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MARCH 2008 |
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Department Colloquium |
Topic: |
The harmonic mean curvature flow of a 2-dimensional hypersurface |
Presenter: |
Natasa Sesum, Columbia University |
Date: |
Wednesday, March 5, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The harmonic mean curvature flow is the flow that moves a hypersurface embedded in R^3 by the speed given by a ratio of the Gauss and the mean curvature of the given surface in the direction of its normal. It is a fully nonlinear, weakly parabolic equation, degenerate at the points at which our hypersurface changes its convexity and fast diffusion when the mean curvature tends to zero. We prove a short time existence of such a flow in a nonconvex case. We also prove that if the mean curvature does not go to zero, the flow becomes strictly convex at some time and shrinks to a round point. This is an example of a curvature flow in higher dimension (besides the curve shortening flow in a plane which has been known for a long time) that exhibits a nice shrinking property in a spherical manner in a finite time, even if we start evolving nonconvex hypersurfaces. In that sense this flow behaves better that the mean curvature flow that in the most nonconvex cases develops singularities before shrinking to a point. |
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Graduate Student Seminar |
Topic: |
Prime Splitting Laws |
Presenter: |
Stefan Patrikis, Princeton University |
Date: |
Thursday, March 6, 2008, Time: 12:30 p.m., Location: Fine Hall 314 |
Abstract: |
Algebraic number theory seeks to understand and somehow classify all Galois extensions of a number field K. One perspective on this basic classification problem emerges from the Cebotarev density theorem, which implies that such extensions L/K are determined by the primes of K that split completely in L. When L/K is abelian, associating such a 'splitting law' is classical, and after defining the relevant terms I will illustrate this theory with some representative examples. The corresponding question for non-abelian extensions remains a great mystery, however, but I hope to use this to motivate a very concrete introduction to some of the modern machinery of number theory and the Langlands program. No knowledge of number theory will be assumed. |
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Discrete Mathematics Seminar |
Topic: |
Star-coloring planar graphs with high girth |
Presenter: |
Dan Cranston, DIMACS and Bell Labs |
Date: |
Thursday, March 6, 2008, Time: 2:15 p.m., Location: Fine Hall 314 |
Abstract: |
A star-coloring is a proper vertex-coloring such that the graph induced by the union of any 2 color classes is a star-forest. Equivalently, it is a proper vertex-coloring with no 2-colored P_4. Star-coloring has been studied extensively, even for planar graphs. However, little is known about improved upper bounds for planar graphs with large girth. We prove that a planar graph with girth at least 13 has star-chromatic number at most 4. We use the discharging method to prove a structural lemma about planar graphs with girth at least 13. It is then straightforward to construct the 4-star-coloring using this lemma. This is joint work with Craig Timmons and Andre Kundgen of Cal State, San Marcos. |
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Geometry, Representation Theory, and Moduli Seminar ***Please note special time, date, and location |
Topic: |
Rational curves, relative maps, and the vertex group |
Presenter: |
Rahul Pandharipande, Princeton University |
Date: |
Thursday, March 6, 2008, Time: 2:30 p.m., Location: Fine Hall 1201 |
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Princeton University and Institute for Advanced Study Number Theory |
Topic: |
Counting rational points on a cubic surface |
Presenter: |
Ritabrata Munshi, Rutgers University |
Date: |
Thursday, March 6, 2008, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
A conjecture of Manin predicts precise asymptotic for the density of rational points on del Pezzo surfaces. This has been satisfactorily settled for del Pezzo surfaces of higher degree. But for lower degree not much is known. At present, most research in the field is concentrated around del Pezzo surfaces of degree four (intersections of two quadratics in $\mathbb P4$), and degree three (cubic surfaces). Although many special cases of singular cubic and quartic surfaces have been successfully dealt with, it is generally believed that the problem is much harder for smooth surfaces and for surfaces with `mild' singularities. In this talk I will describe a joint work with Iwaniec, where we use sieves and methods from analytic number theory to prove an almost sharp lower bound for the density of rational points in case of a family of cubic surfaces. |
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Topology Seminar |
Topic: |
Real Projective Structures and Non-standard analysis |
Presenter: |
Daryl Cooper, UCSB |
Date: |
Thursday, March 6, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We investigate the analog of the Thurston boundary of Teichmuller space in the context of convex real projective structures on closed manifolds. In particular we give a new interpretation of measured laminations in terms of non-standard hyperbolic structures over the hyper-reals. |
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Symplectic Geometry Seminar |
