SEPTEMBER 2011 |
|
Discrete Mathematics Seminar |
Topic: |
Erdos-Ko-Rado-like theorems for rainbow matchings. |
Presenter: |
Ron Aharoni, Technion, Haifa |
Date: |
Thursday, September 22, 2011, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
Let f(n,k,r) be the smallest number such that every set of more than f(n,k,r) r-sets in [n] contains a matching of size k. The Erdos-Ko-Rado theorem states that f(n,2,r)=\binom{n-1}{r-1}. A natural conjecture is that if F_1, F_2, ...F_k \subseteq \binom{[n]}{r} are all of size larger than f(n,k,r) then they possess a rainbow matching, that is, a choice of disjoint edges, one from each F_i. This is known for k=2 (Matsumoto-Tokushige) and r=2 (Meshulam). We consider the analogue of this conjecture in r-partite hypergraphs, and prove the cases r=3 and k=2. Joint work with David Howard. |
|
Topology Seminar |
Topic: |
Transverse invariants in Heegaard Floer homology |
Presenter: |
Vera Vertesi, IAS/MIT |
Date: |
Thursday, September 22, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Using the language of Heegaard Floer knot homology recently two invariants were defined for Legendrian knots. One in the standard contact 3-sphere defined by Ozsvath, Szabo and Thurston in the combinatorial settings of knot Floer homology, one by Lisca, Ozsvath, Stipsicz and Szabo in knot Floer homology for a general contact 3--manifold. Both of them naturally generalizes to transverse knots. In this talk I will give a characterization of the transverse invariant, similar to the one given by Ozsvath and Szabo for the contact invariant. Namely for transverse braids both transverse invariants are given as the bottommost elements with respect to the filtration of knot Floer homology given by the axis. The above characterization allows us to prove that the two invariants are the same in the standard contact 3--sphere. This is a joint work with J. Baldwin and D.S. Vela-Vick. |
|
Inaugural Math-Physics GR Seminar: Princeton University Gravity Group Astrophysics/Cosmology Lunch |
Topic: |
The mathematical approach to general relativity |
Presenter: |
Mihalis Dafermos, University of Cambridge |
Date: |
Friday, September 23, 2011, Time: 12:00 p.m., Location: Jadwin Hall, Room 102 - Lunch will be provided |
|
Differential Geometry and Geometric Analysis Seminar |
Topic: |
Hessian estimates for special Lagrangian equations with critical and supercritical phases |
Presenter: |
Yu Yuan, University of Washington |
Date: |
Friday, September 23, 2011, Time: 3:00 p.m., Location: Fine 314 |
Abstract: |
We talk about a priori Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. The "gradient" graphs of solutions are minimal Lagrangian submanifolds. Our unified approach leads to sharper estimates even for the previously known three dimensional or convex solution cases. Recent counterexamples for subcritical phase equations will also be mentioned. This is joint work with Dake Wang. |
|
Analysis Seminar |
Topic: |
Long-time strong instability and unbounded orbits for some nonlinear Schrodinger equations |
Presenter: |
Zaher Hani, New York University |
Date: |
Monday, September 26, 2011, Time: 4:00 p.m., Location: Fine Hall 314 |
Abstract: |
We establish a relation between long-time strong instability and the existence (in a certain generic sense) of unbounded orbits for dynamical systems on a Banach space. We then discuss some consequences of this relation for nonlinear Schrodinger equations. Namely, we prove long-time strong instability of plane wave solutions for the cubic nonlinearity and the existence of unbounded orbits for certain nonlinearities that are close (but not quite equal) to the cubic one. |
|
PACM Colloquium |
Topic: |
Understanding 3D Shapes Jointly |
Presenter: |
Leonidas Guibas, Stanford University |
Date: |
Monday, September 26, 2011, Time: 4:30 p.m., Location: Fine 214 |
Abstract: |
The use of 3D models in our economy and life is becoming more prevalent, in applications ranging from design and custom manufacturing, to prosthetics and rehabilitation, to games and entertainment. Although the large-scale creation of 3D content remains a challenging problem, there has been much recent progress in design software tools, like Google SketchUp for buildings or Spore for creatures, or in low cost 3D acquisition hardware, like the Microsoft Kinect scanner. As a result, large commercial 3D shape libraries, such as the Google 3D Warehouse, already contain millions of models. These libraries, however, can be unwieldy, when the need arises to efficiently incorporate models into various workflows. Mathematical formulations, efficient algorithms, and software tools are required to support navigation and search over 3D model repositories. In this talk we examine the problem of facilitating these navigation and search tasks by automatically extracting relationships between shapes in a collection and understanding their common or shared