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| NOVEMBER 2009 |
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| Algebraic Topology Seminar |
| Topic: |
Spaces of knots and configuration spaces |
| Presenter: |
Fred Cohen, University of Rochester |
| Date: |
Thursday, November 5, 2009, Time: 3:00 p.m., Location: Fine Hall 1201 |
| Abstract: |
The structure of the space of 'long knots in \R3' was developed in a series of papers by R. Budney with applications in joint work with Budney. An introduction to this space together with homological properties, and their connections to configuration spaces will be developed. For example, the singular homology of the space of knots will be considered. |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
Mean values with GL(2) times GL(3) functions |
| Presenter: |
M. Young, TAMU |
| Date: |
Thursday, November 5, 2009, Time: 4:30 p.m., Location: IAS S-101 |
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| PACM Colloquium |
| Topic: |
Geometry and Analysis of point sets in high dimensions |
| Presenter: |
Mauro Maggioni, Duke University |
| Date: |
Monday, November 9, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The analysis of high dimensional data sets is useful in a large variety of applications, from machine learning to dynamical systems: data sets are often modeled as low-dimensional, noisy data sets embedded in high-dimensional spaces; dynamical systems often have very high-dimensional state spaces but sometimes interesting dynamics occurs on low-dimensional sets. We discuss several problems associated with the analysis of the geometry of such sets, and with the approximation of functions on such sets, together with some solutions: in particular we discuss how to construct random walks on such data sets and perform multiscale analysis of them and their applications (especially to machine learning); how to construct robust coordinate systems for data sets; how to estimate reliably the intrinsic dimensionality of the data when only few noisy samples are available. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
In search of families of dg-algebras related to resolutions of Gorenstein toric singularities |
| Presenter: |
L. Borisov, Rutgers University |
| Date: |
Monday, November 9, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
A Gorenstein toric singularity can be described by simple combinatorial data, namely a convex polytope P in Z^n with integer vertices. Different triangulations of P with vertices given by integer points of P give rise to different resolutions of the singularity. It has been shown that bounded derived categories of coherent sheaves on these resolutions are equivalent. It is reasonable to expect that there is in fact a continuous family of triangulated categories that includes these categories as its limit points. This is very much work in progress, and the main questions are still wide open. It is my hope that by bringing this problem to your attention I can inspire someone to find such construction. |
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| Group Actions Seminar |
| Topic: |
Equidistribution and counting points on orbits of geometrically finite hyperbolic groups |
| Presenter: |
Nimish Shah, Ohio State University |
| Date: |
Tuesday, November 10, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
| Abstract: |
In this joint work with Hee Oh, we consider various sphere packing configurations that are invariant under actions of geometrically finite hyperbolic groups, and estimate the cardinality of spheres of curvature at most T with respect to euclidean, or spherical, or hyperbolic metric. This sphere counting problem is studied by proving "weighted equidistribution" results related to translates of certain co-dimension one submanifolds under the geodesic flow on the unit tangent bundle of M a hyperbolic n-manifold, where the fundamental group of M is a geometrically finite discrete subgroup of the group of isometries of the n dimensional hyperbolic space. |
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| Algebraic Geometry Seminar |
| Topic: |
Rational Simple Connectedness |
| Presenter: |
Matt DeLand, Stony Brook University |
| Date: |
Tuesday, November 10, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
Rational simple connectedness is an analog of simple connectedness for complex varieties having important applications: every 2-parameter family of rationally simply connected varieties has a rational section, and a 1-parameter family has so many rational sections that they approximate every power series section to arbitrary order. Unfortunately the condition is quite difficult to verify and is known to hold only for homogeneous spaces and also for some projective hypersurfaces satisfying a list of hypotheses. My new approach for verifying this condition works by studying a canonically defined foliation on the moduli space of rational curves on the variety. By proving integrability of this foliation, I prove every smooth complete intersections $X$ of type $(d_1, \ldots, d_c)$ in $\mathbb{P}^n$ is rationally simply connected whenever $\sum d_i^2 \leq n$ and when the associated moduli space of lines on $X$ is smooth. This degree range is sharp. |
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| Mathematical Physics Seminar |
| Topic: |
A variational model for crystals with defects |
| Presenter: |
Mathieu Lewin, Université de Cergy-Pontoise |
| Date: |
Tuesday, November 10, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
| Abstract: |
This talk will be devoted to the reduced Hartree-Fock model for crystals with defects.