Topic: |
Knotted surfaces in 4-manifolds |
Presenter: |
Tom Mark, University of Virginia |
Date: |
Friday, March 7, 2008, Time: 2:00 p.m., Location: Fine Hall 314 |
Abstract: |
We revisit Fintushel and Stern's ``rim surgery'' construction from the point of view of Heegaard Floer theory. Our main result is that given a symplectic surface S with simply-connected complement in a symplectic 4-manifold, there exist infinitely many smoothly non-isotopic surfaces representing the topological isotopy class of S, so long as the self-intersection of the surface in question is not ``too negative.'' This extends the result of Fintushel and Stern, who were obliged to assume that the self-intersection was at least 0. The proof makes use of a result giving the behavior of relative Ozsvath-Szabo invariants under Fintushel-Stern knot surgery, together with a calculation of the twisted Floer homology of circle bundles with ``large'' Euler number over surfaces. We will give an outline of the proof, in particular attempt to indicate why the restriction on the self-intersection of S arises. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
No mass drop for mean curvature flow of mean convex hypersurfaces |
Presenter: |
Felix Schulze, Stanford University |
Date: |
Friday, March 7, 2008, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
A possible evolution of a compact hypersurface in R^{n+1} by mean curvature past singularities is defined via the level set flow. In the case that the initial hypersurface has positive mean curvature, we show that the Brakke flow associated to the level set flow is actually a Brakke flow with equality. We obtain as a consequence that no mass drop can occur along such a flow. As a further application of the techniques used above we give a new variational formulation for mean curvature flow of mean convex hypersurfaces. |
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Group Actions Seminar |
Topic: |
Translates of horospherical measures and counting problems |
Presenter: |
Alireza Salehi Golsefidy, Princeton University |
Date: |
Monday, March 10, 2008, Time: 12:15 p.m., Location: Fine Hall 224 |
Abstract: |
(Joint with A. Mohammadi) In this talk, I will briefly explain the relation between some of the counting problems, mixing, and ergodic theory. The counting problems might be of geometric or number theoretic nature. For instance consider V=G/H a homogeneous variety, and one would like to study the integer or rational points on V. Eskin, Mozes, and Shah attacked this problem via unipotents flows. However they had to assume that H is maximal and reductive (in particular not inside any parabolic subgroup of G.) I will explain an ergodic theoretic approach toward such problem for a flag variety.
For a geometric example, consider SL(n,Z)-translates of a horosphere in the symmetric space of SL(n,R). Question is how many of them intersect a ball of radius R. In fact, Eskin and McMullen answered this question for n=2, using mixing. I will explain why mixing is not enough and how one can get such a result for any n.
I will show that the main ingredient for both of the mentioned questions is understanding the limits of translates of horospherical measures, i.e. the probability measure supported on U SL(n,Z)/SL(n,Z), where U is the set of upper triangular unipotent matrices. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Scott Sheffield, Courant Institute |
Date: |
Monday, March 10, 2008, Time: 4:00 p.m., Location: Fine Hall 110 |
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PACM Colloquium |
Topic: |
Branched Polymers |
Presenter: |
Peter Winkler, Mathematics, Dartmouth College |
Date: |
Monday, March 10, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
A branched polymer is a finite, connected set of non-overlapping unit balls in space. The powerful "dimension reduction" theorem of Brydges and Imbrie permits computation of the volume of the space of branched polymers of size N in dimensions 2 or 3. We will show how these and some related computations can be done using elementary calculus and combinatorics. New results include methods for random generation, asymptotic diameter in 3-space, and a combinatorial proof of the notorious "random flight" problem of Rayleigh and Spitzer. Joint work with Rick Kenyon (Brown). |
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Algebraic Geometry Seminar ***Please note special date and location |
Topic: |
Maps between moduli spaces of curves and Gieseker-Petri divisors |
Presenter: |
Gavril Farkas, Humboldt Universität zu Berlin |
Date: |
Monday, March 10, 2008, Time: 4:30 p.m., Location: TBA |
Abstract: |
We study contractions of the moduli space of stable curves beyond the minimal model of M_g by resolving and giving a complete enumerative description of the rational map between moduli spaces of curves Mg --> Mh which associates to a curve C of genus g, the Brill-Noether locus of special divisors in the case this locus is a curve. As an application we construct myriads of moving effective divisors on M_g of small slope. For low g, our calculation can be used to study the intersection theory of the moduli space of Prym varieties of dimension 5. |
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Princeton University and Institute for Advanced Study Number Theory ***Please note special date and time |
Topic: |
Arithmetic invariants of discrete Langlands parameters |
Presenter: |
B. Gross, Harvard University |
Date: |