structure. By effectively organizing the collection into (possibly overlapping) groups of related shapes, by separating what is common from what is variable within each group and across groups, and by understanding the main axes of variability, we can facilitate a whole slew of operations that make large 3D repositories much more navigable, searchable, compressible, and visualizable. We will present a quick summary of tools for efficiently computing informative shape descriptors as well as structure preserving maps between shapes at different levels of resolution. The main part of the talk, however, is aimed beyond pairwise relationships, to the study and analysis of many shapes jointly, looking at networks of maps between shapes in order to extract joint structure, derive consistent segmentations, infer phenotypic relationships, etc. This is preliminary work on what we believe to be a large open area for research -- the joint understanding of collections of related geometric data sets. |
|
Algebraic Geometry Seminar |
Topic: |
Recent advances in connecting and contrasting test ideals and multiplier ideals |
Presenter: |
Kevin Tucker, Princeton University |
Date: |
Tuesday, September 27, 2011, Time: 4:30 p.m., Location: Fine 322 |
Abstract: |
This talk will focus on two distinct measures of singularities: test ideals (in positive characteristic) and multiplier ideals (characteristic zero). Though known for over a decade to be related via reduction to characteristic p > 0, recent advances have provided a uniform description of these invariants using regular alterations. This description, which shall be presented in detail, simultaneously sheds new light on both the connection and differences between test and multiplier ideals. Parts of the talk are based on joint works with Manuel Blickle, Karl Schwede, and Wenliang Zhang. |
|
Statistical Mechanics Seminar |
Topic: |
Some new results on the ground state of the strong coupling (solid)limit of the Bose-Hubbard Model; Possible applicability to solid He-4 |
Presenter: |
P.W. Anderson, Princeton University |
Date: |
Wednesday, September 28, 2011, Time: 2:00 p.m., Location: Fine 224 |
Abstract: |
The Mott insulator is accepted as the appropriate ground manifold for the strongly interacting Fermion Hubbard model, with solid He-3 as the simplest exemplar. It is a manifold because of the spin degrees of freedom, which order antiferromagneticallly due to atom exchange, below a critical temperature. No corresponding effect of exchange has been known for the Bose solid. I show that in fact the Bose-Hubbard model solid has a corresponding manifold of phase degrees of freedom which can conduct particle currents and which exhibit an ordering transition. The possible applicability to the observed "supersolidity " phenomena in solid He-4 will be discussed. |
|
Department Colloquium |
Topic: |
The black hole stability problem |
Presenter: |
Mihalis Dafermos, University of Cambridge |
Date: |
Wednesday, September 28, 2011, Time: 4:30 p.m., Location: Fine 314 |
|
Discrete Mathematics Seminar |
Topic: |
The size of a hypergraph and its matching number |
Presenter: |
Benny Sudakov, UCLA |
Date: |
Thursday, September 29, 2011, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
More than 40 years ago, Erdos asked to determine the maximum possible number of edges in a k-uniform hypergraph on n vertices with no matching of size t (i.e., with no t disjoint edges). Although this is one of the most basic problem on hypergraphs, progress on Erdos' question remained elusive. In addition to being important in its own right, this problem has several interesting applications. In this talk we present a solution of Erdos' question for t < n/(3k2). This improves upon the best previously known range t = O (n/k3), which dates back to the 1970's. Joint work with H. Huang and P. Loh. |
|
Algebraic Topology Seminar |
Topic: |
v1-periodic homotopy groups of SU(n) |
Presenter: |
Don Davis, Lehigh University |
Date: |
Thursday, September 29, 2011, Time: 3:00 p.m., Location: Fine Hall 214 |
Abstract: |
I will survey the various results that have been obtained during the past 22 years on the v1-periodic homotopy groups of SU(n). The most recent work has been combinatorial fine tuning to make the statements more explicit. I will discuss conceptual differences between 2-primary and odd-primary groups and implications for actual homotopy groups. |
|
|
Differential Geometry and Geometric Analysis Seminar |
Topic: |
A Bernstein type theorem for entire Willmore graphs |
Presenter: |
Jingyi Chen, University of British Columbia |
Date: |
Friday, September 30, 2011, Time: 3:00 p.m., Location: Fine 314 |
Abstract: |
We show that every two-dimensional entire graphical solution to the Willmore equation with square integrable second fundamental form is a plane. This is joint work with Tobias Lamm. |
|
IAS-PU Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Andras Stipsicz, Renyi/IAS |