The main idea is to describe at the same time the electrons bound by the defect and the (nonlinear) behavior of the infinite crystal. This leads to a bounded-below nonlinear functional whose variable is however an operator of infinite-rank.
I will provide the correct functional setting for this functional, state the existence of global-in-time solutions to the associated time-dependent Schrödinger equation, and discuss the existence, the properties and the stability of bound states. In particular I will define the dielectric permittivity of the perfect crystal and relate this to some properties of ground states. This is a review of joint works with Eric Cancès and Amélie Deleurence (Ecoledes Ponts, Paris). |
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| Special Analysis Seminar |
| Topic: |
Strongly Focused Gravitational Waves |
| Presenter: |
Michael Reiterer, ETH Zurich |
| Date: |
Wednesday, November 11, 2009, Time: 3:00 p.m., Location: Fine Hall 110 |
| Abstract: |
Christodoulou (2008) proved that trapped spheres can form in evolution, through the focusing of gravitational waves. Recently, with E. Trubowitz, we considered the same physical problem, using very different mathematical methods. Our approach is based on a systematic use of formal expansions, scaling symmetries and energy estimates. We give a direct construction of vacuum solutions by a far field expansion and exhibit trapped spheres that first appear deep inside the far field region. |
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| Department Colloquium |
| Topic: |
A model-theoretic approach to certain diophantine problems |
| Presenter: |
Jonathan Pila, University of Bristol |
| Date: |
Wednesday, November 11, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
I will describe some results and problems about the distribution of rational points on certain non-algebraic sets in real space. They find their natural setting in the model-theoretic notion of an `o-minimal structure over the real numbers'. I will describe a result joint with Alex Wilkie in this setting. A surprising strategy, proposed by Umberto Zannier, uses this result to approach diophantine problems in the Manin-Mumford-Andre-Oort circle of conjectures. I will describe some implementations of this strategy highlighting the use of o-minimality at different junctures, and discuss its prospects. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Andrew King, Columbia University |
| Date: |
Thursday, November 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Algebraic Topology Seminar |
| Topic: |
Some results in toric topology |
| Presenter: |
Sam Gitler, Cinvestav, Mexico |
| Date: |
Thursday, November 12, 2009, Time: 3:00 p.m., Location: Fine Hall 1201 |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
On the areas of rational triangles or How did Euler (and how can we) solve xyz(x+y+z) = a |
| Presenter: |
Noam Elkies, Harvard University |
| Date: |
Thursday, November 12, 2009, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
By Heron's formula there exists a triangle of area $\sqrt{a}$ all of whose sides are rational if and only if $a > 0$ and $xyz(x + y + z) = a$ for some rationals $x, y, z$. In a 1749 letter to Goldbach, Euler constructed infinitely many such $(x, y, z)$ for any rational $a$ (positive or not), remarking that it cost him much effort but not explaining his method. We suggest one approach, using only tools available to Euler, that he might have taken, and use it to construct several other infinite families of solutions. Then we reconsider the problem as a question in arithmetic geometry: $xyz(x+y+z) = a$ gives a K3 surface, and each family of solutions is a singular rational curve on that surface defined over {\bf Q}. The structure of that Néron--Severi group of that K3 surface explains why the problem is unusually hard. Along the way we also encounter the Niemeier lattices (the even unimodular lattices in ${\bf R}^{24}$) and the non-Hamiltonian Petersen graph. |
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| Topology Seminar |
| Topic: |
A combinatorial approach to harmonic maps |
| Presenter: |
Peter Scott, University of Michigan |
| Date: |
Thursday, November 12, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
I will discuss joint work with Hass on a combinatorial approach to harmonic maps. This work is still in progress. Such an approach has been used previously by other authors for computational reasons, but we are developing our approach with an eye to theoretical applications. Some applications in low dimensional topology will be discussed. |
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| Algebraic Topology Seminar ***Please note special date and location |
| Topic: |
Homotopy theory and spaces of representations |
| Presenter: |
Alejandro Adem, UBC |
| Date: |
Friday, November 13, 2009, Time: 3:00 p.m., Location: Fine Hall 601 |
| Abstract: |