Tuesday, March 11, 2008, Time: 1:00 p.m., Location: IAS SH-101 |
Abstract: |
Let G be a reductive algebraic group over a local field k. Hiraga, Ichino and Ikeda have recently proposed a general conjecture for the formal degree of a discrete series representation of G(k), using special values of the adjoint L-function and epsilon factor of its (conjectural) Langlands parameter. I will reformulate this conjecture using Euler-Poincare measure on G(k) and the motive of G, establish a key rationality property of the ratio of special values in the non-Archimedean case, and explore some of its implications for supercuspidal parameters. This is joint work with Mark Reeder. |
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Mapping Class Group Dynamics Seminar |
Topic: |
Mapping class group dynamics (an overview) |
Presenter: |
Jayadev Athreya, Princeton University |
Date: |
Tuesday, March 11, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
This talk will survey known results, due to Masur and Veech on the dynamics of mapping class groups on spaces of measured foliations and their relationship to the dynamics of the Teichmueller geodesic flow and the SL(2,R)-action on the moduli space of holomorphic quadratic differentials (half-translation surfaces). |
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Mathematical Physics Seminar |
Topic: |
The Resolvent Algebra: A Novel Approach to Canonical Quantum Systems |
Presenter: |
Detlev Buchholz, University of Goettingen |
Date: |
Tuesday, March 11, 2008, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the automorphic action of physically interesting dynamics nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. In this talk a novel C*-algebra of the canonical commutation relations is presented which is based on the resolvents of the canonical operators. It has many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, it provides a convenient framework for the study of (infinite) interacting quantum systems and of constraints, as will be illustrated by several examples. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
Y. Soibelman, Kansas State University |
Date: |
Wednesday, March 12, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
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Department Colloquium |
Topic: |
Chaoticity of the Teichm\"uller flow |
Presenter: |
Artur Avila, IMPA and Clay Math. Inst. |
Date: |
Wednesday, March 12, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
A non-zero Abelian differential on a compact Riemann surface determines an atlas, outside the singularities, whose coordinate changes are translations. The vertical flow with respect to this translation structure generalizes the genus one notion of rational and irrational flows on tori. A fundamental tool in the understanding of the dynamics of vertical flows is the Teichm\"uller flow (acting on the moduli space of Abelian differentials), regarded as a renormalization operator. The chaotic nature of the dynamics of the Teichm\"uller flow has been a much researched topic, and currently it is known that it displays exponential decay of correlations. (This is equivalent to the spectral gap for the ambient SL(2) action, a very familiar result in genus 1.) Even much weaker aspects of the chaoticity of the Teichm\"uller flow however can be exploited in the description of the dynamics of typical vertical flows. Two such results are the proofs of the Kontsevich-Zorich conjecture and of weak mixing for interval exchange transformations. |
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Discrete Mathematics Seminar |
Topic: |
Sumsets in finite fields and Cayley sum graphs |
Presenter: |
Noga Alon, Tel Aviv University and IAS |
Date: |
Thursday, March 13, 2008, Time: 2:15 p.m., Location: Fine Hall 314 |
Abstract: |
I will sketch a proof of the fact that for a prime p, every complement of a set of roughly sqrt p elements of the finite field Z_p is a sumset, that is, is of the form A+A, whereas there are complements of sets of size roughly p^{2/3} which are not sumsets. This improves estimates of Green and Gowers, and can also be used to settle a recent problem of Nathanson. The proofs combine probabilistic arguments with properties of Cayley sum graphs derived from their eigenvalues. |
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Topology Seminar |
Topic: |
Variational principles on triangulated surfaces |
Presenter: |
Feng Luo, Rutgers University |
Date: |
Thursday, March 13, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We will discuss various applications of recently discovered 2-dimensional counterparts of the Schlaefli formula. |
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Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Denis Auroux, MIT |
Date: |
Friday, March 14, 2008, Time: 2:00 p.m., Location: Fine Hall 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Micah Warren, University of Washington |
Date: |
Friday, March 21, 2008, Time: 3:00 p.m., Location: Fine Hall 314 |
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Special Analysis Seminar ***Please note special time |
Topic: |
The abstract concept of Duality and some related facts (part of a joint project with Shiri Artstein-Avidan) |
Presenter: |
Vitali Milman, Tel Aviv University |
Date: |
Monday, March 24, 2008, Time: 2:30 p.m., Location: Fine Hall 110 |
Abstract: |