Date: |
Friday, September 30, 2011, Time: 4:30 p.m., Location: IAS, Room S-101 |
|
OCTOBER 2011 |
|
Analysis Seminar |
Topic: |
On the uniqueness of solutions to the 3D periodic Gross-Pitaevskii hierarchy |
Presenter: |
Vedran Sohinger, University of Pennsylvania |
Date: |
Monday, October 3, 2011, Time: 4:00 p.m., Location: Fine Hall 314 |
Abstract: |
In this talk, we present a uniqueness result for solutions to the Gross-Pitaevskii hierarchy on the three-dimensional torus, under the assumption of an a priori spacetime bound. We show that this a priori bound is satisfied for factorized solutions coming from a solution of the nonlinear Schrodinger equation, thus obtaining a periodic analogue of the uniqueness result on R3 previously proved by Klainerman and Machedon. This is joint work with Gigliola Staffilani. |
|
PACM Colloquium |
Topic: |
Complexity theory applied to voting theory |
Presenter: |
Don Saari, University of California - Irvine |
Date: |
Monday, October 3, 2011, Time: 4:30 p.m., Location: Fine 214 |
Abstract: |
As it will be shown with results and examples, the paradoxes associated with standard voting rules are surprisingly likely and are so complex that one must worry about the legitimacy of election outcomes. To extract an understanding of what can happen and why, it is shown how lessons from complexity theory, where complicated behavior is due to a combination of simple interactions, explain many mysteries both in this area and for related topics such as nonparametric statistics, etc. Indeed, all paradoxes of standard rules, including Arrow's seminal "Impossibility Theorem," reflect simple but hidden symmetry structures connecting the preferences of voters. |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Claudiu Raicu, Princeton University |
Date: |
Tuesday, October 4, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
Statistical Mechanics Seminar |
Topic: |
Time Evolution and Stationary States of Classical and Quantum Systems |
Presenter: |
J. L. Lebowitz, Rutgers University |
Date: |
Wednesday, October 5, 2011, Time: 2:00 p.m., Location: Fine 224 |
Abstract: |
I will review both old and recent work about the time dependence and steady states of isolated macroscopic systems as well as those in contact with infinite thermal reservoirs. The emphasis will be on quantum systems and will include a discussion of the micro/macro connection in isolated ones and the derivation of a master equation for open oes. |
|
Department Colloquium |
Topic: |
Stability Theorems for some Sharp Inequalities and their Applications |
Presenter: |
Eric Carlen, Rutgers University |
Date: |
Wednesday, October 5, 2011, Time: 4:30 p.m., Location: Fine 314 |
Abstract: |
We explain recent results on stability theorems for some classical functional and ge- ometric inequalities, along with two applications: one to evolution equations, and one to statistical mechanics. The inequalities in question include certain Gagliardo-Nirenberg- Sobolev inequalities, the Brun-Minkowski inequality, for example. In these inequalities, all of the cases of equality are known, and indeed, Minkowski's contribution to the Brun- Minkowski inequality was to both determine the cases of equality. One can now ask if, in such an inequality, one almost has equality, is one in some sense near to one of the known cases of equality? A stability theorem is a theorem that provides a positive answer to this sort of question, and as indicated above, we shall explain and sketch the proofs of several such results, and we shall also explain two of the applications that motivated these investigations, which were carried out in collaboration with Alessio Figalli and Francesco Maggi. Though we shall keep the discussion of the applications non-technical as bets a colloquium talk, we nonetheless hope to convey an understanding of why it might be very useful to solve some of the many open problems in this field. |
|
Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Eli Berger |
Date: |
Thursday, October 6, 2011, Time: 2:15 p.m., Location: Fine Hall 224 |
|
PACM Colloquium |
Topic: |
A new model for self-organized dynamics: From particle to hydrodynamic descriptions |
Presenter: |
Eitan Tadmor, University of Maryland |
Date: |
Monday, October 10, 2011, Time: 4:30 p.m., Location: Fine 214 |
Abstract: |