Using spaces of homomorphisms and the descending central series of the free groups, simplicial spaces are constructed for each integer q>1 and every topological group G, with realizations B(q,G) that filter the classifying space BG. In particular for q=2 this yields a single space B(2,G) assembled from all the n-tuples of commuting elements in G. Homotopy properties of the B(q,G) will be described for finite groups, and cohomology calculations provided for compact Lie groups. Recent results on understanding both the number and stable homotopy type of the components of related spaces of representations will also be discussed. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
The geometry of static and stationary matter configurations in relativity |
| Presenter: |
Rick Schoen, Stanford University |
| Date: |
Friday, November 13, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
There are a number of interesting questions and some recent results concerning the geometry of equilibrium matter and black hole configurations for the Einstein equations. In this talk we will give background on these questions and survey known results. We will then describe recent work with R. Beig and G. Gibbons on the problem. |
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| Joint Columbia-Courant-Princeton University Algebraic Geometry Seminar *** Please note special date, time, and location |
| Topic: |
Analogue of the Narasimhan-Seshadri theorem in higher dimensions and holonomy |
| Presenter: |
Vikraman Balaji, Chennai Mathematical Institute |
| Date: |
Friday, November 13, 2009, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: |
We will discuss some recent work on natural analogues of the Narasimhan-Seshadri theorem on higher dimensional varieties with some applications to stable bundles on surfaces. The classical result related stability of bundles on projective smooth curves with irreducible unitary representations of the fundamental group. Analogues of holonomy groups and their representations play the corresponding role. |
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| Joint Columbia-Courant-Princeton University Algebraic Geometry Seminar *** Please note special date, time, and location |
| Topic: |
Mirror symetry for del Pezzo surfaces |
| Presenter: |
Tony Pantev, University of Pennsylvania |
| Date: |
Friday, November 13, 2009, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
I will discuss the general mirror symmetry question for del Pezzo surfaces in a setup that goes beyond the Hori-Vafa ansatz. I will describe the mirror map explicitly and will describe non-trivial consequences of homological mirror symmetry that can be proven directly. This is a joint work with Auroux, Katzarkov and Orlov. |
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| Analysis Seminar |
| Topic: |
Astala's conjecture on Hausdorff measure distortion under planar quasiconformal mappings and related removability problems |
| Presenter: |
Ignacio Uriarte-Tuero, Michigan State University |
| Date: |
Monday, November 16, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
In his celebrated paper on area distortion under planar quasiconformal mappings (Acta 1994) (for which he received the Salem prize), Astala proved that if $E$ is a compact set of Hausdorff dimension $d$ and $f$ is $K$-quasiconformal, then $fE$ has Hausdorff dimension at most $d' = \frac{2Kd}{2+(K-1)d}$, and that this result is sharp. He conjectured (Question 4.4) that if the Hausdorff measure $\mathcal{H}^d (E)=0$, then $\mathcal{H}^{d'} (fE)=0$. This conjecture was known to be true if $d'=0$ (obvious), $d'=2$ (Ahlfors), and $d'=1$ (Astala, Clop, Mateu, Orobitg and UT, Duke 2008.) The approach in the last mentioned paper does not generalize to other dimensions. UT showed that Astala's conjecture is sharp in the class of all Hausdorff gauge functions (IMRN, 2008). Lacey, Sawyer and UT jointly proved completely Astala's conjecture in all dimensions (Acta, 2009?) The proof uses Astala's 1994 approach, geometric measure theory, and new weighted norm inequalities for Calder\'{o}n-Zygmund singular integral operators which cannot be deduced from the classical Muckenhoupt $A_p$ theory. These results are intimately related to removability problems for various classes of quasiregular maps. I will particularly mention sharp removability results for bounded $K$-quasiregular maps recently obtained in joint work of Tolsa and UT. The talk will be self-contained. |
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| PACM Colloquium |
| Topic: |
Testable New Theory about Early-Universe Density Fluctuations and Origins of Solar Systems: Applied-Probability and Quantum-Physics Aspects |
| Presenter: |
Erik Vanmarcke, Civil and Environmental Engineering |
| Date: |
