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| NOVEMBER 2009 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Surface Comparison With Mass Transportation |
| Presenter: |
Yaron Lipman, Princeton University |
| Date: |
Friday, November 20, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
A method for transportation of metric between simply-connected surfaces with boundary is presented. The method is based on classical uniformization and optimal mass transportation. One application of the method is a novel definition of distance function between simply-connected surfaces with boundaries. The new distance forms a tractable/constructive alternative to the theoretically sound but hard to compute Gromov-Hausdorff distance. We will also show how this distance can be used to find automatic correspondences between some "real-life" surfaces. |
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| Special Ergodic Theory and Statistical Mechanics Seminar *** Please note special date and time |
| Topic: |
A brief survey of effective equidistribution results in Gamma\G |
| Presenter: |
Elon Lindenstrauss, Princeton University |
| Date: |
Friday, November 20, 2009, Time: 3:00 p.m., Location: Fine Hall 401 |
| Abstract: |
Equidistribution results for orbits and more general configurations in Gamma\G are a central focus of the theory of flows on homogeneous spaces. A notable example that comes to mind is Ratner's equidistribution theorem. I will survey some old and new quantitive equidistribution results of this flavor by several authors. |
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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: |
Rigidity properties of Fano varieties |
| Presenter: |
Tommase deFernex, University of Utah |
| Date: |
Tuesday, November 24, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
From the point of view of the Minimal Model Program, Fano varieties constitute the building blocks of uniruled varieties. Important information on the biregular and birational geometry of a Fano variety is encoded, via Mori theory, in certain combinatorial data corresponding to the Neron–Severi space of the variety. It turns out that, even when there is actual variation in moduli, much of such combinatorial data remains unaltered, provided that the singularities are "mild" in an appropriate sense. The talk is based on joint work with C. Hacon. |
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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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| Algebraic Topology Seminar |
| Topic: |
Codes, arithmetic and topology |
| Presenter: |
Matthias Kreck, University of Bonn |
| Date: |
Thursday, December 3, 2009, Time: 3:00 p.m., Location: Fine Hall 1201 |
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| Topology Seminar |
| Topic: |
Knots with small rational genus |
| Presenter: |
Cameron Gordon, University of Texas at Austin |
| Date: |
Thursday, December 3, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
If $K$ is a rationally null-homologous knot in a 3-manifold $M$ then there is a compact orientable surface $S$ in the exterior of $K$ whose boundary represents $p[K]$ in $H_1(N(K))$ for some $p > 0$. We define $\Vert K \Vert$, the {\it rational genus} of $K$, to be the infimum of $-\chi^-(S)/2p$ over all $S$ and $p$. If $M$ is a homology sphere then this is essentially the genus of $K$. By doing surgery on knots in $S3$ one can produce knots in 3-manifolds with arbitrarily small rational genus. We show that such knots can be characterized geometrically. More precisely we show that there is a positive constant $C$ such that if $K$ is a knot in a 3-manifold $M$ with $\Vert K \Vert < C$ then $(M,K)$ belongs to one of a small number of classes; for example, $M$ is hyperbolic and $K$ is a core of a Margulis tube, $M$ is Seifert fibered and $K$ is a fiber, $K$ lies in a JSJ torus in $M$, etc. Conversely we show that there are pairs $(M,K)$ in each of these classes with $\Vert K \Vert$ arbitrarily small. This is joint work with Danny Calegari. |
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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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| Discrete Mathematics Seminar |
| Topic: |
Proof of the Bollobas-Catlin-Eldridge conjecture |
| Presenter: |
Gabor Kun, IAS |
| Date: |
Thursday, December 10, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
We say that two graphs G and H pack if G and H can be embedded into the same vertex set such that the images of the edge sets do not overlap. Bollobas and Eldridge, and independently Catlin conjectured that if the graphs G and H on n vertices with maximum degree M(G) and M(H), respectively, satisfy (M(G) + 1)(M(H) + 1) ≤ n + 1 then G and H pack. Aigner and Brandt and, independently, Alon and Fischer proved this in the case M(G),M(H) < 3, Csaba, Shokoufandeh and Szemeredi proved the conjecture if M(G),M(H) < 4. Bollobas, Kostochka and Nakprasit settled the case when one of the graphs is degenerate. Kaul, Kostochka and Yu showed that if M(G)M(H) < 3/5n and the maximal degrees are large enough then G and H pack. We prove the conjecture for graphs with at least 10^8 |
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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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