Self-organized dynamics is driven by "rules of engagement", which describe how each agent interacts with its neighbors. They consist of long-term attraction, mid-range alignment and short-range repulsion. Many self-propelled models are driven by the balance between these three forces, which yield emerging structures of interest. Examples range from consensus of voters and traffic flows to the formation of flocks of birds or school of fish, tumor growth etc. We introduce a new particle-based model, driven by self-alignment, which addresses several drawbacks of existing models for self-organized dynamics. The model is independent of the number of agents: only their geometry in phase space is involved. We will explain the emerging flocking behavior of the proposed model in the presence of non-symmetric interactions which decay sufficiently slow, and discuss the difficulties of tracing graph connectivity otherwise. The methodology is based on the new notion of active sets, which carries over from particle to kinetic and hydrodynamic descriptions, and we discuss the unconditional flocking at the level of hydrodynamic description. |
|
Algebraic Geometry Seminar |
Topic: |
Toric mirror maps revisited |
Presenter: |
Hsian-Hua Tseng,
Ohio State University |
Date: |
Tuesday, October 11, 2011, Time: 4:30 p.m., Location: Fine 322 |
Abstract: |
For a compact semi-Fano toric manifold X, Givental's mirror theorem says that a generating function of 1-point genus 0 descendant Gromov-Witten invariants, the J-function of X, coincides up to a mirror map with a function I_X which is written using the combinatorics of X. The procedure of obtaining the mirror map, which involves expanding I_X as a suitable power series, is somewhat mysterious. In this talk we'll describe some attempts at understanding the mirror maps more geometrically. |
|
Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Shachar Lovett |
Date: |
Thursday, October 13, 2011, Time: 2:15 p.m., Location: Fine Hall 224 |
|
Topology Seminar |
Topic: |
TBA |
Presenter: |
Kristen Hendricks, Columbia University |
Date: |
Thursday, October 13, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
|
Special Seminar (no Joint IAS-PU Seminar) |
Topic: |
Quasimorphisms, almost complex structures and moment maps |
Presenter: |
Egor Shelukhin, Tel Aviv University |
Date: |
Friday, October 14, 2011, Time: 4:30 p.m., Location: Fine 322 |
Abstract: |
We consider the action of the group of Hamiltonian diffeomorphisms on the space of compatible almost complex structures of a symplectic manifold, with the scalar curvature as an equivariant moment map (due to Donaldson and Fujiki). While the Mabuchi K-energy measures 'displacement' transverse to the orbits, we propose a way to measure 'displacement' along an orbit, to obtain a function on the universal cover of the group satisfying the homomorphism property up to a uniformly bounded error - a quasimorphism. This construction agrees with previous results of Ruelle, Barge-Ghys, Entov and Py. Moreover, the same construction works in finite-dimensional settings, giving the (essentially unique) Guichardet-Wigner quasimorphisms on Hermitian Lie groups. |
|
PACM Colloquium |
Topic: |
Optimization of Polynomial Roots, Eigenvalues and Pseudospectra |
Presenter: |
Michael L. Overton, Courant Institute of Mathematical Sciences, NYU |
Date: |
Monday, October 17, 2011, Time: 4:30 p.m., Location: Fine 214 |
Abstract: |
The root radius and root abscissa of a monic polynomial are respectively the maximum modulus and the maximum real part of its roots; both these functions are nonconvex and are non-Lipschitz near polynomials with multiple roots. We begin the talk by giving constructive methods for efficiently minimizing these nonconvex functions in the case that there is just one affine constraint on the polynomial's coefficients. We then turn to the spectral radius and spectral abscissa functions of a matrix, which are analogously defined in terms of eigenvalues. We explain how to use nonsmooth optimization methods to find local minimizers and how to use nonsmooth analysis to study local optimality conditions for these nonconvex, non-Lipschitz functions. Finally, the pseudospectral radius and abscissa of a matrix $A$ are respectively the maximum modulus or maximum real part of elements of its pseudospectrum (the union of eigenvalues of all matrices within a specified distance of $A$). These functions are also nonconvex but, it turns out, locally Lipschitz, although the pseudospectrum itself is not a Lipschitz set-valued map. We discuss applications from control and from Markov chain Monte Carlo as examples throughout the talk. Coauthors of relevant papers include Vincent Blondel, Jim Burke, Kranthi Gade, Mert Gurbuzbalaban, Adrian Lewis and Alexandre Megretski. |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Zsolt Patakfalvi,
Princeton University |
Date: |
Tuesday, October 18, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
Department Colloquium |
Topic: |
TBA |
Presenter: |
Tsachik Gelander, Hebrew University of Jerusalem |
Date: |
Wednesday, October 19, 2011, Time: 4:30 p.m., Location: Fine 314 |
|
Topology Seminar |
Topic: |
TBA |
Presenter: |
Andras Stipsicz, Renyi/IAS |
Date: |
Thursday, October 20, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
|
PACM Colloquium |
Topic: |
Existence and regularity for a class of degenerate diffusions arising in population genetics |
Presenter: |
Charles Epstein, University of Pennsylvania |