We discuss in the talk an unexpected observation that very minimal basic properties essentially uniquely define some classical transforms which traditionally are defined in a concrete and quite involved form. We start with a characterization of a very basic concept in Convexity: Duality and the Legendre transform. We show that the Legendre transform is, up to linear terms, the only involution on the class of convex lower semi-continious functions in R^n which reverses the (partial) order of functions. This leads to a different understanding of the concept of duality, which we call an ``abstract duality concept'', and which we then apply also to many other well known settings. It is also true that any involutive transform (on this class) which exchanges summation with inf-convolution, is, up to linear terms, the Legendre transform. The classical Fourier transform may be also defined (essentially) uniquely by the condition of exchanging convolution with product together the form of the square of the transform (the last fact is a joint work also with Semyon Alesker). |
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Analysis Seminar |
Topic: |
Mass inequalities for Cauchy data in general relativity |
Presenter: |
Gilbert Weinstein, University of Alabama at Birmingham |
Date: |
Monday, March 24, 2008, Time: 4:00 p.m., Location: Fine Hall 110 |
Abstract: |
We will survey a number of inequalities involving the total mass and other invariants for initial data for the Einstein equations in general relativity. |
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PACM Colloquium |
Topic: |
A worldwide web of images |
Presenter: |
Blaise Aguera y Arcas, Microsoft Live Labs |
Date: |
Monday, March 24, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
In this talk we'll explore the emerging potential of computer vision to transform the way we think about the interconnectedness of digital imagery and the Web, and how these relate to our physical environment. We'll begin with an introduction to the foundations of "3D computer vision", a bag of tricks which has been developing steadily for three decades, combining classical photogrammetry with machine vision. We'll then dive specifically into Photosynth, based on a combination of the Photo Tourism project (a collaboration between Microsoft Research and the University of Washington) and Seadragon, a multiresolution networked platform allowing one to play with arbitrarily many arbitrary large visual objects using only constant-time and constant-bandwidth operations. The aim of Photosynth is to allow meaningful 3D navigation within real-world environments reconstructed entirely from the photos. Interesting social dimensions are added to this application when one considers that the source photos can be mined from the existing Web, aggregated from user communities, and actively contributed to and interconnected. We'll end with some preliminary findings about the latent graph structure of Internet photography, and a glimpse of where we're heading next. |
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Algebraic Geometry Seminar |
Topic: |
The birational geometry of Kontsevich moduli spaces |
Presenter: |
Izzet Coskun, University of Illinois at Chicago |
Date: |
Tuesday, March 25, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
I will describe the stable base loci of linear systems on the Kontsevich moduli spaces of maps to projective spaces and Grassmannians. This description allows us to run the log minimal model program for these moduli spaces in small degree. I will give some examples where interesting classical moduli spaces occur. This is joint work with Dawei Chen and builds on previous work with Joe Harris and Jason Starr. |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
M. Loss, Georgia Tech. |
Date: |
Tuesday, March 25, 2008, Time: 4:30 p.m., Location: Jadwin 343 |
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Operations Research and Financial Engineering Colloquium |
Topic: |
On dimensionality of mean structure from a single data matrix |
Presenter: |
Xuming He, University of Illinois at Urbana-Champaign |
Date: |
Tuesday, March 25, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
Abstract: |
See http://orfe.princeton.edu/papers/he-abstract.pdf |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
E. Carlsson, Princeton University |
Date: |
Wednesday, March 26, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Logarithm laws for horocycles |
Presenter: |
Jayadev Athreya, Princeton University |
Date: |
Thursday, March 27, 2008, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
In joint work with G. Margulis, we prove a logarithm law for unipotent flows on the space of unimodular lattices in R^n. |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Danijela Damjanovic, Harvard University |
Date: |
Monday, March 31, 2008, Time: 12:15 p.m., Location: Fine Hall 224 |
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PACM Colloquium |
Topic: |
Mathematical and Computational Challenges in Shear Stiffness Imaging of Tissue: Can cancerous and benign lesions be distinguished? |
Presenter: |
Joyce McLaughlin, Mathematical Sciences, Rensselaer Polytechnic Institute |
Date: |
Monday, March 31, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