Monday, November 16, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The talk will summarize, with a focus on applied-probability aspects, the main findings, testable predictions and research opportunities stemming from a new probabilistic model of how complex patterns of energy-density fluctuations may have arisen during the inflation phase of the Big Bang. Based on first (quantum-physical) principles and requiring a minimum number of (observationally-accessible) parameters, the "embryonic inflation model" yields a coherent set of testable (hence falsifiable) hypotheses about the formation, evolution, composition, internal structure and cosmic environment of galaxies, stars and planets, and is consistent with key findings from observations of the Cosmic Microwave Background (CMB). Implying a robust alternative (and challenge) to the dual paradigm of spatially-uniform light-element primordial nucleosynthesis and stellar "recycling" of matter as the sole mechanism of heavy-element production, the theory holds the promise of integrating astrophysical and planetary sciences with cosmology and galaxy formation in a coherent evolutionary framework. Observations indicating overall cosmic flatness, the existence of an accelerating component, dark matter and dark energy all fit, in quantifiable and testable ways, into the framework of the theory. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
Z. Yun, IAS |
| Date: |
Monday, November 16, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Group Actions Seminar |
| Topic: |
Inhomogeneous quadratic forms |
| Presenter: |
Amir Mohammadi, University of Chicago |
| Date: |
Tuesday, November 17, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
| Abstract: |
We will address a recent join work with G. Margulis on a quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms. This generalizes the previous works of Eskin, Margulis and Mozes in the homogeneous setting also the work of J. Marklof. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Paul Hacking, University of Massachusetts Amherst |
| Date: |
Tuesday, November 17, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Mathematical Physics Seminar |
| Topic: |
The emergence of a giant vortex in a fast rotating Bose gas. |
| Presenter: |
Jakob Yngvason, University of Vienna |
| Date: |
Tuesday, November 17, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
| Abstract: |
A Bose gas in fast rotation normally exhibits a growing number of vortices of unit strength if the angular velocity is increased. In an anharmonic trap at sufficiently high velocity, however, a phase transition is expected: Vortices in the bulk should disappear and all vorticity become concentrated in a region where the density is very low. Moreover, the critical velocity for the transition is expected to increase with on the interaction strength in a definite manner. In the lecture rigorous results on this behavior within two-dimensional Gross-Pitaevskii theory will be presented. This is joint work with Michele Correggi and Nicolas Rougerie. |
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| Department Colloquium |
| Topic: |
Abelian sandpile model and self-similar groups |
| Presenter: |
Tatiana Smirnova, University of Geneva |
| Date: |
Wednesday, November 18, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The sandpile model was introduced in 1987 by physisists Bak, Tang and Wiesenfeld as a tool to study what they called {\it the self-organized criticality} - spontaneous appearance of power laws or fractal interfaces, observed in some natural phenomena. The mathematical study of the model was initiated a couple of years later by Deepak Dhar. It begins with a simple cellular automaton (also known in combinatorics under the name of {\it chip-firing game} on a finite graph, and leads to interesting long time and large volume limit dynamics when considered on increasing sequences of graphs. After an introduction to the Abelian sandpile model (ASM), I will show that the recent theory of self-similar groups (also known as automata groups) is a natural source of such families of graphs, giving rise to new interesting asymptotics and providing new evidence for the limit behaviour of the ASM. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Lai-Sang Young, Courant Institute |
| Date: |
Thursday, November 19, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Winkler, Dartmouth College |
| Date: |
Thursday, November 19, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Analysis Seminar |
| Topic: |
Quasi-local horizons |
| Presenter: |
Abhay Ashtekhar, Penn State University |
| Date: |
Monday, November 23, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
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| PACM Colloquium |
| Topic: |
Solving High-Dimensional Stochastic Optimization Problems using Approximate Dynamic Programming |
| Presenter: |
Warren Powell, ORFE |
| Date: |
Monday, November 23, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