Date: |
Monday, October 24, 2011, Time: 4:30 p.m., Location: Fine 214 |
Abstract: |
Infinite population limits of standard Markov chain models lead to Markov processes on polyhedral domains that are formally generated by degenerate elliptic operators. These operators are characterized, in part, by the first order vanishing, along the boundary, of the coefficient of the second normal derivative term. This fact places these operators beyond those which have thus far been successfully analyzed using methods of geometric analysis. I will present an approach to these operators, which I have been pursuing with Rafe Mazzeo, based on an-isotropic Holder spaces, which leads to a rather complete existence, uniqueness and regularity theory. |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Javier Fernández de Bobadilla de Olazabal, ICMAT, CSIC |
Date: |
Tuesday, October 25, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
IAS-PU Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Fraydoun Rezakhanlou, UC Berkeley |
Date: |
Friday, October 28, 2011, Time: 4:30 p.m., Location: IAS, Room S-101 |
|
NOVEMBER 2011 |
|
Algebraic Topology Seminar |
Topic: |
TBA |
Presenter: |
Herman Gluck, University of Pennsylvania |
Date: |
Thursday, November 3, 2011, Time: 3:00 p.m., Location: Fine Hall 214 |
|
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Claire Voisin, Institut de Mathématiques de Jussieu |
Date: |
Tuesday, November 8, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
Algebraic Topology Seminar |
Topic: |
TBA |
Presenter: |
Roman Mikhailov, IAS |
Date: |
Thursday, November 10, 2011, Time: 3:00 p.m., Location: Fine Hall 214 |
|
|
IAS-PU Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Penka Georgieva, Princeton University |
Date: |
Friday, November 11, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
PACM Colloquium |
Topic: |
TBA |
Presenter: |
Vladimir Rokhlin, Yale University |
Date: |
Monday, November 14, 2011, Time: 4:30 p.m., Location: Fine 214 |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Franklin Vera Pacheco, University of Toronto |
Date: |
Tuesday, November 15, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
Department Colloquium |
Topic: |
TBA |
Presenter: |
Alessio Figalli, University of Texas-Austin |
Date: |
Wednesday, November 16, 2011, Time: 4:30 p.m., Location: Fine 314 |
|
Topology Seminar |
Topic: |
TBA |
Presenter: |
Ciprian Manolescu, UCLA |
Date: |
Thursday, November 17, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
|
IAS-PU Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Tara Holm, Cornell University |
Date: |
Friday, November 18, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
PACM Colloquium |
Topic: |
TBA |
Presenter: |
Frederik Simons, Princeton University |
Date: |
Monday, November 21, 2011, Time: 4:30 p.m., Location: Fine 214 |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
J. M. Landsberg, Texas A&M University |
Date: |
Tuesday, November 22, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
PACM Colloquium |
Topic: |
TBA |
Presenter: |
Andrea Montanari, Stanford University |
Date: |
Monday, Novermber 28, 2011, Time: 4:30 p.m., Location: Fine 214 |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
David Eisenbud, UC Berkeley, MSRI |
Date: |
Tuesday, November 29, 2011, Time: 4:30 p.m., Location: Fine 322 |
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DECEMBER 2011 |
|
PACM Colloquium |
Topic: |
TBA |
Presenter: |
Peter Constantin, Princeton University |
Date: |
Monday, December 5, 2011, Time: 4:30 p.m., Location: Fine 214 |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Wenliang Zhang, University of Michigan |
Date: |
Tuesday, December 6, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
IAS-PU Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Nigel Hitchin, Oxford University and Simons Center |
Date: |
Friday, December 9, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Ching-Jui Lai, University of Utah |
Date: |
Tuesday, December 13, 2011, Time: 4:30 p.m., Location: Fine 322 |
|
IAS-PU Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Urs Frauenfelder, IAS visitor |
Date: |
Friday, December 16, 2011, Time: 4:30 p.m., Location: IAS, Room S-101 |
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FEBRUARY 2012 |
|
Algebraic Topology Seminar |
Topic: |
TBA |
Presenter: |
Dave Anderson, University of Washington |
Date: |
Thursday, February 9, 2012, Time: 3:00 p.m., Location: Fine Hall 214 |
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Algebraic Topology Seminar |
Topic: |
TBA |
Presenter: |
Suyoung Choi, Ajou University, Korea |
Date: |
Thursday, February 19, 2012, Time: 3:00 p.m., Location: Fine Hall 214 |
|
Algebraic Topology Seminar |
Topic: |
TBA |
Presenter: |
Alex Suciu, Northeastern University |
Date: |
Thursday, February 23, 2012, Time: 3:00 p.m., Location: Fine Hall 214 |
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