For centuries doctors have palpated tissue to detect abnormalities. We target imaging the stiffness the doctor feels in the palpation exam, including imaging deeper than what can be felt in this exam and distinguishing between benign and cancerous lesions. Current applications include breast and prostate cancer. Current experimentalists with whom we collaborate are: Dr. Richard Ehman, Mayo Clinic; Mathias Fink, ESPCI, Paris; and Dr. Kevin Parker at the University of Rochester. We describe the challenges and opportunities for imaging, including mathematical modeling and algorithmic development, with the data from the individual experiments |
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APRIL 2008 |
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Algebraic Geometry Seminar |
Topic: |
Real singular Del Pezzo surfaces and rationally connected threefolds |
Presenter: |
Frédéric Mangolte, Université de Savoie |
Date: |
Tuesday, April 1, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
Recent results on classification of real algebraic threefolds will be described. Let W -> X be a real smooth projective threefold fibred by rational curves. J. Kollár proved that if the set of real points W(R) is orientable, then a connected component N of W(R) is essentially either a Seifert fibred manifold or a connected sum of lens spaces. We proved sharp estimates on the number and the multiplicities of the Seifert fibres and on the number and the torsions of the lens spaces whenever X is a geometrically rational surface. These results answer in the affirmative three questions of Kollár. They are derived from a careful study of real singular Del Pezzo surfaces with only Du Val singularities. This is joint work with F. Catanese. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
B. Fantechi, SISSA and IAS |
Date: |
Wednesday, April 2, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
János Pach, NYU and Courant Institute |
Date: |
Thursday, April 3, 2008, Time: 2:15 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Water Information Networks & Efficiency in Irrigation Systems |
Presenter: |
Iven Mareels, Electrical & Electronic Engineering, The University of Melbourne |
Date: |
Monday, April 7, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
The world's sustainable water supply is heavily used (it is estimated that annually 65% of the available water resources are extracted), and with very poor efficiency (typically less than half the water taken from the environment serves the objective for which it was intended). The UNESCO World Water reports 2003/2005 identify management as one of the main issues to be addressed in order to avoid a water catastrophe. Australia is in a particularly critical situation, where management has to deal with significant climate change effects.
In this lecture we outline a sensor networks and systems engineering approach to underpin the management of an entire water catchment basin. The technology exists to construct a sensor network to monitor at a global scale the water resource and manage in closed loop the resource through the distribution infrastructure using the data derived from the sensor network. The control objective is to deliver water on demand with maximal overall efficiency. Such technology would provide the necessary data to implement a sustainable water policy in an adaptive way, where economic, environmental and social issues are properly taken into account.
We review the results from a number of substantial pilot projects in Victoria and New South Whales Australia in which, where Rubicon Systems Australia Pty. Ltd., who commercialise the technology, have realized significant gains in water efficiency in irrigation distribution. We show how this experience may lead to substantial gains in water management overall, and leads to better on farm practices, building further water savings. At present the state government of Victoria is backing this technoly with a 1 billion dollar investment to create significant water savings across the state. We discuss aspects of modeling of water dynamics followed by the control aspects enabled in the present and envisaged hardware upgrades. |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
E. Akkermans, Technion |
Date: |
Tuesday, April 8, 2008, Time: 4:30 p.m., Location: Jadwin 343 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
B. Kim, KIAS |
Date: |
Wednesday, April 9, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Marc Levine, Northeastern University |
Date: |
Wednesday, April 9, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
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Topology Seminar |
Topic: |
On the renormalized volume of quasifuchsian manifolds |
Presenter: |
Jean-Marc Schlenker, Toulouse |
Date: |
Thursday, April 10, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The renormalized volume of quasifuchsian hyperbolic 3-manifolds was originally introduced for physical reasons. Takhtajan and Zograf (and others) discovered that it provides a Kähler potential for the Weil-Petersson metric on Teichmüller space. We will give an elementary, differential-geometric account of this result. It can be extended to quasifuchsian manifolds having cone singularities along infinite lines, yielding results on the Teichmüller space of hyperbolic metrics with cone singularities (of prescribed angles) on a closed surface. (Based on joint works with K. Krasnov, C. Lecuire, S. Moroianu.) |
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Symplectic Geometry Seminar |
Topic: |
Mirror symmetry of Fano toric A-model and Landau-Ginzburg B-model |
Presenter: |
Yong-Geun Oh,University of Wisconsin |
Date: |
Friday, April 11, 2008, Time: 2:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Airplane boarding and space-time geometry |