There are many stochastic resource allocation problems arising in transportation, energy and health that involve high-dimensional state and action variables in the presence of di erent forms of uncertainty. These might involve discrete or continuous resources, and generally involve vectors of random variables that preclude exact computation of expectations. I will also describe our research into the important \exploration vs. exploitation" problem that arises in approximate dynamic programming, where we have the ability to choose the next state we will visit. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
D. Zakharov, Columbia University |
| Date: |
Monday, November 23, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Group Actions Seminar |
| Topic: |
Effective results on actions of commuting toral automorphisms |
| Presenter: |
Zhiren Wang, Princeton University |
| Date: |
Tuesday, November 24, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
| Abstract: |
Let G be an abelian subgroup of SL(d,Z). When G acts totally irreducibly on T^d the d-dimensional torus, has some hyperbolicity and is not virtually-cyclic, Berend proved that every orbit on T^d is either the whole torus or finite. We will discuss effective forms of this theorem and how they are related to number-theoretical problems. This is an analogue of the recent quantitative Furstenberg's theorem concerning the X 2, X 3 action (times 2, times 3 action) on the circle by Bourgain-Lindenstrauss-Michel-Venkatesh. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Tommase deFernex, University of Utah |
| Date: |
Tuesday, November 24, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Mathematical Physics Seminar |
| Topic: |
The spectral edge of random band matrices |
| Presenter: |
Alexander Sodin, Tel Aviv University |
| Date: |
Tuesday, November 24, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
| Abstract: |
We consider random periodic N X N band matrices of band width W. If the band is wide (W >> N^{5/6}), the spectral statistics at the edge behave similarly to those of GUE matrices; in particular, the largest eigenvalue converges in distribution to the Tracy -- Widom law. Otherwise, a different limit appears. The results are consistent with the Thouless criterion for localization, adapted to the band matrix setting by Fyodorov and Mirlin. |
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| Department Colloquium |
| Topic: |
Concentration Compactness for critical Wave Maps |
| Presenter: |
Joachim Krieger, University of Pennsylvania |
| Date: |
Wednesday, November 25, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
This talk will discuss a recent result on global regularity and asymptotic behavior of large critical wave maps with hyperbolic target, obtained jointly with W. Schlag. The proof relies on an adaptation of the recently developed method of Kenig-Merle to the case of systems of wave equations, as well as the harmonic analytic methods devised by Klainerman-Machedon, Tataru and Tao. |
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| PACM Colloquium |
| Topic: |
Looking over the painter’s shoulder |
| Presenter: |
Joris Dik, Delft University of Technology, Netherlands |
| Date: |
Monday, November 30, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstractt: |
Just microns below their paint surface lies a wealth of information on Old Master Paintings. Hidden layers can include the underdrawing, the underpainting or compositional alterations by the artist. All too often artists simply re-used their canvases and painted a new composition on top. Thus, a look /through /the paint layer provides a look /over/ the painter’s shoulder. I will discuss case different subsurface imaging techniques and present case studies from the work of Vincent van Gogh and Rembrandt. |
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DECEMBER 2009 |
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| Group Actions Seminar |
| Topic: |
TBA |
| Presenter: |
Martin Kassabov, Cornell University and IAS |
| Date: |
Tuesday, December 1, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Ekaterina Amerik, IAS |
| Date: |
Tuesday, December 1, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Mathematical Physics Seminar |
| Topic: |
TBA |
| Presenter: |
Vieri Mastropietro, Univ. Rome II |
| Date: |
Tuesday, December 1, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
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| Discrete Mathematics Seminar *** Please note special day |
| Topic: |
TBA |
| Presenter: |
Maria Chudnovsky, Columbia University |
| Date: |
Wednesday, December 2, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Unbiased Random Perturbations of Navier-Stokes Equation |
| Presenter: |
Boris Rozovsky, Lefschetz Center for Dynamical Systems, Brown University |
| Date: |
Thursday, December 3, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an Stochastic PDE with Wick product in the nonlinear term. The equation is solved in the space of generalized stochastic processes using the Cameron-Martin version of the Wiener chaos expansion. The generalized solution is obtained as an inverse of solutions to corresponding quantized equations.
