun Li
(Univ. of Nevada & IPAM) |
Title.
Mathematical and Numerical Study of Maxwell's Equations in Negative Index Material
Abstract. Since 2000, there has been a growing interest in the study of negative index metamaterials across many disciplinaries. In this talk, I'll first derive the Maxwell's equations resulting from negative index metamaterials. Then I'll discuss some time-domain mixed finite elements developed for solving these equations, followed by succinct error estimates. Finally, some numerical results and open issues will be presented. |
Randy Bank |
Nov. 6 |
Prof. Wei Biao Wu
(Univ. of Chicago) |
Title. Simultaneous Confidence Bands in Time Series
Abstract. I will talk about statistical inference of trends in mean non-stationary models, and mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The Simultaneous confidence bands are useful for model specification problems in nonlinear time series. The results are applied to environmental and financial time series. |
Dimitris Politis |
Nov. 13 |
Prof. Michael Hill
(Univ. of Virginia) |
Title. Asymptotics in Homotopy Theory | Nitu Kitchloo |
Nov. 20 |
Prof. Herbert Heyer
(Univ. Tuebingen, Germany) |
Title.
Infinitesimal Arrays of Group-Valued Random Variables
Abstract. The talk is concerned with the limiting behavior of row sums of infinitesimal arrays of independent random variables taking values in a locally compact Abelian group. By a theorem of K.R. Parthasarathy, any possible limit of such row sums is weakly infinite divisible and as such a convolution product of an idempotent measure, a Dirac measure, a Gaussian measure and a generalized Poisson measure. Following the classical lines sufficient conditions in terms of the characteristics of the above factors are established in order to obtain convergence of the row sums. Specialization to symmetric arrays and to the torus group illustrates the slightly technical results. |
Patrick Fitzsimmons |
Nov. 27 | No colloquium. Thanksgiving Holiday. | ||
Dec. 2, Tuesday
(special day) |
Prof. Vera Mikyoung Hur
(MIT) |
Title. Dispersive Properties of the Surface Water-Wave Problem
Abstract. I will speak on the dispersive character of waves on the interface between vacuum and water under the influence of gravity and surface tension. I will begin by giving a preciese account of the formulation of the surface water-wave problem and discusion of its distinct features. They include the dispersion relation, its severe nonlinearity, traveling waves and the Hamiltonian structure. I will describe the recent work of Hans Christianson, Gigliola Staffilani and myself on the local smoothing eect of 1/4 derivative for the fully nonlinear problem under surface tension with some detail of the proof. If time permits, I will explore some oen questions regarding long-time behavior and stability. |
Peter Ebenfelt |
2:00-3:00, Dec. 4
(Special time) |
Prof. Pablo Parrilo
(MIT) |
Title. Computing Equilibria of Continuous Games | Bill Helton |
Dec. 4 |
Prof. Jesper Grodal
(Univ. of Copenhagen) |
Title.
The Steenrod Problem of Realizing Polynomial Cohomology Rings.
Abstract. In 1960 Norman Steenrod asked which graded polynomial rings occur as the cohomology ring of a space. Progress on this question has been made throughout the last fifty years, and the final step in its solution was recently given by K. Andersen and myself. My talk will be a survey of this problem and its solution. |
Nitu Kitchloo |