Presenter: |
Eitan Bachmat, Computer Science, Ben-Gurion University and Brandeis University |
Date: |
Monday, April 14, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
It is hard to think of a process that is more boring than boarding an airplane. In the hope of relieving, or at least shortening, some of the pain, airlines have devised various boarding strategies such as back-to-front, window to aisle, boarding by zones or even unassigned seating. In the talk we will try to overturn the negative image that airplane boarding has and will try to portray it as a very exciting process which is modeled via space-time (a.k.a Lorentzian) geometry with a touch of random matrix theory. Using the model we will try to figure out what are the better strategies. If time permits, we will use insights from the airplane borading process to suggest an interpretation for Einstein's law of motion in which god plays the ultimate dice game. The talk is entirely self contained. Partly based on joint works with D. Berend, L. Sapir, S. Skiena, M. Elkin and V. Khachaturov. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Rajesh Kulkarni, Michigan State University |
Date: |
Tuesday, April 15, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
lya Goldsheid, Queen Mary, University of London |
Date: |
Tuesday, April 15, 2008, Time: 4:30 p.m., Location: Jadwin 343 |
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Mathematical Physics Seminar ***Please note special date |
Topic: |
TBA |
Presenter: |
P. Exner, Physics Inst., Czech Academy |
Date: |
Thursday, April 17, 2008, Time: 4:30 p.m., Location: Jadwin 343 |
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Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Sergio Lukic, Rutgers University |
Date: |
Friday, April 18, 2008, Time: 2:00 p.m., Location: Fine Hall 314 |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Francois Maucourant, Rennes 1 University |
Date: |
Monday, April 21, 2008, Time: 12:15 p.m., Location: Fine Hall 224 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Joachim Krieger, University of Pennsylvania |
Date: |
Monday, April 21, 2008, Time: 4:00 p.m., Location: Fine Hall 110 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Robert Lazarsfeld, University of Michigan |
Date: |
Tuesday, April 22, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
Alessandro Giuliani, University of Rome |
Date: |
Tuesday, April 22, 2008, Time: 4:30 p.m., Location: Jadwin 343 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
P. Johnson, University of Michigan |
Date: |
Wednesday, April 23, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Jim Bryan, UBC |
Date: |
Wednesday, April 23, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Active and Semi-Supervised Learning Theory |
Presenter: |
Rob Nowak, Electrical and Computer Engineering, University of Wisconsin-Madison |
Date: |
Monday, April 28, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Science is arguably the pinnacle of human intellectual achievement, yet the scientific discovery process itself remains an art. Human intuition and experience is still the driving force of the high-level discovery process: we determine which hypotheses and theories to entertain, which experiments to conduct, how data should be interpreted, when hypotheses should be abandoned, and so on. Meanwhile machines are limited to low-level tasks such as gathering and processing data. A grand challenge for scientific discovery in the 21st century is to devise machines that directly participate in the high-level discovery process. Towards this grand challenge, we must formally characterize the limits of machine learning. Statistical learning theory is usually based on supervised training, wherein a learning algorithm is presented with a finite set of i.i.d. labeled training examples. However, modern experimental methods often generate incredibly large numbers of unlabeled data for very little expense, while the task of labeling data is often painstaking and costly. Machine learning methods must leverage the abundance of unlabeled data in scientific problem domains. Active learning (AL) and semi-supervised learing (SSL) are two well known approaches to exploit unlabeled data. In both paradigms one has access to a large pool of unlabeled examples, and only a few labeled examples are provided or selected. AL is a sequential feedback process. Unlabeled examples that are predicted to have very informative labels, based on previously gathered labeled and unlabeled data, are selected for labeling. In SSL, labeled examples are randomly provided, without regard to potential informativeness. Today, little is known about theoretical limits of AL and SSL performance. Sparsity and complexity of the underlying data-generating distributions appear to play a central role in the performance of AL and SSL, and this talk will discuss some of the known theoretical results.
This work is joint with Rui Castro, Aarti Singh and Jerry Zhu. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Brendan Hassett, Rice University |
Date: |
Tuesday, April 29, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
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MAY 2008 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Robert Lipshitz, Columbia University |
Date: |
Thursday, May 1, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
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