An interesting feature of this type of perturbation is that it preserves the mean dynam- ics: the expectation of the solution of the perturbed equation solves the underlying deterministic Navier-Stokes equation. From the stand point of a statistician it means that the perturbed model is unbiased. The talk is based on a joint work with R. Mikulevicius. |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Cameron Gordon, University of Texas at Austin |
| Date: |
Thursday, December 3, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Conformal Structure of Minimal Surfaces with Finite Topology |
| Presenter: |
Christine Breiner, MIT |
| Date: |
Friday, December 4, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
The recent construction of a genus-one helicoid verified the existence of a second example of a complete, embedded minimal surface with finite topology and infinite total curvature in $\mathbb{R}3$. We determine the conformal structure and asymptotic Weierstrass data of all surfaces with these properties. Using this structure and the asymptotics, in the case $g=1$ we establish the existence of an orientation preserving isometry. This is joint work with Jacob Bernstein |
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| PACM Colloquium |
| Topic: |
Imaging Techniques and the Rejuvenation of Artwork |
| Presenter: |
Roy S. Berns, Munsell Color Science Laboratory, Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology, USA |
| Date: |
Monday, December 7, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Advances in digital imaging within the visible spectrum enable the accurate color rendering of artwork. It is possible to generate a colorimetric image with high spatial resolution and high image quality (appropriate sharpness and low noise). When the number of sensor channels exceeds three, it is also possible to generate spectral images. Spectral images can be used to calculate colorimetric images for any illuminant and observer pair, to evaluate color inconstancy, as an aid in retouching (i.e., restorative inpainting), for pigment mapping, and to improve printed reproductions. These digital images, of course, record the color and spectra of the artwork in its current condition. Depending on how the artwork has aged, its color may bear little resemblance to its appearance when first executed. This can dramatically affect the analysis of the painting in terms of its historical context and understanding the artist's working methods. A variety of techniques can be used to determine such color changes including analysing cross-sections, finding protected areas and identical materials that retain their color, early photographic records, and descriptions by art critics and connoisseurs at the time of creation. Having determined that a color change has occurred, it is possible to rejuvenate the colors of a digital image by using the principles of instrumental-based color matching. These principles are used to determine pigments and their concentrations that when mixed, match a particular color. This is equivalent to pigment mapping. The digital rejuvenation is performed by either replacing the spectral properties of the changed pigment with one that hasn't changed or increasing the concentration of a pigment that has faded. These rejuvenated images, while speculative, provide important and interesting new insights. This presentation will review research by the author in digital rejuvenation using examples by Vincent Van Gogh and Georges Seurat. |
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| Group Actions Seminar |
| Topic: |
Homogeneous orbit closures and Diophantine approximations of algebraic numbers |
| Presenter: |
Uri Shapira, Hebrew University |
| Date: |
Tuesday, December 8, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
| Abstract: |
The content of the talk is a joint work with Elon Lindenstrauss. Let X be the space of unimodular (covolume 1) lattices in Euclidean d-space and let A denote the group of diagonal matrices of determinant 1. We prove that any lattice x in X which "comes from a number field" which is not a CM field satisfies a Ratner-like property, namely the closure of the orbit Ax equals to an orbit Hx of a group H containing A. As a consequence we generalize my previous work on Diophantine properties of totally real cubic numbers by dropping the dimension assumption and the totally realness. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Roya Beheshti Zavareh, Washington University in St. Louis |
| Date: |
Tuesday, December 8, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Michael Boshernitzan, Rice University |
| Date: |
Thursday, December 10, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Song Sun, Wisconsin |
| Date: |
Friday, December 11, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Alexandra Ovetsky Fradkin, Princeton University |
| Date: |
Thursday, December 17, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Ozsvath, Columbia University |
| Date: |
Thursday, December 17, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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